Level-set topology optimization for Ductile and Brittle fracture resistance using the phase-field method

This work presents a rigorous mathematical formulation for topology optimization of macrostructure undergoing ductile failure. The prediction solid materials which exhibit dominant plastic deformation is an intriguingly challenging task and plays extremely important role in various engineering applications. Here, we rely on the phase-field approach to fracture widely adopted framework modeling computing failure phenomena solids. first objective optimize structure order minimize its mass, while accounting structural damage. To do so, topological phase transition function (between void phases) introduced, thus resulting extension all governing equations. Our second additionally enhance resistance structure. Accordingly, two different formulations are proposed. One requires only residual force vector field as constraint, formulation, simultaneously have been imposed. An incremental minimization principles class gradient-type dissipative used derive level-set-based employed seek optimal layout with smooth clear boundaries. Sensitivities derived using analytical gradient-based adjoint method update level-set surface both formulations. evolution realized by reaction-diffusion equation maximize strain energy certain volume design domain prescribed. Several three-dimensional numerical examples presented substantiate our algorithmic developments.