Designing brittle fracture-resistant structures:A tensile strain energy-minimized topology optimization

Abstract

This research proposes a novel method for designing fracture-resistant structures. By analyzing the relationship between tensile strain energy and phase field brittle fracture, it has been found that minimizing tensile strain energy can delay fracture and enhance resistance. Capitalizing on this insight, a new topology optimization method is proposed. This method focuses on minimizing tensile strain energy to suppress the well-documented tension-dominated fracture behavior observed in phase field brittle fracture analysis. In contrast to traditional topology optimization methods based on von Mises stress, this method generates more robust structures under tension. Furthermore, the method can incorporate stress constraints to mitigate the potential for stress concentrations arising from geometric discontinuities. Numerical results demonstrate the effectiveness of the proposed method. Using phase-field modeling, the mechanical fracture properties of the optimized structures, including peak load, failure displacement, and absorbed elastic energy before fracture, are quantified. Furthermore, experimental tests are also conducted. Both numerical simulations and experimental results are consistently show that structures designed with minimized tensile strain energy exhibit superior fracture toughness. Furthermore, the method offers significant computational efficiency compared to conventional approaches due to its reliance solely on linear elasticity analysis within the optimization process.