Probabilistic effective characteristics of polymers containing rubber particles of Gaussian random diameter

This study is focused on the problem of statistical distribution of the size of rubber particles as fillers in elastomeric composites. This distribution (average diameter of the injected particles) is assumed to be Gaussian and uniquely defined by its mean value as well as standard deviation. The basic probabilistic parameters of the effective elasticity tensor of the entire elastomer are under consideration by using of the homogenization method. The basic computational ideology is based on strain deformation of the Representative Volume Element under uniaxial and biaxial loads. This deterministic method is enriched with the generalized stochastic perturbation technique and also by semi-analytical strategy, which are used together with the system ABAQUS® as the Stochastic Finite Element Method (SFEM) serving for a solution of the homogenization problem for such a composite. The basic stochastic characteristics of the homogenized elasticity tensor and its deterministic sensitivity coefficients are verified with such coming from analytical deterministic homogenization method extended towards random case in the computer algebra system MAPLE®. The computational study contains additionally computational error analysis as the homogenization problem is solved here with tetrahedral and hexahedral 3D solid finite elements with linear as well as with parabolic shape functions and their meshes with different densities.