稳健性(进化)
数学优化
多边形网格
有限元法
凸性
解耦(概率)
计算机科学
能量泛函
应用数学
算法
数学
结构工程
数学分析
工程类
基因
金融经济学
计算机图形学(图像)
控制工程
生物化学
经济
化学
作者
Tymofiy Gerasimov,Laura De Lorenzis
标识
DOI:10.1016/j.cma.2015.12.017
摘要
Phase-field modeling of fracture phenomena in solids is a very promising approach which has gained popularity within the last decade. However, within the finite element framework, already a two-dimensional quasi-static phase-field formulation is computationally quite demanding, mainly for the following reasons: (i) the need to resolve the small length scale inherent to the diffusive crack approximation calls for extremely fine meshes, at least locally in the crack phase-field transition zone, (ii) due to non-convexity of the related free-energy functional, a robust, but slowly converging staggered solution scheme based on algorithmic decoupling is typically used. In this contribution we tackle problem (ii) and propose a faster and equally accurate approach for quasi-static phase-field computing of (brittle) fracture using a monolithic solution scheme which is accompanied by a novel line search procedure to overcome the iterative convergence issues of non-convex minimization. We present a detailed critical evaluation of the approach and its comparison with the staggered scheme in terms of computational cost, accuracy and robustness.
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