LARGE HAIL PROTECTION SYSTEMS FOR THE FRAGILE PARTS OF PICKUP TRUCKS AND OTHER VEHICLES ON THE GROUND

Abstract

Soft material design methods for developing protective panels against a hail with a diameter of more than 25 mm are provided, wherein the protective panel comprises a soft material layer. The methods comprise: selecting a material for the soft material layer, wherein the material has a Young's modulus E.sub.sm in a range of 1 MPa to 150 MPa, preferably 5 MPa to 100 MPa; and determining a minimum thickness T.sub.sm of the soft material layer based on the size of a hail and the material properties of the soft material and other materials inside the protective panel. A protection system that includes these protective panels covers a whole vehicle or some fragile parts on the ground.

Claims

1. A material design method for designing protective panels against a hail with a radius equal to or smaller than a predetermined value R, wherein the protective panel comprises a soft material layer, the methods comprising: selecting a material for the soft material layer, wherein the material for the soft material layer has a Young's modulus E.sub.sm in a range of 1 MPa to 150 MPa; and determining a minimum thickness T.sub.sm of the soft material layer based on at least the predetermined value R and one or more mechanical properties of the soft material.

2. The method of claim 1, wherein the soft material layer has a density of no more than 200 kg/m.sup.3.

3. The method of claim 1, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer comprises a step of calculating the minimum thickness T.sub.sm according to an energy-based principle for the protective panel to absorb or dissipate all kinetic energy of the hail.

4. The method of claim 3, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using Equation 1: $T_{\mathrm{sm}}={\left(\frac{15W}{8\sqrt{R}{E}_{\mathrm{sm}}}\right)}^{2/5}$ when the material of the soft material layer has a deformation characteristic of a linear elastic material, wherein W is the kinetic energy of a hail having a radius of the predetermined value R, and E.sub.sm is the Young's modulus of the soft material layer.

5. The method of claim 3, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using Equation 2: $W=\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{}_{\mathrm{pi}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{pl}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{pi}}^2\right)T_{\mathrm{sm}}^2,$ when the material of the soft material layer has a deformation characteristic of a nonlinear elastic material, wherein W is the kinetic energy of a hail having a radius of the predetermined value R, E.sub.sm is the Young's modulus of the soft material layer, .sub.pl is a plateau strength of the soft material layer, .sub.pl is a plateau strain of the soft material layer, and .sub.limit is a compressive strain limit of the soft material layer with a value of 0.5 to 0.6.

6. The method of claim 3, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using Equation 3: $W=\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{}_{\mathrm{yd}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{yd}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{yd}}^2\right)T_{\mathrm{sm}}^2$ when the material of the soft material layer has a deformation characteristic of an elastic-plastic material, wherein W is the kinetic energy of a hail having a radius of the predetermined value R, E.sub.sm is the Young's modulus of the soft material layer, .sub.yd is a yielding strength of the soft material layer, .sub.yd is a yielding strain of the soft material layer, and .sub.limit is a compressive strain limit of the soft material layer with a value of 0.5 to 0.6.

7. The method of claim 1, wherein the protective panel further comprises a hard cover layer that contacts one side of the soft material layer and faces directly to the hail, wherein the cover layer has a Young's modulus E.sub.cv that is larger than E.sub.sm, wherein the Young's modulus of the cover layer E.sub.cv ranges from 300 MPa to 10 GPa.

8. The method of claim 7, wherein the cover layer is configured as a sheet having a thickness of 0.1 mm to 3 mm.

9. The method of claim 8, wherein the cover layer is made of a hard polymer selected from Acrylonitrile butadiene styrene (ABS), Polycarbonate (PC), and Acrylic (PMMA).

10. The method of claim 7, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using a largest value of three calculated thicknesses according to Equation 4: $\begin{array}{cc}\frac{0.86{T_{\mathrm{sm}}^{1/4}\left(1-v_{\mathrm{cv}}^2\right)}^{1/4}{\left(1-v_{\mathrm{sm}}^2\right)}^{1/4}{W}^{1/2}}{T_{\mathrm{cv}}^{3/4}{E}_{\mathrm{sm}}^{1/4}{E}_{\mathrm{cv}}^{1/4}}={}_{\mathrm{limit}}{T}_{\mathrm{sm}},\frac{1.03{\left(1-v_{\mathrm{cv}}^2\right)}^{\frac{1}{4}}{W}^{\frac{1}{2}}}{T_{\mathrm{cv}}^{\frac{1}{2}}{E}_{\mathrm{sm}}^{\frac{1}{3}}{E}_{\mathrm{cv}}^{\frac{1}{6}}}={}_{\mathrm{limit}}{T}_{\mathrm{sm}}& \mathrm{Equation}5\end{array}$ $\mathrm{and}$ $\begin{array}{cc}\frac{1.18{\left(1-v_{\mathrm{cv}}^2\right)}^{1/6}{\left(1-v_{\mathrm{sm}}^2\right)}^{1/6}{W}^{1/2}}{T_{\mathrm{cv}}^{1/2}{E}_{\mathrm{sm}}^{1/3}{E}_{\mathrm{cv}}^{1/6}}={}_{\mathrm{limit}}{T}_{\mathrm{sm}}& \mathrm{Equation}6\end{array}$ wherein W is the kinetic energy of a hail having a radius of the predetermined value R, E.sub.cv, .sub.cv and T.sub.cv are the Young's modulus, Poisson's ratio and thickness of the hard cover layer above the soft material layer with its Young's modulus E.sub.sm , Poisson's ratio .sub.sm, and .sub.limit is a compressive strain limit with a value of 0.5 to 0.6.

11. The method of claim 7, wherein the soft material layer has no bonding or partial bonding with the hard cover layer.

12. The method of claim 1, wherein the protective panel further comprises a fabric sheet to wrap around the soft material layer, and the fabric sheet has a tensile strength of more than 500 MPa and a fracture strain of more than 5%.

13. The method of claim 12, wherein the fabric sheet is made of fibers selected from a group consisting of aramid, carbon, glass fabrics, ballistic fabrics Ultra-High-Molecular-Weight Polyethylene (UHMWPE) and S2-glass.

14. The method of claim 12, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using Equation 7: $W=\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{T}_{\mathrm{sm}}^4}{4L^3}+\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{T}_{\mathrm{sm}}^{5/2}$ when the soft material layer has a deformation characteristic of a linear elastic material, wherein W is the kinetic energy of a hail having a radius of the predetermined value R, E.sub.fb is the Young's modulus of the fabric sheet, A.sub.fb is a cross-sectional area of the fabric sheet, E.sub.sm is the Young's modulus of the soft material layer, 2L is a length of the soft material layer.

15. The method of claim 12, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using Equation 8: $W=\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{}_{\mathrm{limit}}^4}{4L^3}{T}_{\mathrm{sm}}^4+\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{}_{\mathrm{pl}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{pl}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{pl}}^2\right)T_{\mathrm{sm}}^2$ when the soft material layer has a deformation characteristic of a nonlinear elastic material, wherein W is the kinetic energy of a hail having a radius of the predetermined value R, E.sub.fb is the Young's modulus of the fabric sheet, A.sub.fb is a cross-sectional area of the fabric sheet, E.sub.sm is the Young's modulus of the soft material layer, 2L is a length of the soft material layer, .sub.pl is a plateau strength of the soft material layer, .sub.pl is a plateau strain of the soft material layer, and .sub.limit is a compressive strain limit of the soft material with a value of 0.5 to 0.6.

16. The method of claim 12, wherein the step of determining the minimum thickness T.sub.sm of the soft material layer calculates T.sub.sm using Equation 9: $W=\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{}_{\mathrm{limit}}^4}{4L^3}{T}_{\mathrm{sm}}^4+\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{}_{\mathrm{yd}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{yd}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{yd}}^2\right)T_{\mathrm{sm}}^2$ when the soft material layer has a deformation characteristic of an elastic plastic material, wherein W is the kinetic energy of a hail having a radius of the predetermined value R, E.sub.fb is the Young's modulus of the fabric sheet, A.sub.fb is a cross-sectional area of the fabric sheet, E.sub.sm is the Young's modulus of the soft material layer, 2L is a length of the soft material layer, .sub.yd is a yielding strength of the soft material layer, .sub.yd is a yielding strain of the soft material layer, and .sub.limit is a compressive strain limit of the soft material layer with a value of 0.5 to 0.6.

17. A protective panel against a hail with a radius equal to or smaller than a predetermined value R, comprising a package, and a soft material layer inside the package, wherein the soft material layer has the Young's modulus E.sub.sm in a range of 1 MPa to 150 MPa.

18. The protective panel of claim 17, wherein the soft material layer has a density of no more than 200 kg/m.sup.3.

19. The protective panel of claim 17, wherein the soft material layer has a minimum thickness T.sub.sm determined based on the predetermined value R and material properties of the soft material layer, wherein the thickness T.sub.sm is no more than 30 mm.

20. The protective panel of claim 19, wherein the protective panel further comprises a hard cover layer attached to one side of the soft material layer, wherein the cover layer has its Young's modulus E.sub.cv that is larger than the Young's modulus E.sub.sm of the soft material layer, wherein the Young's modulus of the cover layer ranges from 300 MPa to 10 GPa.

21. The protective panel of claim 20, wherein the cover layer has a thickness of 0.1 mm to 3 mm.

22. The protective panel of claim 21, wherein the cover layer is made of a thermoplastic polymer selected from Acrylonitrile butadiene styrene (ABS), Polycarbonate (PC), and Acrylic (PMMA).

23. The protective panel of claim 19, wherein the protective panel further comprises a fabric sheet to wrap the soft material layer, wherein the fabric sheet has a tensile strength of more than 500 MPa and a fracture strain of more than 5%.

24. The protective panel of claim 23, wherein the fabric sheet is made of fabrics selected from a group consisting of aramid, carbon, glass fabrics, ballistic fabrics Ultra-High-Molecular-Weight Polyethylene (UHMWPE) and S2-glass fabrics.

25. A protection system against a hail having a radius equal to or smaller than a predetermined value R, comprising at least one protective panel of claim 17, wherein at least one protective panel is shaped and sized to cover at least a portion of a vehicle to be protected from hails.

26. The protection system of claim 25, further comprises a mount assembly to detachably mount the protective panels on at least a part of a vehicle.

27. The protection system of claim 26, further comprises a mount assembly that has sewn pockets to insert the protective panels and sewn Velcro straps to secure the protective panels.

28. The protection system of claim 25, wherein the fragile part to be protected from hails includes the windshield, hood, roof, wing, fuselage, and trunk of a land or air vehicle on the ground.

29. The protection system of claim 25, wherein the protective panels are mounted on the vehicle minor stands and door handles using the Y-shaped joints.

30. The protection system of claim 29, wherein the Y-shaped joint has two long Velcro straps that are sewn on selected protective panels to form a releasable joint and quickly secure the protective panels on the vehicle mirror stands or door handles with strong joint forces.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings referenced herein form a part of the specification. Features shown in the drawing illustrate only some embodiments of the invention, and not of all embodiments of the invention, unless the detailed description explicitly indicates otherwise, and readers of the specification should not make implications to the contrary.

[0033] FIG. 1 schematically illustrates a pickup truck or similar vehicle with a hail protection system according to an embodiment of the present invention attached thereon.

[0034] FIG. 2 illustrates a Y-shaped joint for a protection system mounting on a vehicle.

[0035] FIG. 3 schematically illustrates a hail impact event on a vehicle with a protection system having a soft material layer according to one embodiment of the present invention.

[0036] FIG. 4 schematically illustrates a typical indentation force and depth curve expressed by Hertz's contact law.

[0037] FIG. 5 schematically illustrates typical compressive stress-strain curve of a foam under unidirectional compression which expresses the deformation characteristic of a nonlinear-elastic material.

[0038] FIG. 6 schematically illustrates a hail impact on a vehicle part with a protection system having a soft material layer and a hard cover layer according to one embodiment of the present invention.

[0039] FIG. 7 schematically illustrates a hail impact on a vehicle part with a protection system having a soft material layer wrapped with fabric sheets according to one embodiment of the present invention.

[0040] FIG. 8 shows a protection system having a soft high-density polyethylene foam (HDPE) layer and a hard polycarbonate cover layer above the HDPE layer according to an embodiment of the present invention.

[0041] FIG. 9 shows a protection system having a soft HDPE layer wrapped with a Dyneema ballistic fabrics according to an embodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0042] The following detailed description of exemplary embodiments of the invention refers to the accompanying drawings that form a part of the description. The drawings illustrate specific exemplary embodiments in which the invention may be practiced. The detailed description, including the drawings, describes these embodiments in sufficient details to enable those skilled in the art to practice the invention. Those skilled in the art may further utilize other embodiments of the invention, and make logical, mechanical, and other changes without departing from the spirit or scope of the invention. Readers of the following detailed description should, therefore, not interpret the description in a limiting sense, and only the appended claims define the scope of the embodiment of the invention.

[0043] As used herein, spatially relative terms, such as above, on, in, inside, top, bottom, side and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures.

[0044] FIG. 1 shows an external protection system mounted on a vehicle such as a pickup truck 1. Because of the large protective area, a protection system often consists of several protective panels 3 to cover the fragile vehicle parts (e.g., front and back windshields, hood, roof and trunk) and save the shipping costs. The foldable protection system comprises a mount assembly that has sewn pockets to insert the protective panels and Velcro strips to secure the protective panels. These protective panels are subjected to direct impact from a hail 5 and their designs are based on impact dynamics. The protection system is mounted on the vehicle mirror stands 4 and door handles using the Y-shaped joint 2.

[0045] FIG. 2 illustrates a Y-shaped joint for the quick mounting purpose. Two Velcro straps that are sewn on selected protective panels form the Y-shaped joint to secure the protection system on the mirror stands or door handles. Compared to the common package hooks in previous patents, the Y-shape joint is easy and quick to mount the protection system on different vehicles with strong joint forces due to their long, overlapped Velcro straps.

[0046] The protective panel has at least one soft material layer, which has two functions: (1) absorbing the kinetic energy of a large hail, and (2) reducing the impact force acting on the vehicles. In embodiments of this invention, the Young's modulus of a material is the only parameter to define a soft or hard material.

[0047] The Young's modulus of a hail is 9.39 GPa (which is often considered as a hard material), so the material of the soft material layer according to embodiments of the present invention should have its Young's modulus of 0.15 GPa or less. The Young's modulus of a material is a material constant for its deformation capability which can be measured using a specific material test standard. For example, the Young's modulus can be measured using ASTM E 1876-01 (2009) Standard Test Method for Dynamic Young's Modulus by Impulse Excitation Technique. It is well understood in the art that specific test standards in different countries are slightly different, but their objectives are the same. There are numerous materials to be selected as the material for producing the soft material layer, and a major purpose of embodiments of this invention is to select the suitable materials for the soft material layer based on proposed mechanical properties and determine the minimum thickness of the soft material layer for a specific hail size.

[0048] The current invention does not simply enumerate current materials, because some current materials will become obsolete, and future materials often have great advantages. Hence, simplified equations and principles based on mechanics theory are proposed here for hail protection designs that can be applied to both current and future materials.

[0049] The general idea of the invention is to employ dynamic indentation mechanics theory to model a hail impact problem. Previous research found that the windshield has less impact resistance than the metal part such as the hood of a car. The crack initiation and propagation on the windshield is related to the local stress distribution, which is a complicated 3-D stress tensor problem. The merit of this invention is to employ the energy balance method for simplifying the protection material design, which becomes a 1-D scalar problem. Its cost is that the protection system is conservative.

1. Using Indentation Mechanics to Analyze Hail Impact

[0050] Large hails 5 hit a vehicle or outdoor structure such as a roof 1 and lead to impact damage and fracture. This phenomenon can be explained using indentation mechanics because a hail is model as a spherical object. As shown in FIG. 3, the indentation force P of a spherical indenter (hail 5) is a function of the elastic indentation depth and the hail radius R based on Hertz contact law (See S. Abrate, Impact Engineering of Composite Structures. SpringerWien, New York, 2011, p. 83):

[00001]$\begin{array}{cc}P=\frac{4}{3}\sqrt{R}{E}_r{}^{\frac{3}{2}}=C{}^{\frac{3}{2}},& \left(1\right)\end{array}$

where C is the contact stiffness, and the above relation is shown in FIG 4. The reduced modulus E.sub.r is determined by the Young's modulus E and Poisson's ratio of the hail 5 and the protective material, and the subscripts hail and pm refer to the hail 5 and protective material:

[00002]$\begin{array}{cc}\frac{1}{E_r}=\frac{1-v_{\mathrm{hail}}^2}{E_{\mathrm{hail}}}+\frac{1-v_{\mathrm{pm}}^2}{E_{\mathrm{pm}}}.& \left(2\right)\end{array}$

[0051] According to the series rule-of-mixture for the composite stiffness in mechanics of composite materials (R. M. Jones, Mechanics of Composite Materials. 2nd Edition, Taylor and Francis Group, New York, 1999, p. 138), the Young's modulus of the protective material/panel including a soft material layer 31 is almost equal to the Young's modulus of the soft material 31 E.sub.sm (E.sub.pm), if the Young's moduli of other materials of the protective panels are much larger than that of the soft material layer 31. Therefore, the major task of the protective material design is to determine the thickness of the soft material layer T.sub.sm.

[0052] The maximum tensile stress along the radius direction is responsible for the break of windshield glass or other fragile part 41:

[00003]$\begin{array}{cc}{}_{\mathrm{rr}}^{\max }=\left(\frac{1-2v}{2}\right){\left(\frac{4E_r}{3}\right)}^{2/3}{P}^{1/3}{R}^{-2/3}& \left(3\right)\end{array}$

[0053] Therefore, the maximum stress is an increasing function of the impact force P. On the formation of a dent caused by a hail impact, the kinetic energy W required to produce a visible dent of a metal plate is

W=K.sub.s2.sub.yd.sup.0.915t.sup.0.322 (4)

where .sub.yd is the yield strength of the metal, t is the thickness of the metal plate, and K.sub.S2 is a constant found to be 0.005 for the units MPa and mm (M. F. Shi et al., An Evaluation of the Dynamic Dent Resistance of Automotive Steels, Society of Automotive Engineers, Detroit, MI, USA, SAE No. 970158, 1991). Following Abrate (S. Abrate, Impact on Composite Structures. Cambridge University Press, New York, 1998), the maximum impact force of a hail is determined by its kinetic energy W, and the contact stiffness between the hail and the protective panel C:

[00004]$\begin{array}{cc}{P}_{\max }=\sqrt[5]{W^3{C}^2}2\sqrt[5]{W^3{\mathrm{RE}}_r^2}& \left(5\right)\end{array}$

where is a constant that is independent of the boundary and support conditions (1.73 for a spherical projectile like a hail 5).

[0054] It is expected that two energy levels to cause dents and cracks are different according to equations (4) and (5). So if one protective panel can stop metal damage (dent), it might not prevent windshield 41 fracture. Therefore, we should employ a conservative design, i.e., the protective panel should absorb all kinetic energy W from a hail, i.e., zero kinetic energy transfers to the metal part or the windshield 41. Therefore, the protective panel would prevent any impact damage of the protected targets.

[0055] To achieve the above objectives, embodiments of the present invention provide an external protection system against large hails using material designs. The protection system has at least one soft material layer which is placed above the vehicle surface to reduce the contact force and absorb the kinetic energy of the hail. The protective panel has at least five material design methods: (1) linear-elastic materials as soft protective materials, (2) nonlinear-elastic materials as soft materials, (3) elastic-plastic materials as soft materials, (4) an additional hard material layer that directly contacts hails can be placed above the soft material layer to provide stab resistance and absorb extra energy by its elastic/plastic and deformation, (5) additional high-energy absorption fabrics that wrap the soft material layer for providing extra energy absorption. The linear-elastic material, nonlinear-elastic material and elastic-plastic material have different mechanical properties, so man can distinguish those materials by their respective mechanical properties that will be further discussed below.

2. Linear-Elastic Materials as Soft Protective Materials

[0056] If the soft material 31 is a linear-elastic material, based on the energy balance for protection, the elastic strain energy W.sub.SE inside the soft material caused by impact force (indentation force) is equal to the kinetic energy W of a hail 5 (=0.5 m.sub.0.sup.2), and it can be expressed by

[00005]$\begin{array}{cc}{W}_{\mathrm{SE}}={}_0^{{}_{\max }}\mathrm{Pd}=\frac{2}{5}C{}_{\max }^{5/2}=W& \left(6\right)\end{array}$

where .sub.max is the maximum indentation depth. During a hail impact process, the maximum impact force P.sub.max, is achieved at the maximum indentation depth .sub.max.

[0057] The reduction of impact force P can be demonstrated by an example. The Young's modulus and Poisson's ratio are 9.39 GPa and 0.33 for a hail, and 66 GPa and for window glass. If a hail 5 hits a windshield 41, the reduced modulus E.sub.r is around 9.15 GPa using equation (2). If a soft material that has its Young's modulus of 0.1GPa is placed in front of the windshield, E.sub.r is around 0.1 GPa. The maximum impact force applied on the windshield protected by the soft material layer is around 27% of the maximum impact force applied on the windshield without any protection (i.e., 73% impact force reduction). As used herein, the term soft material in this disclosure refers to a material having a Young's modulus which is no more than 1.5% of the Young's modulus of a hail or 150 MPa.

[0058] Furthermore, according to equation (2), the Young's modulus of the protective panel is much smaller than that of the hail 5, and the square of the Poisson's ratio of the protective panel is close to zero, so we can make an approximation: E.sub.smE.sub.r.

[0059] The thickness of the soft material system T.sub.sm should exceed the maximum indentation depth according to equation (6):

[00006]$\begin{array}{cc}{T}_{\mathrm{sm}}{}_{\max }={\left(\frac{15W}{8\sqrt{R}{E}_{\mathrm{sm}}}\right)}^{2/5}& \left(7\right)\end{array}$

[0060] Therefore, if the protective level in terms of the hail radius R (then its kinetic energy W) is known, the minimum thickness of the soft material layer 31 can be calculated using equation (7) by a person with ordinary skills. Equation (7) also implies that the total compressive strain of the soft protective material .sub.sm=.sub.sm/T.sub.sm<1.0.

[0061] Because the initially flat protective panel should fit a curved surface such as a windshield, its bending stiffness should be as low as possible (soft). Also, the protective panel with small bending stiffness is easy for shipping. According to the Theory of Plates and Shells, the bending stiffness K.sub.p of a plate is mainly determined by its Young's modulus and the plate thickness, and can be simplified using equation (7):

[00007]$\begin{array}{cc}{K}_p~E_{\mathrm{sm}}{T}_{\mathrm{sm}}^3~{\left(\frac{W^6}{R^2{E}_{\mathrm{sm}}}\right)}^{1/5}& \left(8\right)\end{array}$

[0062] For a specific protection level, the radius R and the kinetic energy level W of a hail are fixed, so the soft material with a high Young's modulus will lead to the low plate bending stiffness. But this conclusion is based on shipping costs only.

[0063] The protective panel design is not a pure impact mechanics problem, because it is related to the cost, weight, machining, even shipping issues. It is expected that the protective panel should be thick enough to protect vehicles against large hails. As a result, its weight increases. Although soft materials with high Young's moduli are preferred to reduce the total material volume, the moduli of some materials such as foams and honeycombs are an increasing function of their densities (related to the total weight). Hence, it is preferred that the density of the soft material 31 is less than 200 kg/m.sub.3, preferable 150 kg/m.sup.3.

[0064] Moreover, thick panels lead to high shipping costs, and this factor should be considered during the early product design stage because covering a vehicle requires a very large production area and volume.

[0065] If the thickness of the protective panel for a sedan's windshield is 0.75 (19 mm), its weight is less than 10 lbs. but its volume is very large. Major US shipping companies such as UPS and FedEx employ so-called volume weight (usually larger than the actual weight) to calculate the shipping cost, which is mainly determined by the total volume of the product. The typical shipping cost of a potential hail protection product would be $50 for shipping inside Texas.

[0066] US 2005/0264026A1 describes a thick vehicle cover of six inches (152 mm), so its potential product would have a huge shipping cost. It is suggested that the thickness of the protective panel should be less than 30 mm, or as small as possible.

[0067] From the viewpoint of impact energy absorption, the thicker panel is better. But from the viewpoints of the total cost and weight, the thinner panel is better. Therefore, embodiments of this invention provide several design methods and define some parameter ranges to seek balanced results for future feasible products.

[0068] If a soft material is selected and its Young's modulus is known, its required minimum thickness of protection against a large hail 5 can be calculated by equation (7). Table 1 lists some material design data against different sizes of hails, which can be used by a person without advanced mechanics background.

[0069] As an example, if a hail protection system is designed to stop damage caused by a large hail 5 with a diameter of 2.25 inches (57.1 mm), and a soft material with a Young's modulus of 10 MPa is chosen (E.sub.rE.sub.sm), its minimum thickness for protection is 20.5 mm.

[0070] The minimum protection thicknesses against very large hails with their diameters of more than 64 mm are not listed in Table 1, but they can be calculated using equation (7). However, the large hail protection requires very thick soft material layers and significantly increases the costs of soft materials and shipping. The Young's modulus of the soft material should be around 1 MPa to 150 MPa.

[0071] For the Young's moduli listed in Table 1, if the Young's modulus E of one soft material is 1 MPa, its required soft material thickness easily exceeds 30 mm, which is not recommended due to the high shipping cost (the preferred thickness is no more than 20 mm). So the preferred Young's modulus range of candidate materials is 5 MPa to 100 MPa.

TABLE-US-00001 TABLE 1 Minimum soft material thicknesses (mm) related to hail diameters and material moduli (MPa) Young's modulus Hail diameter (inch/mm) 100 50 20 10 1 1.25/31.8 3.6 4.7 6.8 9.0 22.6 1.5/38.1 4.6 6.1 8.8 11.6 29.2 1.75/44.4 5.7 7.6 10.9 14.4 36.3 2.0/50.8 6.9 9.1 13.2 17.4 43.7 2.25/57.1 8.2 10.8 15.6 20.5 51.6 2.5/63.5 9.5 12.5 18.0 23.8 59.7

[0072] In reality, engineering materials are rarely linear-elastic materials. Glass has linear-elastic deformation before fracture, but it is a very hard material. Spring systems can be viewed as linear-elastic materials for protection too, but they are hard to use. However, there are many soft materials that show nonlinear-elastic deformation with plateau deformation, and these protective materials are better than pure linear-elastic materials, because they can significantly reduce the impact force and stress.

3. Nonlinear-Elastic Materials With Plateau Deformation as Soft Protective Materials

[0073] Particularly, foams are typical nonlinear-elastic soft materials. During hail impact, protective materials are subjected to high compressive stresses. The stress-strain responses of soft foams in compression tests show very similar deformation characteristics for different types of foams. FIG. 5 shows a typical compressive stress-strain curve of a nonlinear-elastic material. A region of linear elasticity at a low stress level is followed by a long collapse plateau in which the stress does not vary a lot, truncated by a region of densification in which the stress rises steeply. If the stress is reduced to zero, no permanent deformation is found, i.e., no plastic deformation or damage inside the foam material. As shown in FIG. 5, the initial slope of the linear stress-strain relation is the Young's modulus E. The plateau strength .sub.pl is the stress when the nonlinear deformation starts, and it is a material property. This is a critical material property in addition to the Young's modulus. The Young's modulus and plateau strength can be measured using ASTM D3574-17 Standard Test Methods for Flexible Cellular MaterialsSlab, Bonded, and Molded Urethane Foams (ASTM or American Society for Testing and Materials is an international standards organization). In other countries, the test standards might be different, but their goals are the same.

[0074] The Young's modulus E can be measured accurately. However, .sub.pl is not very accurate as shown in FIG. 5. Therefore, the plateau strain .sub.pl (.sub.pl/E), and the plateau displacement .sub.pl (.sub.pl*T.sub.sm) are convenient to use. The strain energy of the soft material during the linear-elastic deformation stage is:

[00008]$\begin{array}{cc}{W}_{\mathrm{le}}={}_0^{{}_{pl}}{P}_{1}d=\frac{2}{5}C{}_{\mathrm{pl}}^{5/2}=\frac{2}{5}C{}_{\mathrm{pl}}^{5/2}{T}_{sm}^{5/2}& \left(9\right)\end{array}$

The average contact pressure P.sub.m at the plateau deformation stage is defined by

[00009]$\begin{array}{cc}{P}_m=\frac{P_2}{a^2}={}_{\mathrm{pl}}.& \left(10\right)\end{array}$$\left(a^2=R\right),$$\mathrm{so}$$P_2=R{}_{\mathrm{pl}}$

[0075] If the compressive deformation caused by hail 5 impact reaches the densification stage, the stress inside foams will significantly increase and may damage the window glass behind the soft material 31. Therefore, a compressive strain limit .sub.limit (preferred value 0.50.6), and an indentation depth limit (.sub.limit=.sub.limitT.sub.sm) should be employed. The energy absorption of the soft material during the plateau deformation stage is:

[00010]$\begin{array}{cc}{W}_{\mathrm{pl}}={}_{{}_{pl}}^{{}_{\mathrm{limit}}}{P}_{2}d=\frac{1}{2}R{}_{\mathrm{pl}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{pl}}^2\right)=\frac{1}{2}R{}_{\mathrm{pl}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{pl}}^2\right)T_{sm}^2& \left(11\right)\end{array}$

Based on the total energy balance principle,

[00011]$\begin{array}{cc}{W}_{\mathrm{le}}+W_{\mathrm{pl}}=\frac{8}{15}\sqrt{R}{E}_{sm}{}_{\mathrm{pl}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{pl}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{pl}}^2\right)T_{sm}^2=W& \left(12\right)\end{array}$

By numerically solving nonlinear equation (12) (online tools are available), the thickness of the soft material layer T.sub.sm can be obtained. Many foams can be employed as soft materials such as PE and PU foams.

[0076] However, both linear-elastic or nonlinear-elastic soft materials only absorb kinetic energy, i.e., the hail 5 hits the protective material system, but it rebounds at the same kinetic energy. So the same hail might hit the other vehicles nearby. Therefore, some materials such as elastic-plastic materials can be employed to dissipate the kinetic energy of a hail 5 (i.e., reduce the total kinetic energy).

4. Elastic-Plastic Materials as Soft Protective Materials

[0077] The deformation characteristic of an elastic-plastic material is similar to that of the nonlinear-elastic material, but the elastic-plastic material has plastic deformation. Particularly, some soft materials such as honeycombs also have plateau deformation after elastic deformation, which is caused by plastic deformation/yielding. When the yielding starts, the average pressure P.sub.m is equal to the yielding strength .sub.yd (a material constant that is similar to the plateau strength which can be measured using ASTM C365/C365M-22 Standard Test Method for Flatwise Compressive Properties of Sandwich Cores)

[00012]$\begin{array}{cc}{P}_m=\frac{P_{yd}}{a^2}={}_{yd}.P_{yd}=R{}_{\mathrm{yd}}& \left(13\right)\end{array}$

where P.sub.yd is the compressive force at yielding. Similar to the nonlinear equation (12), the thickness of the elastic-plastic material T.sub.sm is determined by a new nonlinear equation (14), the energy dissipation during the yielding deformation stage W.sub.yd, the strain energy of the soft material during the linear-elastic deformation stage W.sub.le:

[00013]$\begin{array}{cc}{W}_{\mathrm{le}}+W_{yd}=\frac{8}{15}\sqrt{R}{E}_{sm}{}_{yd}^{5/2}{T}_{sm}^{5/2}+\frac{1}{2}R{}_{yd}\left({}_{\mathrm{limit}}^2-{}_{yd}^2\right)T_{sm}^2=W& \left(14\right)\end{array}$ [0078] where .sub.yd is the compressive strains at the yielding (material constant) and .sub.limit is a pre-defined design limit (preferred value 0.50.6). The major difference between equations (12) and (14) is that W.sub.yd dissipates the kinetic energy of the hail, so the residual kinetic energy is reduced.

[0079] Almost all honeycomb materials have elastic-plastic deformation, so they are the candidate materials for protection especially they are very light. Typical honeycombs include Nomex and aluminum honeycombs.

5. Hard Cover Layer Above the Soft Material Layer

[0080] Cellular materials such as foams and honeycombs are very weak to a point/concentrated load such as a sharp knife. Also, many foams tend to tear from the surface when heavy hailstones strike.

[0081] As a solution, the protective panel can have a hard/solid cover layer 32 or strong fabrics 33 to face concentrated load directly, as illustrated in FIGS. 6 and 7. The definition of a hard cover layer is based on its Young's modulus with a range of 300 MPa to 10 GPa. This hard cover layer 32 (only one material) can be bonded or not bonded to the soft material layer 31. No bonding is preferred because it will significantly lower the bending stiffness of the whole protection system, i.e., the protective panel becomes soft for easy storage or shipping. The new mechanics model can be modified from the impact model of a sandwich structure with a central soft core and two hard cover sheets.

[0082] According to previous experimental research (S. Abrate, Impact Engineering of Composite Structures. SpringerWien, New York, 2011, p. 91), the indentation/impact force and depth of a sandwich plate can be expressed by

P=C.sup.n where n0.8 (15)

[0083] In order to determine the contact stiffness C, a beam on an elastic foundation model was employed (J. L. Abot, I. M. Daniel, E. E. Gdoutos, Contact Law for Composite Sandwich Beams, Journal of Sandwich Structures and Materials, Vol. 4, pp. 157-173, 2002):

[00014]$\begin{array}{cc}\frac{P}{2\mathrm{Mb}}f\left(\sinh \left(l\right),\cosh \left(l\right)\right)& \left(16\right)\end{array}$

The bending stiffness of the cover layer 32 is modeled as a beam

[00015]$\begin{array}{cc}{D}_{cv-b}=\frac{b{E}_{cv}{T}_{cv}^3}{12}& \left(17\right)\end{array}$

where the subscript cv refers to the cover layer 32, and E.sub.cv, T.sub.cv and b are the Young's modulus, thickness and width of the cover layer 32. The foundation modulus M is defined by

[00016]$\begin{array}{cc}M=0.28{E_{sm}\left(\frac{b{E}_{sm}}{D_{cv-b}}\right)}^{1/3}0.64\frac{E_{sm}}{T_{cv}}{\left(\frac{E_{sm}}{E_{cv}}\right)}^{1/3}& \left(18\right)\end{array}$$\mathrm{Also},$$\begin{array}{cc}={\left(\frac{bM}{4D_{cv-b}}\right)}^{1/4}\frac{1.18}{T_{cv}}{\left(\frac{E_{sm}}{E_{cv}}\right)}^{1/3}& \left(19\right)\end{array}$

where the subscript sm refers to the soft material, and E.sub.sm and T.sub.sm are the Young's modulus and the thickness of the soft material. Therefore, the contact law is defined by

P1.08bE.sub.sm(20)

Equation (20) is similar to equation (15). However, the indentation force is not related to any mechanical property of the cover layer 32 in equation (20), which is not enough to characterize the system properties. So a new contact law should be developed.

[0084] The plate on an elastic foundation model leads to a new contact law of a linear indentation force-depth relation (R. Olsson, Engineering Method for Prediction of Impact Response and Damage in Sandwich Panels, Journal of Sandwich Structures and Materials, Vol. 4, pp. 3-29, 2002)

P8{square root over (MD.sub.cv-p)}(21)

where the bending stiffness of the hard cover layer 32 modeled as a plate is

[00017]$\begin{array}{cc}{D}_{\mathrm{cv}-p}=\frac{E_{cv}{T}_{cv}^3}{12\left(1-{}_{cv}^2\right)}& \left(22\right)\end{array}$

where .sub.cv is the Poisson's ratio of the cover layer 32. Using equation (18) for M, one new indentation law can be defined by

[00018]$\begin{array}{cc}P\frac{1.85T_{cv}}{\sqrt{1-v_{cv}^2}}{\left(E_{sm}^2{E}_{cv}\right)}^{\frac{1}{3}}=C_1& \left(23\right)\end{array}$

However, the foundation stiffness M is not a material constant, so Olsson proposed different M values to match the deflections of the soft material layer 31:

[00019]$\begin{array}{cc}M=\frac{E_{sm}}{\left(1-{}_{sm}^2\right)h_c^{*}}& \left(24\right)\end{array}$

where h*.sub.c is an intermediate variable without any physical meaning (1) h*.sub.c=0.725T.sub.sm if T.sub.smh.sub.cmax, or (2) h*.sub.c=2h.sub.cmax if T.sub.sm>h.sub.cmax.

[00020]$\begin{array}{cc}{h}_{\mathrm{cmax}}1.3{T_{cv}\left(\frac{\left(1-{}_{sm}^2\right)E_{cv}}{\left(1-{}_{cv}^2\right)E_{sm}}\right)}^{1/3}& \left(25\right)\end{array}$

For case (1), i.e., thin and soft materials,

[00021]$\begin{array}{cc}M=\frac{1.38E_{sm}}{\left(1-{}_{sm}^2\right)T_{sm}}& \left(26\right)\end{array}$

[0085] Substituting equation (26) into equation (21), one new indentation law can be obtained

[00022]$\begin{array}{cc}P2.71T_{cv}\sqrt{\frac{E_{sm}{E}_{cv}{T}_{cv}}{\left(1-v_{sm}^2\right)\left(1-v_{cv}^2\right)T_{sm}}}=C_2& \left(27\right)\end{array}$

[0086] It is noticed that the thickness ratio of the cover layer 32 and the thin soft material layer 31 has some influence on the indentation law. However, for case (2), i.e., thick and soft material case, the thickness ratio has no influence on the indentation law:

[00023]$\begin{array}{cc}P1.43{T_{\mathrm{cv}}\left(\frac{E_{\mathrm{sm}}^2{E}_{\mathrm{cv}}}{\left(1-v_{\mathrm{sm}}^2\right){\left(1-v_{\mathrm{cv}}^2\right)}^2}\right)}^{1/3}=C_3& \left(28\right)\end{array}$

[0087] Moreover, the above equation does not include the thickness of the soft material. Energy balance requires

[00024]$\begin{array}{cc}{}_0^{{}_{\max }}\mathrm{Pd}=\frac{1}{2}C{}_{\max }^2=W& \left(29\right)\end{array}$

The maximum indentation depths based on the plate theory using C.sub.1, C2 and C.sub.3 are

[00025]$\begin{array}{cc}{}_{\max }^{\left(1\right)}\frac{1.03{\left(1-v_{\mathrm{cv}}^2\right)}^{\frac{1}{4}}{W}^{\frac{1}{2}}}{T_{\mathrm{cv}}^{\frac{1}{2}}{E}_{\mathrm{sm}}^{\frac{1}{3}}{E}_{\mathrm{cv}}^{\frac{1}{6}}}={}_{\mathrm{limit}}{T}_{\mathrm{sm}}& \left(30\right)\end{array}$$\begin{array}{cc}{}_{\max }^{\left(2\right)}\frac{0.86{T_{\mathrm{sm}}^{1/4}\left(1-v_{\mathrm{cv}}^2\right)}^{1/4}{\left(1-v_{\mathrm{sm}}^2\right)}^{1/4}{W}^{1/2}}{T_{\mathrm{cv}}^{3/4}{E}_{\mathrm{sm}}^{1/4}{E}_{\mathrm{cv}}^{1/4}}={}_{\mathrm{limit}}{T}_{\mathrm{sm}}& \left(31\right)\end{array}$$\begin{array}{cc}{}_{\max }^{\left(3\right)}\frac{1.18{\left(1-v_{\mathrm{cv}}^2\right)}^{1/6}{\left(1-v_{\mathrm{sm}}^2\right)}^{1/6}{W}^{1/2}}{T_{\mathrm{cv}}^{1/2}{E}_{\mathrm{sm}}^{1/3}{E}_{\mathrm{cv}}^{1/6}}={}_{\mathrm{limit}}{T}_{\mathrm{sm}}& \left(32\right)\end{array}$

[0088] For a new design case, the hard cover layer 32 is determined first, then nonlinear equations (30)-(32) can be solved numerically. The largest value of the three thicknesses of the soft material layer 31 based on nonlinear equations (30)-(32) is employed for a conservative protective panel design. The preferred materials for the hard cover layers 32 are mainly thermoplastic polymers with low Young's moduli such as Acrylonitrile butadiene styrene (ABS), Polycarbonate (PC), and Acrylic (PMMA). Preferred thicknesses range from 0.1 mm to 3 mm because a thick cove layer will increase the stiffness of the protective panel.

6. Soft Protective Materials Wrapped by High-Energy Absorption Fabrics

[0089] Energy absorption/dissipation of foams and honeycombs is limited and requires large material volumes. This embodiment of the present invention introduces a new protective material design to absorb the hail kinetic energy more effectively, while the system still keeps its light and soft features. As illustrated in FIG. 7, the soft material layer 31 is wrapped by fabrics 33 with high-energy absorption capability such as the ballistic fabrics. These high-energy absorption materials are soft and light, and they can absorb a very large amount of kinetic energy (e.g., 400 J of a handgun bullet) of all kinds of projectiles. The major shortcoming of such fabrics is their high costs. However, even a small number of very thin fabric sheets 33 are employed, the thickness of the soft material layer 31 could be reduced to save shipping costs. Therefore, the final protective panel would be thin, soft and light.

[0090] If the original length of the soft material layer 31 (also the fabric sheet 33) is 2L, the final length of the fabric sheet will increase under the maximum indentation depth. It is expected that the fabric sheet 33 and the soft material layer 31 will deform together under the compressive hail impact force. If S is the half final length of the fabric sheet 33 (a curve according to a side view), the normal strain of the fabric sheet 33 can be defined by

[00026]$\begin{array}{cc}=\frac{S-L}{L}& \left(33\right)\end{array}$

[0091] In order to derive some equations for estimation, a straight line is assumed to replace the curve as the final length of the fabric sheet S. According to the geometry of a rectangular triangle which is related to the indentation depth ,

[00027]$\begin{array}{cc}{S}^2=L^2+{}^2\mathrm{then},=\frac{S-L}{L}=\sqrt{1+{\left(/L\right)}^2}-1& \left(34\right)\end{array}$

The elastic strain energy of the fabric sheet 33 can be expressed by

[00028]$\begin{array}{cc}{W}_{\mathrm{fs}}=\frac{1}{2}{E}_{\mathrm{fb}}{}^2\left(2L*A_{\mathrm{fb}}\right)& \left(35\right)\end{array}$

where E.sub.fb and A.sub.fb are the Young's modulus and the cross-sectional area of the fabric sheet 33, and .sup.2 can be approximated using Taylor series expansion because /L is very small:

.sup.2=2+(/L).sup.22{square root over (1+(/L).sup.2)}0.25(/L).sup.4 (36)

Therefore, equation (35) can be approximated as

[00029]$\begin{array}{cc}{W}_{\mathrm{fs}}\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{}_{\max }^4}{4L^3}& \left(37\right)\end{array}$

If these fabrics are employed to wrap 1) linear-elastic materials, 2) nonlinear-elastic materials, and 3) elastic-plastic materials, the extra energy absorption expressed by equation (37) is added into equations (6), (12) and (14), and three new nonlinear equations based on the energy balance principle are employed to estimate the required thicknesses of the soft material layer 31:

[00030]$\begin{array}{cc}\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{T}_{\mathrm{sm}}^4}{4L^3}+\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{T}_{\mathrm{sm}}^{5/2}=W& \left(38\right)\end{array}$$\begin{array}{cc}\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{}_{\mathrm{limit}}^4}{4L^3}{T}_{\mathrm{sm}}^4+\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{}_{\mathrm{pl}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{pl}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{pl}}^2\right)T_{\mathrm{sm}}^2=W& \left(39\right)\end{array}$$\begin{array}{cc}\frac{E_{\mathrm{fb}}{A}_{\mathrm{fb}}{}_{\mathrm{limit}}^4}{4L^3}{T}_{\mathrm{sm}}^4+\frac{8}{15}\sqrt{R}{E}_{\mathrm{sm}}{}_{\mathrm{yd}}^{5/2}{T}_{\mathrm{sm}}^{5/2}+\frac{1}{2}R{}_{\mathrm{yd}}\left({}_{\mathrm{limit}}^2-{}_{\mathrm{yd}}^2\right)T_{\mathrm{sm}}^2=W& \left(40\right)\end{array}$

For a new design case, one fabric and its thickness are determined first, then one of the above nonlinear equations can be solved numerically to obtain the minimum thicknesses of the specific soft material layer 31 chosen.

[0092] Any fabric with a very large tensile strength (preferably more than 500 MPa) and a fracture strain (preferably more than 5%) can be used to wrap the soft material layer 31. These fabrics often have a layer thickness of 0.1 to 0.2 mm, and at least one or more layers should be employed. Preferred fabrics include aramid, carbon, glass fabrics, especially ballistic fabrics Ultra-High-Molecular-Weight Polyethylene (UHMWPE) and S2-glass fabrics (low cost compared to UHMWPE).

[0093] Although rubbers and other elastomers are soft materials with low Young's moduli, their densities (also weights and costs) are too high compared to foams or honeycombs, so they are not good candidate materials because they are heavy and costly.

EXAMPLES

[0094] FIG. 8 shows an example of a hard cover layer 32 of Polycarbonate with a minor surface (thickness of 0.5 mm) above a soft material layer 31 of black high-density polyethylene HDPE (thickness of 19.0 mm, nonlinear elastic material). This combined protection system is employed to protect windshields against the impact of a golf-ball-sized hail. A real golf ball 7 (white, diameter of 44.45 mm) is placed above the material system, along with a shining steel ball 6 (diameter of 50.8 mm) to conduct equivalent hail impact tests.

[0095] FIG. 9 shows the same soft material layer 31 (HDPE) wrapped with high-energy absorption UHMWPE fabrics 33 (white ballistic fabrics Dyneema, thickness of 0.2 mm).

[0096] EXPERIMENTAL VALIDATION: There is no test standard to evaluate the hail-resistance of a protection system on a vehicle worldwide. The hail-resistance test of a protection system on a house roof is available in the US, and a steel ball is dropped from a certain height to simulate the hail impact on the roof.

[0097] In our impact tests, the weight of the steel ball shown in FIGS. 8 and 9 is 0.53 kg. In order to simulate the golf-ball-sized hail with the kinetic energy of 20 joules, the steel ball was dropped from 4.0 meters above the protection system, which was placed above windshield glass. Ten identical impact tests were conducted for each protection system shown in FIGS. 8 and 9, and no crack was found on windshield glass.

[0098] Although the above tests were based on the similarity rule on impact energy, they also obeyed the similarity rule on impact force. According to the series rule-of-mixture in mechanics of composite materials, the Young's modulus of the combined protective material system shown in FIGS. 7 and 8 is almost equal to the Young's modulus of the soft material (foam) E.sub.sm. Therefore, the reduced moduli of the real hail/protective material system impact and the steel ball impact/protective material system impact are almost equal to E.sub.sm according to equation (2).

[0099] According to equation (1), the contact stiffness of the steel ball impact is 6.9% higher than that of the hail impact. As a result, steel ball impact tests lead to slightly higher impact force and more conservative or safer results.

[0100] DE102015102984A1 describes the comparable hail impact tests of one PU foam (thickness of 6 mm) and one PE foam (thickness of 10 mm). When the diameter of the hail 5 was 30 mm and its speed was 25 m/s, the PU foam had small impression points (not a good result because its damage affects the full protection capability). While the PE foam had cracks and the target had distinct deformation, i.e., a complete failure case of protection.

[0101] However, the two kinds of foams did not have a fair comparison. Although their major material properties were close, or at least the same level, the density of the PU foam (240 kg/m.sup.3) was about eight times the density of the PE foam. It means that the weights/costs and Young's moduli of these two foams were very different. Therefore, the density of the soft material in this embodiment should be less than 200 kg/m.sup.3, preferably less than 150 kg/m.sup.3.

[0102] The above impact tests exactly support the results of embodiments of the present invention. Although the name of the above PE foam was not disclosed by DE102015102984A1, based on its low density of 30 kg/m.sup.3, its Young's modulus was around 0.5 to 1.0 MPa (see M F Ashby, Materials Selection in Mechanical Design, 4.sup.th Edition, Elsevier, Burlington, USA, 2011, pp. 503-505). According to Table 1, the required thickness for protection against a hail of 30 mm is at least 22.6 mm. So, it is not surprising that the PE foam with a thickness of 10 mm failed in their impact test.

[0103] About the specific PU foam in the same impact test, no Young's modulus was found from the manufacturer and open literature, so our modeling method was not able to predict. Anyway, the device of DE102015102984A1 was effective for limited hail protection (diameter of no more than 30 mm). But its narrow thickness range of 5 mm to 9.5 mm hindered its applications against large hails. On the other hand, embodiments of the present invention provide several general material design methods for protection against much larger hails (diameter>30 mm).

[0104] COMPUTER SIMULATION OF ONE DESIGN/EXAMPLE: A large panel of a HDPE foam (nonlinear elastic material) with a thickness of 11 mm was placed above the back windshield of a sedan. The sizes of the windshield (also the HDPE panel) were 1050 mm1050 mm and its thickness was 4 mm. The diameter of the hail was 44 mm (kinetic energy of 20 J) and the impact site was at the center of the windshield. The Young's modulus and the plateau strength of one specific HDPE foam were 7 MPa and 0.5 MPa. LS-DYNA software, which is specialized for impact/dynamics simulation was employed to simulate the above impact problem. The maximum tensile stress (principal stress) at the bottom surface of the windshield was always below the tensile strength of glass (50-70 MPa). Therefore, this HDPE foam and its thickness are effective to protect the back windshield against impact from a hail with a diameter of 44 mm.