Level set topology optimization of elasto-plastic materials with local stress constraints

This paper presents a level set-based framework for structural topology optimization submitted to local elasto-plastic stress constraints. While stresses are mostly limited to (a fraction of) the yield stress in a linear elastic setting, a design based on an elasto-plastic material model that allows for some degree of plasticity, especially in extreme loading scenarios, can result in much more efficient structures. Such problems typically involve both a large number of design variables and a large number of restrictions. A remedy which takes advantage of the Augmented Lagrangian approach is proposed here, and leads to a formulation which requires only one adjoint vector for all the stresses, which reduces the computational effort of both the sensitivity evaluation and of the iterative solver. Furthermore, to allow for a sufficient freedom in the design, an automated hole seeding during the optimization process is achieved by combining appropriately the level set and the density-based geometrical descriptions. The extended finite element method (XFEM) is used to represent the non-conforming material interface on a fixed mesh of the design domain. The performance of the local elasto-plastic stress constraints in the level set geometry description is demonstrated on classical 2D and 3D stress-constrained topology optimization benchmarks.