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.

翻译：Strain 梯度理论是捕捉大小效应和本地化现象的精确模型。然而,在确定相应的构成参数方面的挑战限制了这种理论的实际应用。我们在此提出并利用无症状的同质化。所有四、五、六等分级参数都是通过演示的计算方法确定的。环氧碳纤维复合、金属矩阵复合和铝泡沫的例子说明了拟议方法的有效性和多功能性。调查了矩阵体积分数、RVES堆积和不同单位细胞长度对所确定参数的影响。同质化计算工具适用于大类材料,并在FEniCS中使用了开放源代码。