论文标题
在具有高泊松比的L形样本上测试的混合形式的相场断裂模型的自适应数值模拟
Adaptive Numerical Simulation of a Phase-field Fracture Model in Mixed Form tested on an L-shaped Specimen with High Poisson Ratios
论文作者
论文摘要
这项工作为几乎不可压缩的固体中的裂缝的相位场模型进行数值模拟提供了一种新的自适应方法。为了应对锁定效应，我们使用最近提出的混合形式，除位移场和相位场变量外，我们的水力静压是其他未知的。为了满足骨折的不可逆性约束，我们将表述视为相处变量中的变异不平等。对于自适应网格的细化，我们使用最近开发的残留型后验误差估计器来有效且可靠，并且相对于相位场正则化参数，这是有效且可靠的。所提出的模型和基于自适应的改进策略是通过最初用于混凝土开发的L形面板测试的数值测试来证明的。在这里，泊松的比率从标准设置更改为不可压缩的限制$ν\，更改为0.5 $。
This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson's ratio is changed from the standard setting towards the incompressible limit $ν\to 0.5$.
