The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction between incompressibility and smeared crack opening. Drawing on the stiffness-degradation idea in PFM, we resolved this contradiction through loosening incompressible constraint of the damaged phase without affecting the incompressibility of intact material. By modifying the perturbed Lagrangian approach, we derived a novel mixed formulation. In numerical aspects, the finite element discretization uses the classical Q1/P0 and high-order P2/P1 schemes, respectively. To ease the mesh distortion at large strains, an adaptive mesh deletion technology is also developed. The validity and robustness of the proposed mixed framework are corroborated by four representative numerical examples. By comparing the performance of Q1/P0 and P2/P1, we conclude that the Q1/P0 formulation is a better choice for finite strain fracture in nearly incompressible cases. Moreover, the numerical examples also show that the combination of the proposed framework and methodology has vast potential in simulating complex peeling and tearing problems
翻译:偏好级场法(PFM)在近于或真正不压缩的超弹性材料的有限线断裂模型中遇到了挑战。我们发现,根本原因在于不压缩和涂片裂开之间的内在矛盾。根据PFM中的硬性降解理念,我们通过在不影响完整材料的不压缩性能的情况下放松受损阶段的不压缩限制而解决了这一矛盾。通过修改周遭的拉格朗格方法,我们得出了一种新型混合配方。在数字方面,有限分解元素分别使用典型的Q1/P0和高级P2/P1方案。为了减轻大菌株的网状扭曲,还开发了适应性网状删除技术。四个有代表性的数字实例证实了拟议混合框架的有效性和稳健性。通过比较Q1/P0和P2/P1的性能,我们得出结论,Q1/P0配方在几乎可压缩的案例中是选择有限质质断裂的更好选择。此外,数字例子还表明,拟议框架和方法的组合和方法在模拟复杂离心机方面有着巨大的潜力。