Topology Optimization for Fracture Resistance using Differentiable Programming and Peridynamics

Abstract

Fracture resistance is a critical consideration in engineering structures, particularly in applications where material failure can have catastrophic consequences. Traditional topology optimization methods often struggle to account for fracture propagation due to the inherently nonlocal nature of crack formation and growth. This work presents a framework for topology optimization that integrates bond-based peridynamics, a nonlocal continuum theory capable of modeling fracture without external failure criteria, with differentiable programming via JAX to enable gradient-based optimization of fracture-resistant designs. The peridynamic damage variable, defined as the volume-averaged fraction of broken bonds at each material point, is adopted as the optimization objective, providing a more direct indicator of discrete fracture than strain energy density or total fracture energy. Using this framework, optimized geometries are identified that provide highly localized reinforcement, forming impedance mismatches that reflect shock waves and suppress fracture. In one-dimensional examples, damage-based optimization produced fracture-resistant structures using substantially less material than strain energy density minimization and converged in less than 0.5% of the iterations required by the strain energy approach. These results are extended to two dimensions, where consistent trends are observed. The combination of automatic differentiation, just-in-time compilation, and GPU acceleration makes damage-based peridynamic topology optimization computationally tractable, demonstrating the potential of this approach for designing robust, fracture-resistant structures under dynamic loading.