Level set method for structure topology optimization with asymmetrical microstructure model

Granular materials and structures, which are prevalent in nature and replicated in numerous engineering applications across various fields, display complex mechanical behaviors, notably asymmetry in tension and compression under external loading conditions. When designing structures utilizing these materials, addressing only material anisotropy is inadequate from a macroscopic viewpoint. Existing methods for the topology optimization of granular materials often do not yield smooth boundaries, which can create challenges in practical engineering applications, especially during the post-processing of jagged edges. This work offers a parametric level set topology optimization methodology for granular material structures to handle zig-zagged borders. The stiffness matrix for each element is derived using the granular micromechanics methodology, which links micro-scale interactions to macro-scale phenomena to define material constitutive relationships. Furthermore, this constitutive relationship is integrated into the radial basis function framework for the level set topology optimization method. Benchmark issues are addressed using the provided mathematical approach, resulting in topologies with smooth borders. In the resulting optimal topologies, areas experiencing tension and compression are distinctly marked in red and blue, respectively. These results illustrate the dependability and accuracy of the presented mathematical model for topology optimization.