发表机构
Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究向量值几何非线性黏聚断裂的相场泛函$\Gamma$-收敛，将向量胞元问题约化为一维变分问题，并推广黏聚定律重建程序以设计相场势恢复各向异性牵引-分离定律。
AI 中文摘要
我们研究了一类一般各向异性相场泛函的$\Gamma$-收敛，这些泛函用于模拟多维、向量值且几何非线性情形下的黏聚断裂。极限能量包含一个拟凸化的体项、一个由其回收函数控制的Cantor部分，以及一个通过渐近胞元问题定义的黏聚表面能量密度。在建立极限表面密度的结构性质和等价表述之后，我们证明：只要弹性能量的回收函数是与相场各向异性相容的算子范数的平方，向量胞元问题就显式地约化为一维变分问题。作为推论，我们将\cite{alessi2025phasefieldpart2}的黏聚定律重建程序推广到向量框架，显式设计了相场势，以恢复形如$g(\zeta,\nu)=\gamma(\nu)g_{\scal}(|\zeta|)$的预定类别的各向异性、依赖于跳变的牵引-分离定律。
英文摘要
We study the $Γ$-convergence of a general class of anisotropic phase-field functionals modelling cohesive fracture in the multidimensional, vector-valued, and geometrically nonlinear setting. The limiting energy comprises a quasiconvexified bulk term, a Cantor part governed by its recession function, and a cohesive surface energy density defined via an asymptotic cell problem. After establishing the structural properties and equivalent formulations of the limiting surface density, we show that, whenever the recession function of the elastic energy is given by the square of an operator norm compatible with the phase-field anisotropy, the vectorial cell problem explicitly reduces to a one-dimensional variational problem. As a consequence, we extend the cohesive law reconstruction procedure of \cite{alessi2025phasefieldpart2} to the vectorial framework, explicitly designing phase-field potentials that recover prescribed classes of anisotropic, jump-dependent traction-separation laws of the form $g(ζ,ν)=γ(ν)g_{\scal}(|ζ|)$.
