Multi-material continuum topology optimization with multiple volume constraints and material nonlinearity

Resumo

Most existing studies in multi-material continuum topology optimization consider linear elastic material
models. Since actual materials, in general, display a nonlinear constitutive relation, this paper presents an initial
study to evaluate the influence of the material nonlinearity in the solutions obtained using a multi-material topology
optimization approach with multiple volume constraints. Material nonlinearity is considered by means of an
Ogden-based model or a bilinear model. To achieve this, a Matlab implementation using the educational code for
multi-material topology optimization, PolyMat, was made. We took advantage of the modular structure of the
educational code to make changes mainly in the structural analysis routine and adapt the optimization formulation
for the maximization of the stationarity total potential energy. Numerical examples are presented to demonstrate
the influence of material nonlinearity in the optimized topological solutions.