Phase-Field Finite Deformation Fracture with an Effective Energy for Regularized Crack Face Contact
Phase-Field Finite Deformation Fracture with an Effective Energy for Regularized Crack Face Contact
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DOI：
10.1016/j.jmps.2022.104994
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Maryam Hakimzadeh;Vaibhav Agrawal;K. Dayal;C. Mora-Corral
中科院分区：
文献类型：
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作者：
Maryam Hakimzadeh;Vaibhav Agrawal;K. Dayal;C. Mora-Corral
相场模型是解决实际裂缝问题的主要方法。它们将裂纹视为第二阶段，并使用梯度项来涂抹裂纹面，从而能够使用标准的数值方法进行模拟。这种正则化会导致裂纹在参考文献中占据有限的体积，并导致无法适当地模拟裂纹面的闭合或接触--而不会愈合。具体地说，经典的理想化裂纹面牵引力是剪切分量为零，裂纹张开时法向分量为零，裂纹闭合时与完整材料相同。相场断裂模型不能复制这一行为。本工作通过引入有效裂纹能量密度来解决这一缺陷，该密度赋予正则(有限体积)相场裂纹具有理想化尖锐裂纹的有效性质。该方法基于基于裂纹的变形梯度张量的QR(上三角)分解，使得能够透明地识别裂纹的变形模式。然后对那些不消耗能量的模式进行松弛，得到了当裂纹面闭合时具有完整响应的有效能量，而当裂纹面打开时有效能量为零。有效能量通常与经典的裂纹面牵引力是一致的，但并不总是一致的；这里表明，通常不存在与经典裂纹面牵引力和裂纹闭合时再现完整响应相一致的存储能量。该方法的一个亮点是它完全位于有限变形的背景下，使得它能够潜在地应用于软材料和其他具有大变形或旋转的环境。该模型被应用于典型的复杂载荷的数值研究，包括(1)软固体中空洞上的循环载荷，它显示了复杂应力状态下裂纹的扩展和闭合；(2)循环剪切，它显示了由裂纹闭合驱动的复杂的裂纹分支模式。
Phase-field models are a leading approach for realistic fracture problems. They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. This regularization causes cracks to occupy a finite volume in the reference, and leads to the inability to appropriately model the closing or contacting – without healing – of crack faces. Specifically, the classical idealized crack face tractions are that the shear component is zero, and that the normal component is zero when the crack opens and identical to the intact material when the crack closes. Phase-field fracture models do not replicate this behavior.This work addresses this shortcoming by introducing an effective crack energy density that endows the regularized (finite volume) phase-field crack with the effective properties of an idealized sharp crack. The approach is based on applying the QR (upper triangular) decomposition of the deformation gradient tensor in the basis of the crack, enabling a transparent identification of the crack deformation modes. By then relaxing over those modes that do not cost energy, an effective energy is obtained that has the intact response when the crack faces close and zero energy when the crack faces are open. The effective energy is often, but not always, consistent with the classical crack-face tractions; it is shown here that there generally does not exist a stored energy that is consistent both with the classical crack-face tractions and with reproducing the intact response when the crack closes.A highlight of this approach is that it lies completely in the setting of finite deformation, enabling potential application to soft materials and other settings with large deformation or rotations. The model is applied to numerically study representative complex loadings, including (1) cyclic loading on a cavity in a soft solid that shows the growth and closing of cracks in complex stress states; and (2) cyclic shear that shows a complex pattern of crack branching driven by the closure of cracks.