反演变形方法中断裂的不可逆条件与平衡点的稳定性
Irreversibility condition and stability of equilibria in the inverse-deformation approach to fracture
AI总结：
本文通过热力学第二定律推导了反演变形方法中断裂的不可逆条件，并证明了所有断裂平衡点的局部稳定性。
摘要：
我们利用热力学第二定律推导了反演变形方法中断裂的不可逆条件。我们考虑了之前由Rosakis等人（2021）解决的弹性杆脆性破坏问题。尽管存在非零界面/表面能，反演变形映射的第三导数在裂纹面处是不连续的。这是由于存在确保反演应变非负且物质方向保持不变的不等式约束所致。裂纹材料位置的变化会导致负熵产生，违反第二定律。因此，此类变化被禁止，从而给出不可逆条件。不等式约束和不可逆条件限制了可接受变化的空间。我们证明了局部稳定的必要和充分条件，这些条件纳入了这些限制。其数值实现表明，Rosakis等人（2021）发现的所有断裂平衡点都是局部稳定的。
英文摘要：
We derive an irreversibility condition for fracture in the inverse-deformation approach using the second law of thermodynamics. We consider the problem of brittle failure in one-dimensional, homogeneous, elastic bars undergoing quasistatic motion. Despite the presence of a non-zero interfacial/surface energy, the third derivative of the inverse deformation is discontinuous at crack faces. This is due to the inequality constraint allowing fracture while ensuring that the orientation of matter is preserved. We show that any change in the location of open cracks in their reference configuration result in negative entropy production. We disallow these changes according to the second law of thermodynamics, fixing the location of cracks in their reference domain. The inequality constraint and the irreversibility condition limit the space of admissible variations. We prove second-order conditions for local stability incorporating these restrictions. Their numerical implementation shows that all broken equilibria of the elastic bar under hard loading are locally stable.
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