用松弛变量方法计算相场断裂不可逆性
Phase-field fracture irreversibility using the slack variable approach
摘要：
在这篇手稿中，相场断裂不可逆性约束转化为一个基于等式的约束，使用松弛变量的方法。然后利用拉格朗日乘子法和罚函数法在相场断裂能泛函中引入基于等式的断裂不可逆性约束。这两种方法是变分一致的传统的变分不等式相场断裂问题，不同于历史变量的方法。随后，数值实验进行基准问题的脆性和准脆性断裂，以证明所提出的方法的有效性。
英文摘要：
In this manuscript, the phase-field fracture irreversibility constraint is transformed into an equality-based constraint using the slack variable approach. The equality-based fracture irreversibility constraint is then introduced in the phase-field fracture energy functional using the Lagrange Multiplier Method and the Penalty method. Both methods are variationally consistent with the conventional variational inequality phase-field fracture problem, unlike the history-variable approach. Thereafter, numerical experiments are carried out on benchmark problems in brittle and quasi-brittle fracture to demonstrate the efficacy of the proposed method.
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