A deeper understanding to predict fracture in soft biological tissues is of crucial importance to better guide and improve medical monitoring, planning of surgical interventions and risk assessment of diseases such as aortic dissection, aneurysms, atherosclerosis and tears in tendons and ligaments. In our previous contribution (Gültekin et al., 2016) we have addressed the rupture of aortic tissue by applying a holistic geometrical approach to fracture, namely the crack phase-field approach emanating from variational fracture mechanics and gradient damage theories. In the present study, the crack phase-field model is extended to capture anisotropic fracture using an anisotropic volume-specific crack surface function. In addition, the model is equipped with a rate-dependent formulation of the phase-field evolution. The continuum framework captures anisotropy, is thermodynamically consistent and based on finite strains. The resulting Euler-Lagrange equations are solved by an operator-splitting algorithm on the temporal side which is ensued by a Galerkin-type weak formulation on the spatial side. On the constitutive level, an invariant-based anisotropic material model accommodates the nonlinear elastic response of both the ground matrix and the collagenous components. Subsequently, the basis of extant anisotropic failure criteria are presented with an emphasis on energy-based, Tsai-Wu, Hill, and principal stress criteria. The predictions of the various failure criteria on the crack initiation, and the related crack propagation are studied using representative numerical examples, i.e. a homogeneous problem subjected to uniaxial and planar biaxial deformations is established to demonstrate the corresponding failure surfaces whereas uniaxial extension and peel tests of an anisotropic (hypothetical) tissue deal with the crack propagation with reference to the mentioned failure criteria. Results favor the energy-based criterion as a better candidate to reflect a stable and physically meaningful crack growth, particularly in complex three-dimensional geometries with a highly anisotropic texture at finite strains.

中文翻译：

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软生物组织中各向异性失效的数值方面有利于基于能量的标准：速率相关的各向异性裂纹相场模型

更深入地了解预测软生物组织的骨折对于更好地指导和改善医疗监测、手术干预计划以及主动脉夹层、动脉瘤、动脉粥样硬化以及肌腱和韧带撕裂等疾病的风险评估至关重要。在我们之前的贡献（Gültekin 等人，2016）中，我们通过应用整体几何断裂方法（即源自变分断裂力学和梯度损伤理论的裂纹相场方法）来解决主动脉组织的破裂问题。在本研究中，裂纹相场模型被扩展为使用各向异性体积特定裂纹表面函数来捕获各向异性断裂。此外，该模型还配备了相场演化的速率相关公式。连续体框架具有各向异性，热力学一致，并且基于有限应变。由此产生的欧拉-拉格朗日方程在时间方面通过算子分裂算法求解，随后在空间方面采用伽辽金型弱公式。在本构层面上，基于不变的各向异性材料模型适应了基底基质和胶原成分的非线性弹性响应。随后，提出了现有各向异性失效准则的基础，重点是基于能量的 Tsai-Wu、Hill 和主应力准则。使用代表性的数值实例研究了对裂纹萌生的各种失效准则以及相关裂纹扩展的预测，即建立了受到单轴和平面双轴变形的均质问题来演示相应的失效表面，而单轴延伸和剥离测试各向异性（假设）组织参考上述失效准则处理裂纹扩展。结果表明基于能量的标准是反映稳定且具有物理意义的裂纹扩展的更好候选标准，特别是在有限应变下具有高度各向异性纹理的复杂三维几何形状中。