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首页> 外文期刊>International Journal of Solids and Structures >A micromechanics-based strain gradient damage model for fracture prediction of brittle materials - Part I: Homogenization methodology and constitutive relations
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A micromechanics-based strain gradient damage model for fracture prediction of brittle materials - Part I: Homogenization methodology and constitutive relations

机译：用于脆性材料断裂的基于微力学的应变梯度损伤模型-第一部分：均质化方法和本构关系

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摘要

In this paper, we first describe a homogenization methodology with the aim of establishing strain gradient constitutive relations for heterogeneous materials. The methodology presented in this work includes two main steps. The first one is the construction of the average strain-energy density for a well-chosen RVE by using a homogenization technique. The second one is the transformation of the obtained average strain-energy density to that for the continuum. An important characteristic of this method is its self-consistency with respect to the choice of the RVE: the strain gradient constitutive law built by using the present method is independent of the size and the form of the RVE. In the frame of this homogenization procedure, we have constructed a strain gradient constitutive relation for a two-dimensional elastic material with many microcracks by adopting the self-consistent scheme. It was shown that the effective behavior of cracked solids depends not only on the crack density but also on the average crack size with which the strain gradient is associated. The proposed constitutive relation provides a starting point for the development of an evolution law of damage including strain gradient effect, which will be presented in the second part of this work.
机译：在本文中，我们首先描述一种均质化方法，旨在为异质材料建立应变梯度本构关系。这项工作中介绍的方法包括两个主要步骤。第一个是通过使用均质化技术为精心选择的RVE构建平均应变能密度。第二个是将获得的平均应变能密度转换为连续体的平均应变能密度。该方法的一个重要特征是其在RVE的选择方面的自洽性：使用本方法建立的应变梯度本构关系与RVE的大小和形式无关。在这种均质化过程的框架内，我们采用自洽方案，为具有许多微裂纹的二维弹性材料建立了应变梯度本构关系。结果表明，裂纹固体的有效行为不仅取决于裂纹密度，还取决于与应变梯度相关的平均裂纹尺寸。所提出的本构关系为包括应变梯度效应在内的损伤演化规律的发展提供了起点，这将在本工作的第二部分中介绍。

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