论文标题
预应力弹性晶格的增量本构张量和应变定位：第一部分 - 准静态响应
Incremental constitutive tensors and strain localization for prestressed elastic lattices: Part I -- quasi-static response
论文作者
论文摘要
在平行凝集的几何形状中组织的弹性杆的晶格可以轴向加载到任意量的情况下，而不会失真，然后受到增量位移。使用准静态均质化理论，该晶格可以等效于预应力的固体固体，以增量变形，以获得极为局部的机械响应。可以参考原则上实现的机械模型来分析这些响应，以便例如剪切带倾斜或单个剪切频带的出现或微观之间的竞争（在晶格中发生，但不在等效的固体中）和宏观（具有晶格和等效的持续性持续性）。使用基于绿色的基于函数的扰动方法进行局部化的分析，以突出相等固体的复合材料和均质反应之间的对应关系。所提出的结果仅限于准静态行为，为连续体中的应变定位提供了新的理解，并开放了新的可能性，以实现和实验表现出这些极端机械行为的材料。动态均匀化和振动定位被推迟到本研究的第二部分。
A lattice of elastic rods organized in a parallelepiped geometry can be axially loaded up to an arbitrary amount without distortion and then be subject to incremental displacements. Using quasi-static homogenization theory, this lattice can be made equivalent to a prestressed elastic solid subject to incremental deformation, in such a way to obtain extremely localized mechanical responses. These responses can be analyzed with reference to a mechanical model which can, in principle, be realized, so that features such as for instance shear bands inclination, or emergence of a single shear band, or competition between micro (occurring in the lattice but not in the equivalent solid) and macro (present in both the lattice and the equivalent continuum) instabilities become all designable features. The analysis of localizations is performed using a Green's function-based perturbative approach to highlight the correspondence between micromechanics of the composite and homogenized response of the equivalent solid. The presented results, limited to quasi-static behaviour, provide a new understanding of strain localization in a continuum and open new possibilities for the realization and experimentation of materials exhibiting these extreme mechanical behaviours. Dynamic homogenization and vibrational localization are deferred to Part II of this study.
