Computational homogenization of inelastic conventional and gradient-extended microstructures by a shear band approach

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This proposal is dedicated to a numerically efficient approach for the computation of the average stress response of periodic microstructures. The method exploits the fact that many heterogeneous microstructures with and without gradient effects mainly deform by the formation of shear bands. By introducing a small number of degrees of freedom on these bands, a computationally very cheap model is obtained being surprisingly accurate for a wide range of microstructures. Thus, the approach allows for efficient two-scale simulations, where a microstructural model is attached to each integration point of a macroscopic finite element model. In contrast to the classical FE²-method, the microscopic model has significantly less degrees of freedom. This makes the fast two-scale simulation of very complex macroscopic structures possible. The microscopic strains of the model are piecewise constant. Thus, the number of stress computations within the microstructure is significantly smaller than in many other order reduction methods being, e.g., based on the proper orthogonal decomposition (POD). As a result, the performance of the method may in certain situations be superior to these latter approaches. As another advantage, the implementation of the method is rather simple and does not require the input of certain data objects like the finite element stiffness matrix or the residual vector, which are needed for the POD but are not always easy to access in finite element programs. Since size effects play a significant role in many microstructures, a concept for the model extension to gradient plasticity is developed.