Perturbed area functionals and brittle damage mechanics

Concentration versus oscillation effects in brittle damage

This work is concerned with an asymptotic analysis, in the sense of $Γ$-convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity. The study is performed as the damaged zone concentrates into a set of zero volume and, at the same time and to the same order $\varepsilon$, the stiffness of the damaged material becomes small. Three main features make the analysis highly nontrivial: at $\varepsilon$ fixed, minimizing sequences of each brittle damage model oscillate and develop microstructures; as $\varepsilon\to 0$, concentration and saturation of d…

完美塑性与损伤：不可逆性与$\Gamma$-收敛通过变分演化的不稳定相互作用

Perfect plasticity versus damage: an unstable interaction between irreversibility and $Γ$-convergence through variational evolutions

本文针对一维时变边界条件下的损伤力学问题，结合已有标度律与准静态脆性损伤演化模型，研究松弛与不可逆性的相互作用，发现该相互作用随时间演化不稳定，极限演化未必为完美塑性类型。

离散脆性损伤模型中振荡尺度的影响

Effects of oscillation scales in discrete brittle damage models

本文针对二维离散环境下Francfort和Marigo脆性损伤模型的离散版本开展渐近分析，发现仅当网格大小与受损区域集中性同阶时，才能渐近捕获类似脆性断裂的集中现象，解决了有效模型对空间离散化尺度的依赖性问题。

基于非局部公式的动态脆性断裂的能量平衡与损伤

Energy balance and damage for dynamic brittle fracture from a nonlocal formulation

本文提出一种近场动力学型非局部动态脆性损伤模型，通过位移-失效对满足能量平衡，在非局部性趋于零时恢复Griffith断裂能，并模拟了裂纹扩展路径。

Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.

Visco-Energetic solutions to some rate-independent systems in damage, delamination, and plasticity

This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic and Balanced Viscosity solutions. Visco-Energetic solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a `viscous' correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter. The resulting solution notion turns out to describe a kind of evolution in …