Tracking crack propagation at large strains of hyperelastic solids is a challenging task due to the high nonlinearity, nearly incompressibility and ordered tendency in microstructure of the rubbery material under stretch. On the basis of the diffusive crack model, this work presents a new phase-field model by combining the strain energy decomposition and the enhanced assumed strain method. The proposed fracture formulation is indeed Griffith's theory-based framework but further accounting for the coupled effects of the stretches, damage and incompressibility to predict the crack growth in both compressible and incompressible hyperelastic solids. There are three innovations contained in this study: (i) The developed phase-field framework is capable to capture the effect of hole collapse, which is an intrinsic phenomenon of hyperelastic material and difficult to be detected by the others. (ii) The developed energy decomposition method provides a reasonable description of the physical reality that the hyperelastic fracture is driven by the changes in the internal energy of the stretched molecular chains in the polymer network. This continuum description automatically distinguishes the strain energy that really contributes to crack growth at multiaxial stress states, reducing significantly the numerical instability caused by material softening. (iii) By introducing the assumed strain method to the present fracture scheme, the physical consistency of energy decomposition and the mathematical nonnegativeness of strain energy can be satisfied simultaneously for incompressible problem. We demonstrate the performance of the enhanced phase-field framework through representative examples and highlight the importance of positive deviatoric energy for incompressible problem by comparing with experiments and classical models.

由于高非线性，几乎不可压缩以及橡胶材料在拉伸下的微观结构的有序化趋势，因此在大应变的超弹性固体应变下跟踪裂纹扩展是一项艰巨的任务。在扩散裂纹模型的基础上，结合应变能分解和改进的假定应变方法，提出了一种新的相场模型。提出的断裂公式的确是格里菲斯基于理论的框架，但进一步考虑了拉伸，损伤和不可压缩性的耦合效应，以预测可压缩和不可压缩的超弹性固体中的裂纹扩展。这项研究包含三项创新：（i）已开发的相场框架能够捕获空穴塌陷的影响，这是超弹性材料的一种固有现象，很难被其他人发现。（ii）发达的能量分解方法提供了对物理现实的合理描述，即超弹性断裂是由聚合物网络中拉伸的分子链的内部能量的变化驱动的。该连续描述自动区分了在多轴应力状态下真正有助于裂纹扩展的应变能，从而大大降低了由材料软化引起的数值不稳定性。（iii）通过将假定的应变方法引入当前的裂缝方案，可以同时解决不可压缩问题的能量分解的物理一致性和应变能量的数学非负性。