Although the primacy and utility of higher-gradient theories are being increasingly accepted, values of second gradient elastic parameters are not widely available due to lack of generally applicable methodologies. In this paper, we present such values for a second-gradient continuum. These values are obtained in the framework of finite deformations using granular micromechanics assumptions for materials that have granular textures at some ‘microscopic’ scale. The presented approach utilizes so-called Piola's ansatz for discrete-continuum identification. As a fundamental quantity of this approach, an objective relative displacement between grain-pairs is obtained and deformation energy of grain-pair is defined in terms of this measure. Expressions for elastic constants of a macroscopically linear second gradient continuum are obtained in terms of the micro-scale grain-pair parameters. Finally, the main result is that the same coefficients, both in the 2D and in the 3D cases, have been identified in terms of Young's modulus, of Poisson's ratio and of a microstructural length.

中文翻译：

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基于颗粒微力学的弹性几何非线性变形各向同性应变梯度参数识别

尽管更高梯度理论的首要性和实用性越来越被接受，但由于缺乏普遍适用的方法，第二梯度弹性参数的值并没有被广泛使用。在本文中，我们为二梯度连续体提供了这些值。这些值是在有限变形的框架中获得的，使用颗粒微观力学假设，对于在某些“微观”尺度上具有颗粒纹理的材料。所提出的方法利用所谓的 Piola's ansatz 进行离散连续识别。作为该方法的基本量，获得了颗粒对之间的客观相对位移，并根据该度量定义了颗粒对的变形能。宏观线性第二梯度连续体的弹性常数表达式是根据微观颗粒对参数获得的。最后，主要结果是在 2D 和 3D 情况下，已根据杨氏模量、泊松比和微观结构长度确定了相同的系数。