Topology optimization using the discrete element method. Part 2: Material nonlinearity

Structural Topology Optimization typically features continuum-based descriptions of the investigated systems. In Part 1 we have proposed a Topology Optimization method for discrete systems and tested it on quasi-static 2D problems of stiffness maximization, assuming linear elastic material. However, discrete descriptions become particularly convenient in the failure and post-failure regimes, where discontinuous processes take place, such as fracture, fragmentation, and collapse. Here we take a first step towards failure problems, testing Discrete Element Topology Optimization for systems with nonlinear material responses. The incorporation of material nonlinearity does not require any change to the optimization method, only using appropriately rich interaction potentials between the discrete elements. Three simple problems are analysed, to show how various combinations of material nonlinearity in tension and compression can impact the optimum geometries. We also quantify the strength loss when a structure is optimized assuming a certain material behavior, but then the material behaves differently in the actual structure. For the systems considered here, assuming weakest material during optimization produces the most robust structures against incorrect assumptions on material behavior. Such incorrect assumptions, instead, are shown to have minor impact on the serviceability of the optimized structures.