A framework for polyconvex large strain phase-field methods to fracture
A framework for polyconvex large strain phase-field methods to fracture
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DOI：
10.1016/j.cma.2016.12.035
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发表时间：
2017-04
影响因子：
7.2
通讯作者：
C. Hesch;A. J. Gil;R. Ortigosa;M. Dittmann;Carola Bilgen;P. Betsch;M. Franke;A. Janz;K. Weinberg
中科院分区：
文献类型：
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作者：
C. Hesch;A. J. Gil;R. Ortigosa;M. Dittmann;Carola Bilgen;P. Betsch;M. Franke;A. Janz;K. Weinberg
变相一致相场方法已被证明能够预测复杂的三维裂纹模式。然而，目前的计算方法在大变形的背景下缺乏必要的数值稳定性，以确保在不同的加载情况下的鲁棒性。在这项工作中，我们通过引入基于右Cauchy-Green张量的主不变量的新各向异性分裂，提出了有限应变多凸弹性的新公式，该公式始终确保所得到的应变能函数的多凸性。所提出的相场方法嵌入到一个复杂的等距框架中，该框架具有分层细化的三维问题，使用具有高阶收敛率的四阶Cahn-Hilliard裂纹密度泛函用于断裂问题。此外，我们首次在相场问题的背景下引入了一个Hu-Washizu混合变分公式，它允许新颖地引入变相一致的应力驱动分裂。新的多凸相场断裂公式保证了全变形范围和任意超弹性材料的数值稳定性。
Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy–Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn–Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu–Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials.