A Strategy for Adaptive Scale-Bridging in Computational Material Modeling

Research Project, 2017 – 2020

The proposed project concerns the further development and refinement of a strategy for adaptive scale-bridging in the modeling of micro-heterogeneous composites. Such scale-bridging is computationally desirable in analyzing structures when strong gradients are pronounced from a macroscale viewpoint, e.g. in the presence of stress concentrations of various types. The most important feature of a scale-bridging strategy is a sufficiently versatile variational format that allows for a virtually "seamless" transition from a direct resolution of the fine scales (as one extreme) to solutions based on homogenization (as the other) extreme. It then appears that socalled "discretization-based" homogenization emerges naturally from the variational framework in the spirit of the classical Variational MultiScale Method (denoted VMS). A key novelty in the proposed project is to establish and implement a "dual mixed" variational format, which is complementary to the standard VMS-format and which allows for Neumann boundary conditions on subscale domains.<br /><br />The following main tasks are identified as part of the proposed Ph.D. project: (1) Establish and implement the <em>complementary</em> variational format of <em>discretization-based homogenization</em>. (2) Carry out an in-depth analysis of discretization-based homogenization. (3) Develop further the scale-bridging strategy based on goal-oriented adaptivity. (4) Apply the developed computational tool to asphalt-concrete with cracks present.