Strain gradient theory is an accurate model for capturing size effects and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of such theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS.

中文翻译：

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应变梯度连续介质中周期性结构材料渐近均匀化方法的验证

应变梯度理论是捕捉尺寸效应和定位现象的准确模型。然而，识别相应本构参数的挑战限制了这种理论的实际应用。我们在此提出并利用渐近同质化。排名四、五和六张量中的所有参数都是用演示的计算方法确定的。环氧碳纤维复合材料、金属基复合材料和泡沫铝的例子说明了所提出方法的有效性和多功能性。研究了基质的体积分数、RVE 的堆叠和不同的晶胞长度对识别参数的影响。均质化计算工具适用于广泛类别的材料，并利用 FEniCS 中的开源代码。