Strain Energy Density-Based Topology Optimization Using SIMP and Local Failure Criteria for 3D-Printed Concrete Structures (2025-12)¶

This paper presents a strain energy density–based topology optimization method tailored for brittle materials such as 3D-printed concrete. Extending the SIMP framework, the approach incorporates a local failure criterion derived from a Lode–Nadai ultimate strain energy model, allowing each element to adapt to tension-, compression-, or shear-dominated stress states. A memory-locking mechanism preserves elements that exceed their local energy limits, preventing unstable material removal and improving structural robustness. The method is implemented in the FEniCS finite element environment, enabling full customization of material behavior and numerical routines. Benchmark simulations of a slab, cantilever beam, and foundation block demonstrate that the proposed strategy generates manufacturable, failure-resistant layouts and produces more physically consistent topologies than traditional compliance-based designs, particularly for materials with limited tensile capacity.