Microstructure topology optimization by targeting prescribed nonlinear stress-strain relationships.

In this paper, we proposed a new material design method by microstructure topology optimization. Novelty of the proposed method is to target the whole nonlinear volume-averaged effective stress-strain curve of microstructure representative volume element (RVE) rather than aiming specific values such as strength, stiffness or Poisson ratio. J2 plasticity model with a linear isotropic hardening model was chosen for local residuals. Global residuals are computed within nonlinear finite element framework for the topology optimization. Sensitivities of the objective function augmented with the residuals and adjoint response vectors with respect to design variables are derived with details and their numerical computational procedures were also presented. Microstructure topologies showing two different targeted stress-strain curves under uniaxial and biaxial loadings were obtained by using the method of moving asymptotes (MMA) optimization algorithm. Accuracy of the sensitivity computations was verified and numerical examples demonstrated a potential of the proposed method in applications to multiscale topology optimization. • A new topology optimization method of microstructure by targeting nonlinear volume-averaged stress-strain path is proposed. • Derivations of sensitivities by adjoint method and detailed computational algorithm are presented. • We verified the sensitivity of the new objective function with respect to SIMP type design variables. • Numerical examples of nonlinear RVE microstructure topology were demonstrated under uniaxial and biaxial loadings. [ABSTRACT FROM AUTHOR]