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首页> 外文期刊>International journal of nanomechanics science and technology >STRUCTURE OF GENERALIZED THEORIES OF ELASTICITY OF MEDIA WITH DEFECTIVE FIELDS AND OF GRADIENT THEORIES
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STRUCTURE OF GENERALIZED THEORIES OF ELASTICITY OF MEDIA WITH DEFECTIVE FIELDS AND OF GRADIENT THEORIES

机译：含递减场的介质的广义弹性理论和梯度理论的结构

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Generalized theories of elasticity, including theories of media with defective fields and gradient theories, are considered. In contrast to classical elasticity, which does not have scaling parameters characterizing the inner structure of material, such parameters are natural in nonlocal theories of elasticity and theories of media with defective fields. Therefore, they are applied in the solution of numerous applied problems for inhomogeneous structures when scaling effects are to be considered. Generalized models of continuous media are especially attractive in simulating properties of various microanostructures, elastic properties of composite materials and structured materials with submicron and nanosized internal structures wherein effective properties are significantly defined by scaling effects (effects of close interaction (cohesion) and adhesion). Nonclassical physical properties of generalized media are determined in terms of a sixth-rank tensor of gradient modulus of elasticity, which should obey some symmetry conditions. In the present work we discuss general fundamental properties and structure of nonclassical sixth-rank tensor of elasticity moduli in the theories of generalized media and propose a classification of models that provides grounds for building correct models of continua with account for scaling effects. An orthogonal basis of fifteen tensors of "moment" moduli is built and investigated in the sixth-rank tensor space. The structure of reversible models of deformation of solid media, including, both ideal (nondefective) media and media with conserved dislocation fields, is indicated. It is demonstrated that eleven basic tensors determine reversible properties of gradient media, whereas the remaining four tensors determine their dissipative properties. Eleven basic tensors, defining the properties of reversible deformations processes, were used to build five tensors of gradient moduli, substantial for nonlocal gradient theories. As a result, a structure of tensors for correct versions of gradient theories of elasticity is presented, and the type of tensors of elasticity for a very simple fully symmetric gradient two-parameter theory that can be proposed as an applied theory for simulating microanosized effects is established. The notion of the media space (models) has been introduced in accordance with the number of nonclassical moduli. It is demonstrated that in a general case the density of potential energy of curvatures is represented as a sum of densities of potential energies of subspaces of the Mindlin-Toupin gradient theories, theories of media with the Mindlin defective fields, and a bilinear form defining their interaction.
机译：考虑了广义弹性理论，包括具有缺陷场的介质理论和梯度理论。与经典弹性不同，经典弹性不具有表征材料内部结构的缩放参数，而在非局部弹性理论和具有缺陷场的介质理论中，此类参数是很自然的。因此，当考虑缩放效应时，它们可用于解决非均质结构的众多应用问题。连续介质的通用模型在模拟各种微观/纳米结构的特性，具有亚微米和纳米尺寸内部结构的复合材料和结构材料的弹性特性方面尤其有吸引力，其中有效特性由缩放效应（紧密相互作用（内聚力）和附着力的影响）显着定义。 ）。广义介质的非经典物理特性是根据梯度弹性模量的第六张量确定的，该张量应服从某些对称条件。在当前的工作中，我们讨论了广义媒体理论中非经典六阶张量弹性模量的一般基本性质和结构，并提出了一种模型分类，为建立考虑尺度效应的正确连续体模型提供了基础。在第六级张量空间中建立和研究了“矩”模量的十五张量的正交基础。指出了固态介质变形的可逆模型的结构，包括理想（无缺陷）介质和具有错位场的介质。结果表明，十一个基本张量确定了梯度介质的可逆性质，而其余四个张量确定了它们的耗散性质。定义可逆形变过程特性的11个基本张量用于构建5个梯度模量张量，对于非局部梯度理论而言是实质性的。结果，提出了一种用于正确形式的弹性梯度理论的张量结构，以及一种非常简单的完全对称的梯度两参数理论的弹性张量的类型，可以将其用作模拟微观/纳米尺寸的应用理论效果已建立。媒体空间（模型）的概念是根据非经典模数引入的。证明了在一般情况下，曲率势能的密度表示为Mindlin-Toupin梯度理论，具有Mindlin缺陷场的介质理论以及定义它们的双线性形式的子空间的势能密度的总和。相互作用。

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