An iterative method for coupling of deformation and failure mechanisms on different length scales

An iterative method for coupling of numerical simulations on two length scales is presented. The computations on the microscale and on the macroscale are linked via a suitable macroscopic constitutive law. The parameters of this material law depend on the deformation history and are obtained from simulations using microstructurally representative volume elements (RVEs) subjected to strain paths derived from the associated material points in the macroscopic structure. Thus, different constitutive parameter sets are assigned to different regions of the macrostructure. The microscopic and macroscopic simulations are performed iteratively and interact mutually via the strain paths and the constitutive parameters, respectively. As an example, the strip tension test for a porous material is modelled using the finite element (FE) method. The coupling procedure, the material law and its numerical implementation are described. The method is shown to allow for a detailed simulation of the deformation mechanisms both on the micro- and the macroscale as well as for an assessment of their interactions while keeping the computational efforts reasonably low.