A Microstructurally Motivated Hyperelastic Model for Elastomer Materials

In this work we propose a microstructurally motivated hyperelastic model to describe the behavior of elastomer materials. At the scale of the Representative Volume Element (RVE), composed of randomly oriented macromolecular chains, we assume that the segments of the chains are deformable and that there is a bending energy between two consecutive segments. We propose to model each macromolecular chain using micromechanical elements: linear elastic bars to represent the segments between the cross-linking points and non linear elastic spires to represent the flexibility of rotations around the cross-linking points. Numerical simulations, on different structured RVEs composed of 3, 4, and 8 chains in the case of three boundary conditions: uniaxial compressible tension, uniaxial incompressible tension, and shear, show that this modeling allows to find the classical response curves of hyperelastic elastomeric. In the proposed model, we have to identify only three parameters: a, \( M_0 \) and K. From numerical simulations, we show that the first parameter, a, control the first phase of activation of rotations between chain segments, the second parameter, \( M_0 \) , control the unfolding phase, and that the third parameter K control the stiffening phase at large deformations.