发表机构
Université catholique de Louvain; University of Twente（天主教鲁汶大学; 特温特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过约束增量最小化建立率无关系统连续时间极限，证明简化剪切转变区模型通过相邻转变区连续激活形成剪切带，为局部化机制提供严格数学框架。
AI 中文摘要
我们研究率无关系统，其中演化通过弹性能量和一次齐次耗散的增量最小化获得，并受制于允许的非弹性增量约束。此类约束在多种非弹性材料模型中自然出现，包括剪切转变区模型、间歇塑性、量子化塑性，其中演化通过规定的基元激活事件而非任意塑性增量进行。我们在适当假设下建立了相应约束增量方案连续时间极限的存在性。作为应用，我们构建了一个简化剪切转变区模型，该模型由嵌入二维弹性介质中的晶格上的局部激活事件组成。我们证明该模型通过相邻转变区的连续激活产生剪切带形成。更精确地，我们表明在无限域设置中，每个允许的演化都保持在一个增长线段上的局部化，并且相同机制在足够大的有界域上持续存在。这些结果为约束激活模型提供了严格的数学框架，并表明对允许基元事件的限制本身构成率无关系统中局部化的机制。
英文摘要
We study rate-independent systems in which the evolution is obtained by incremental minimization of elastic energy and one-homogeneous dissipation under constraints on the admissible inelastic increments. Such constraints arise naturally in several models of inelastic materials, including shear-transformation-zone models, intermittent plasticity, and quantized plasticity, where evolution proceeds through prescribed elementary activation events rather than arbitrary plastic increments. We establish the existence of a continuous-time limit for the corresponding constrained incremental scheme under suitable assumptions. As an application, we formulate a simplified shear-transformation-zone model consisting of localized activation events on a lattice embedded in a two-dimensional elastic medium. We prove that this model generates shear-band formation through the successive activation of neighboring transformation zones. More precisely, we show that every admissible evolution remains localized on a growing line segment in the infinite-domain setting and that the same mechanism persists on sufficiently large bounded domains. These results provide a rigorous mathematical framework for constrained activation models and show that restrictions on admissible elementary events alone constitute a mechanism for localization in rate-independent systems.
Comments34 pages, 1 figure
