论文标题
来自离散有限差异模型的Griffith功能的推导
A derivation of Griffith functionals from discrete finite-difference models
论文作者
论文摘要
我们分析了在离散裂缝中，分析了Ambrosio tortorelli类型的功能，在离散到颈部限制中的有限差异近似。在竞争量表之间的合适制度中，即，如果离散化步骤$δ$小于椭圆度参数$ \ varepsilon $，我们显示该模型的$γ$ - 对Griffith函数的融合，仅包含执行dirichlet边界的术语dirichlet边界和无$ l^p $ fidelity术语。限制在两个维度上，我们还解决了以Chambolle，Conti和Francfort的最新作品精神的精神，在极限功能中添加了（线性化的）限制物质的约束。
We analyze a finite-difference approximation of a functional of Ambrosio-Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step $δ$ is smaller than the ellipticity parameter $\varepsilon$, we show the $Γ$-convergence of the model to the Griffith functional, containing only a term enforcing Dirichlet boundary conditions and no $L^p$ fidelity term. Restricting to two dimensions, we also address the case in which a (linearized) constraint of non-interpenetration of matter is added in the limit functional, in the spirit of a recent work by Chambolle, Conti and Francfort.
