CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Material Models for Polymeric Materials

Polymer is a chemical notion comprising many different materials that strongly differ from the physical behaviour of metals. From an engineering point of view it is instructive to subdivide polymers broadly according to their mechanical behaviour into materials with and without permanent defor- mation. In automotive structures, these are typically: „ „ Elastomers, recoverable foams, plastics at small deformation „ „ Crushable foams, plastics at large deformation All polymers consist of long chain molecules. The differences relate to the number of crosslinks between them (Figure 1).

a) Setup b) Head certification test c) Resultant acceleration

Figure 2: Head impactor for pedestrian protection

Foams Polymer foams are unique gas-polymer composites that are used in a variety of applications based on their ability to absorb energy. Under compression, foams can be considered as materials with a Poisson coefficient close to zero (Figure 3).

a) Thermoplastic

b) Thermoset

c) Elastomer

Figure 1: Molecular structure of polymers

Figure 3: Compression test of an EPP foam

Elastomers Elastomers are types of polymers that exhibit rubber-like qualities where disorder of the molecule arrangement is a measure of loading (entropy elasticity). Elastomers can be described phenomenologically by hyperelasticity where the stress σ can be obtained by derivation of an appropriate en - ergy functionWwith respect to the principle stretch ratio λ:

If they are completely recoverable, i.e. there is no permanent deformation during mechanical loading, the mathematical description of the material response can be formulated by the same theory as for elastomers, i.e. hyperelasticity. Contrary for foams that exhibit permanent deformation, a non-isochoric elasto-plastic description can be used. In both cases, modern explicit finite element packages allow for a tabulated input of the stress-strain relation, even strain rate dependent. It is therefore sufficient to describe the principal stress-strain behavior mathematically, e.g. by

As an example, Ogden’s energy functions is given as

where and In the case of strain-rate sensitive rubbers, some linear dampers are considered additionally in parallel. As an exam- ple, Figure 2 shows the head certification test for pedestrian protection where the skin of the head impactor consists of highly strain rate dependent rubber.

where the parameters

and describe the strain-rate dependency of the

material, see Figure 4.

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