Yongbin Choi, M. Sc.

In simulating materials with microstructure development, the macroscopic behavior of a component depends on the physical processes at the microscale. However, it is not feasible to model an entire component in a level of detail that allows for the direct consideration of these effects in point of cost. One approach is to use effective internal variables. The temporal evolution of these thermodynamic state variables can be described, in cases of simple materials, by a set of coupled generally nonlinear ordinary differential equations. The solution of these equations must then be considered separately at each integration point on the macroscopic level.
For more complex material behavior, multiscale approaches are also employed. As the complexity of the material models increases, solving the material equations dominates the computational time. In the extreme case of homogenization, the computational time scales approximately linearly with the number of integration points on the macroscale. It is thus an imperative to limit this number to a minimum.
The aim of this project is to apply the method of moment integration with higher-order element approximations for simulating materials with complex microstructure development. In moment integration, instead of evaluating functions multiple times at different spatial points, the same polynomial accuracy can be achieved by evaluating additional derivatives at a single spatial point and thus, the computational efficiency can be increased.