  The concept of concurrent material and structure optimization aims at
alleviating the computational discovery of optimum microstructure
configurations in multiphase hierarchical systems, whose macroscale behavior is
governed by their microstructure composition that can evolve over multiple
length scales from a few micrometers to centimeters. It is based on the split
of the multiscale optimization problem into two nested sub-problems, one at the
macroscale (structure) and the other at the microscales (material). In this
paper, we establish a novel formulation of concurrent material and structure
optimization for multiphase hierarchical systems with elastoplastic
constituents at the material scales. Exploiting the thermomechanical
foundations of elastoplasticity, we reformulate the material optimization
problem based on the maximum plastic dissipation principle such that it assumes
the format of an elastoplastic constitutive law and can be efficiently solved
via modified return mapping algorithms. We integrate continuum micromechanics
based estimates of the stiffness and the yield criterion into the formulation,
which opens the door to a computationally feasible treatment of the material
optimization problem. To demonstrate the accuracy and robustness of our
framework, we define new benchmark tests with several material scales that, for
the first time, become computationally feasible. We argue that our formulation
naturally extends to multiscale optimization under further path-dependent
effects such as viscoplasticity or multiscale fracture and damage.
