Sensitivity strategies in modelling heterogeneous media undergoing finite deformation

This paper deals with homogenization of microscopically heterogeneous media which are subjected to finite deformations. The updated Lagrangian scheme is applied to obtain linear subproblems which can be homogenized using the two-scale convergence. Microscopic equations and homogenized stiffness coefficients are derived for the hyperelastic material with incompressible inclusions. A sensitivity analysis of homogenized coefficients is proposed to study their dependence on local deformations of the microstructure. This approach can assist in reducing the number of the local microscopic equations that have to be solved in each iteration of macroscopic problems.