Model Reduction on 3D Fracture Resistance Design

Fracture resistance design of materials and structures has recently attracted attention, while heavy numerical calculations hindered its development and application. In this work, reduced order model-based phase field method is proposed to accelerate the fracture simulation of composite structures. The reduced order basis is constructed to efficiently approximate the displacement and crack phase fields and enriched adaptively based on its effectiveness. We then extend the reduced order model to the phase field-based topology optimization for maximizing the fracture resistance of the 3D composite structures composed of contrasting soft and stiff phases. During the optimization, morphological structure of the soft phase is tailored under the Mode-I test by taking into account the whole fracture process from damage initiation, multiple crack propagation and ultimately to failure. Numerical result shows that the reduced order-based phase field modeling can achieve significant time speedup, while the accuracy of mechanical performance prediction in terms of stiffness, peak load, and mechanical work is guaranteed. Furthermore, by the reduced order model-based phase field topology optimization, all concerned mechanical properties are enhanced simultaneously compared with three representative interpenetrating phase composites, while the computation cost is greatly alleviated.