An Efficient Strategy to Implement Local Porosity Constraints in the Multiscale Design of Solids with Parameterized Biomimetic Microstructures

•A novel approach to efficiently handle non-linear constraints is presented.•Impressive reductions of computing cost are achieved.•The obtained designs have microstructures that mimic the trabecular bone.•The prescribed bounds are honored at every point of the macroscopic domain.•The method can be used to set constraints on several properties in the microscale.