Dr.-Ing. Tobias Bode

The investigation and modelling of complex materials often requires the characterization of their microstructure, which has a significant influence on the reaction of the material to external influences. Evolution equations based on variational principles are used to describe the material behavior. By taking into account characteristic observations, such as volume conservation during a microstructure change, the accuracy of the evolution equations can be significantly improved. In this research project, Hamilton's principle for materials with microstructure evolution is used. Using the Lagrange multiplier method, evolution equations can be derived that satisfy the constraints of the microstructural change.

The approach is investigated using examples such as isochoric plasticity and a phase transformation model. In the case of plasticity, the continuous evolution equations coincide with those resulting from the often used principle of maximum dissipation. However, a deeper understanding of these equations simplifies a consistent discretization. The figure visualizes the difference between a constraint-consistent and a conventional discretization of the evolution equations of finite elastoplasticity using the backward Euler method for the necking region of cylindrical tension test.