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 \(\delta >0\), 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 \(\delta >0\) and then consider the vanishing viscosity limit \(\delta \rightarrow 0\).

这项工作致力于在裂缝的相场模型框架内分析替代（交错）最小化算法的收敛性。该系统的能量以拉伸应变和压缩应变的非线性分裂为特征，其特征是断裂唇缘不互穿。交替方案与由粘性参数\（\ delta> 0 \）驱动的相位场变量中的\（L ^ {2} \）惩罚结合 ，并且具有不可逆性约束，迫使相位单调性字段仅保留时间，而不是沿整个迭代最小化。我们首先显示这种方案对于\（\ delta> 0 \）的粘性演变的收敛性，然后考虑消失的粘度极限\（\ delta \ rightarrow 0 \）。