Abstract
Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the 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. We make all of the codes publicly available in order to encourage a transparent scientific exchange.
Highlights
Composite materials have been widely used in engineering practice
The conventional homogenization fails to describe the mechanical response when the heterogeneity of the material is of the same order of the macroscale
Numerical examples for 2D and 3D, stiff and soft inclusions, cubic and transverse material symmetry cases have been conducted. In both 2D and 3D numerical examples, the effective strain gradient parameters vanish when materials are purely homogeneous, they are independent of repetitions of RVEs and sensitive to microstructural sizes
Summary
Composite materials have been widely used in engineering practice. Due to the heterogeneous nature of composites, the mechanical properties of such materials are dependent on their substructures, for example, the material properties of matrix and reinforcements, the shape of inclusions, or the volume fraction of matrix, etc. The conventional homogenization fails to describe the mechanical response when the heterogeneity of the material is of the same order of the macroscale This inaccuracy is due to the fact that the conventional homogenization methods are based on a separation of scales, given by = l/L, l L. The homogenization computational tool is developed based on open-source codes in FEniCS It allows for all kinds of 2D or 3D composite materials constructed by periodic microstructures. The codes are made publicly available in [39] in order to enable a transparent scientific exchange
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