A method for quasistatic cohesive fracture is introduced that uses an alternating direction method of multipliers (ADMM) to implement an energy approach to cohesive fracture. The ADMM algorithm minimizes a non-smooth, non-convex potential functional at each strain increment to predict the evolution of a cohesive-elastic system. The optimization problem bypasses the explicit stress criterion of force-based (Newtonian) methods, which interferes with Newton iterations impeding convergence. The model is extended with an extrapolation method that significantly reduces the computation time of the sequence of optimizations. The ADMM algorithm is experimentally shown to have nearly linear time complexity and fast iteration times, allowing it to simulate much larger problems than were previously feasible. The effectiveness, as well as the insensitivity of the algorithm to its numerical parameters is demonstrated through examples. It is shown that the Lagrange multiplier method of ADMM is more effective than earlier Nitsche and continuation methods for quasistatic problems. Close spaced minima are identified in complicated microstructures and their effect discussed.
翻译:采用准静态内聚性断裂的方法,采用一种交替方向的倍数法(ADMM)来对凝聚性断裂实施一种能量法。ADMM算法最大限度地减少了每种递增的无悬浮、非凝固的潜在功能,以预测一个凝聚弹性系统的演进。优化问题绕过了以力为基础的(Newtonian)方法的明确压力标准,该标准干扰牛顿的迭代作用。模型采用一种外推法来扩展,该方法大大缩短了优化序列的计算时间。ADMM算法实验性地显示,ADMM算法具有近线性的时间复杂性和快速迭代时间,从而能够模拟比以前可行的问题大得多的问题。实例表明,ADMMM的拉格兰特倍增法比早先的Nitsche法和准静态问题的持续方法更为有效。在复杂的微结构中发现了近空间微型微粒子及其效果。