Goal-oriented adaptive finite elements for parameter identification of conventional and additive micromorphic continuum models

Due to deficiencies of local continua, in particular pathological mesh dependency of FE solutions on the numerical side and failure to simulate length scale dependent problems on the theoretical side, generalized continuum theories have wide areas of applications. In this project, we address the class of micromorphic continua, containing micropolar (Cosserat) continua and microstrain continua as important special cases. In the previous project, we dealt with goal-oriented adaptive FEM for micromorphic elasticity and plasticity towards an error-controlled simulation of the direct problem. In addition, a novel continuum type labeled as additive micromorphic continuum has been proposed for finite strain elasticity, enabling a flexible transition of different continua and weighting them differently if required. On this basis, this project primarily addresses the following issues:

• With conventional micromorphic theories in the sense of Eringen, we consider size effects in linear elasticity. New experiments will be designed for identifying parameters of related micromorphic models, where notches of varying sizes are used to activate size effects in sand specimens for cold-box casting.
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• The novel additive micromorphic model will be extended to elastoplasticity including damage. Since it contains micropolar and microstrain continua as special cases, a selection of a proper continuum is expected to be done automatically via an inverse problem based on experimental data. It will be illustrated by simulating the whole damaging process of a cold-box sand. The advantage of the new additive model is to account for the rotation of sand particles and the deformation of the binder with proper weights.
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• Inverse problems for parameter identification will be handled for both conventional and additive micromorphic models based on experimental data. As a heterogeneous deformation state is required, a sensitivity analysis will be carried out on the basis of discretized variational formulations for the FEM. Special care will be paid to the additive model with a time-dependent character.
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• To enhance the numerical efficiency of the parameter identification, adaptive FEM will be developed for an effective meshing (spatial and temporal discretization for time-dependent problems). The challenging part is to develop appropriate goal-oriented error estimators to drive the corresponding adaptive algorithms.