Meso-scopic 3D-finite element analysis of filled elastomer

In most industrial applications the elastomers are used as reinforced materials with filler such as carbon-black and silica, but the mechanical behaviours in meso-scopic scale have not been fully understood due to the limitation of the mechanical analysis in meso-scopic scale. Combination of 3D-TEMT (Transmission Electron Micro Tomography) and 3D-FEA (Finite Element Analysis) enables us to investigate the deformation of the filled elastomer in meso-scopic scale. The polymer phase between carbon black aggregates showed a large strain concentration over 200%, even if the overall strain was only 15%(1). Hence, a constitutive equation, which can cover the stress-strain behaviours up to higher strain region as a function of temperature, has been investigated. Since the stress-strain behaviour shows a transition to the glass-hard state at lower temperature, where the contribution of the internal energy is increased, a constitutive equation was derived from the statistical thermodynamics with Hamiltonian equations considering the change in internal energy.