论文标题
矢量，几何非线性内聚骨折能的相位近似
Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy
论文作者
论文摘要
我们考虑了一个用于内聚骨折的矢量模型家族，它可能包含$ \ mathrm {so}（n）$ - 不变性。变形属于有界变异的广义函数的空间，并且能量包含（弹性）体积能，依赖开口的跳跃能集中在裂缝表面上，而cantor部分代表弥漫性损伤。我们表明，这种功能自然可以作为适当相位模型的$γ$限制。进入限制功能的能量密度可以以部分隐式的方式以出现在相位场近似中的那些方式表示。
We consider a family of vectorial models for cohesive fracture, which may incorporate $\mathrm{SO}(n)$-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an opening-dependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage. We show that this type of functional can be naturally obtained as $Γ$-limit of an appropriate phase-field model. The energy densities entering the limiting functional can be expressed, in a partially implicit way, in terms of those appearing in the phase-field approximation.
