Phenomenological constitutive laws for the dissipative behaviour of highly compressible elastomers and their finite element implementation

This paper deals with the development of constitutive equations to model the mechanical behaviour of compressible elastomers. These materials are naturally incompressible but can be made compressible by the addition of hollow microspheres, for example. Such a material is referred to as syntactic foam. The CEA (French Commission for Atomic and Alternative Energies) employs such compressible materials as seals in complex structures to reduce the internal stresses in vulnerable components and prevent their failure. The behaviour of these structures is predicted by finite element simulations. It is important to know and model the mechanical behaviour of the seals. Like elastomers, they can undergo large deformations. The microspheres enable the material to undergo large volume change unlike pure elastomer that is nearly incompressible. This compressibility also intensifies dissipative phenomena encountered in elastomers such as viscosity or plasticity. Furthermore, the Mullins stress softening effect is also intensified even for loadings that only bring about volumetric changes. To model these behaviours, a phenomenological approach was developed based on the isochoric/volumetric decomposition of the deformation gradient. The method of intermediate dissipative configurations was employed to introduce multiple phenomena, including viscosity (with several characteristic times) and viscoplasticity, for these two parts of the deformation. The constitutive equations and their flow rules were implemented in Abaqus through a UMAT subroutine and using a numerical approach to define the tangent operator. The parameters of the behaviour law were identified using a model reduction technique known as shape manifold approach. The resulting model can be compared with experimental data.