A phase-field model for fractures in nearly incompressible solids
A phase-field model for fractures in nearly incompressible solids
复制标题
几乎不可压缩固体中裂缝的相场模型
作者：
K. Mang;T. Wick;W. Wollner
在这项工作中，我们开发了一个相场描述模拟几乎不可压缩材料的裂缝。众所周知，低阶近似通常会导致体积锁定行为。我们提出了一种方法，建立在一个混合形式的位移方程与两个未知数：位移场和流体静压变量。必须适当地选择相应的函数空间。在离散层次上，位移-压力系统采用稳定的泰勒-胡德单元。两个额外的变量描述相场解和裂纹不可逆性约束。因此，最终的系统包含四个变量：位移，压力，相场，和一个拉格朗日乘子。所得到的离散系统是非线性的，用牛顿型方法单片求解。我们提出的模型证明了几个数值研究的基础上，三个数值试验。首先，不同的有限元选择进行比较，以调查高阶元素在建议的设置的影响。此外，数值结果，包括空间网格细化研究和泊松比的变化近似不可压缩的限制，提出。
Within this work, we develop a phase-field description for simulating fractures in nearly incompressible materials. It is well-known that low-order approximations generally lead to volume-locking behaviors. We propose an approach that builds on a mixed form of the displacement equation with two unknowns: a displacement field and a hydro-static pressure variable. Corresponding function spaces have to be chosen properly. On the discrete level, stable Taylor–Hood elements are employed for the displacement-pressure system. Two additional variables describe the phase-field solution and the crack irreversibility constraint. Therefore, the final system contains four variables: displacements, pressure, phase-field, and a Lagrange multiplier. The resulting discrete system is nonlinear and solved monolithically with a Newton-type method. Our proposed model is demonstrated by means of several numerical studies based on three numerical tests. First, different finite element choices are compared in order to investigate the influence of higher-order elements in the proposed settings. Further, numerical results including spatial mesh refinement studies and variations in Poisson’s ratio approximating the incompressible limit, are presented.
DOpElib：微分方程和优化环境；
DOI：
10.11588/ans.2017.2.11815
发表时间：
2017
期刊：
影响因子：
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作者：
C. Goll;T. Wick;W. Wollner
通讯作者：
W. Wollner