断裂的逆变形方法
The inverse-deformation approach to fracture
摘要：
我们提出了一个一维的，非凸的弹性本构模型，具有较高的梯度，可以预测自发断裂在临界载荷通过分叉分析。它克服了不连续变形的问题，没有额外的场变量，如损伤或相场变量，没有先验指定的表面能。我们的主要工具是使用的逆变形，它可以扩展到一个分段光滑映射，即使当原始变形有不连续性描述裂纹开口。我们利用这一点，通过逆变形制定有限弹性由于盾和卡尔森，包括更高的梯度的能量。该问题是服从严格的全球分歧分析中存在的单边约束。断裂硬加载下发生在一个分叉的解决方案分支在一个关键的应用拉伸水平和断裂的解决方案被发现具有较高的梯度效应所产生的表面能。
英文摘要：
We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without additional field variables, such as damage or phase-field variables, and without a priori specified surface energy. Our main tool is the use of the inverse deformation, which can be extended to be a piecewise smooth mapping even when the original deformation has discontinuities describing cracks opening. We exploit this via the inverse-deformation formulation of finite elasticity due to Shield and Carlson, including higher gradients in the energy. The problem is amenable to a rigorous global bifurcation analysis in the presence of a unilateral constraint. Fracture under hard loading occurs on a bifurcating solution branch at a critical applied stretch level and fractured solutions are found to have surface energy arising from higher gradient effects.
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