Unified Approach to Sensitivity Analysis Based Automation of Multi-scale Modelling

Use of different kinds of multi-scale methods is limited with specifications of the problem to be solved. Standard two-level finite element homogenization approach FE2 is appropriate for problems with weakly coupled scales. If the difference between two scales is finite, or in the region of high gradients the FE2 multi-scale approach fails, then some sort of domain decomposition method can be applied. Our motivation was to create computational environment, where the multi-scale code is automatically derived and various types of multi-scale approaches can be freely mixed. The described approach uses an advanced feature of software tools AceGen and Acel-LM, that is automatic generation of the finite element codes for analytical first and second order sensitivity analysis with respect to prescribed essential boundary conditions as a unifying factor. The automatic-differentiation-based formulation (ADB) enables unification and automation of various multi-scale approaches for an arbitrary nonlinear, time dependent, coupled problem (e.g. general finite strain plasticity).