预应力弹性格构的增量本构张量和应变局部化：第一部分--准静态响应
Incremental constitutive tensors and strain localization for prestressed elastic lattices: Part I -- quasi-static response
摘要：
平行六面体几何形状的弹性杆的网格可以轴向加载到任意量而不变形，然后受到增量位移。使用准静态均匀化理论，这种晶格可以等效为一个预应力弹性固体受到增量变形，在这样一种方式，以获得非常本地化的机械响应。这些响应可以参照原则上可以实现的力学模型进行分析，使得诸如剪切带倾斜或单个剪切带的出现或微观（发生在晶格中而不是等效固体中）和宏观（存在于晶格和等效连续体中）不稳定性之间的竞争等特征成为所有可设计的特征。本地化的分析是使用基于格林函数的微扰方法来突出的对应关系的复合材料的微观力学和均匀化的等效固体的响应。所提出的结果，仅限于准静态行为，提供了一个新的理解应变局部化的连续和开放的实现和实验的材料表现出这些极端的机械行为的新的可能性。动力均匀化和振动局部化推迟到本研究的第二部分。
英文摘要：
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.
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