相场破裂中的不可逆性和交替最小化：粘性方法
Irreversibility and alternate minimization in phase field fracture: a viscosity approach
摘要：
这项工作是致力于分析的收敛性交替（交错）最小化算法的框架相场模型的裂缝。该系统的能量的特点是由拉伸和压缩应变的非线性分裂，具有非互穿的断裂唇。交替方案与相场变量中的$L^{2}$ -惩罚耦合，由粘性参数$δ>0$驱动，并且具有不可逆性约束，迫使相场的单调性仅关于~时间，但不是沿着整个迭代最小化。我们首先证明了这样一个计划的收敛性，粘性演化$δ>0$，然后考虑消失的粘性极限$δ\to 0$。
英文摘要：
This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and compressive strains, featuring non-interpenetration of the fracture lips. The alternating scheme is coupled with an $L^{2}$-penalization in the phase field variable, driven by a viscous parameter~$δ>0$, and with an irreversibility constraint, forcing the monotonicity of the phase field only w.r.t.~time, but not along the whole iterative minimization. We show first the convergence of such a scheme to a viscous evolution for $δ>0$ and then consider the vanishing viscosity limit $δ\to 0$.
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