SUMMARYA framework for variationally consistent homogenization, combined with a generalized macrohomogeneity condition, is exploited for the analysis of non-linear transient heat conduction. Within this framework the classical approach of (model-based) first-order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are (in practice) introduced in quadrature points in standard fashion. Along with the classical averages, a higher order conservation quantity is obtained. An iterative FE 2 -algorithm is devised for the case of non-linear diffusion and storage coefficients, and it is applied to transient heat conduction in a strongly heterogeneous particle composite. Parametric studies are carried out, in particular with respect to the influence of the 'internal length' associated with the second-order conservation quantity.

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SUMMARYThis paper describes how gradient hardening can, in a thermodynamically consistent fashion, be included into a crystal plasticity model. By assuming that the inelastic part of the free energy includes contributions from the gradient of hardening along each slip direction, a hardening stress due to the second derivative of the hardening along each slip direction can be derived. For a finite element model of the grain structure a coupled problem with displacements and gradient hardening variables as degrees of freedom is thereby obtained. This problem is solved using a dual mixed approach. In particular, an algorithm suitable for parallelization is presented, where each grain is treated as a subproblem. The numerical results show that the macroscopic strength increases with decreasing grain size as a result of gradient hardening. Finally, the results of different prolongation assumptions, i.e. how to impose the macroscopic deformation gradient on a representative volume element, are compared.