Influence of microstructure on size effect for metamaterials applied in composite structures

Infill density used in additive manufacturing incorporates a structural response change in the structure. Infill pattern creates a microstructure that affects the mechanical performance as well. Whenever the length ratio of microstructure to geometry converges to one, metamaterials emerge and the strain-gradient theory is an adequate model to predict metamaterials response. All metamaterial parameters are determined by an asymptotic homogenization, and we investigate the effects of infill density and pattern on these parameters. In order to illuminate the role of infill characteristics on the strain-gradient parameters, an in-depth numerical investigation is presented for one, widely used case in three-dimensional (3D) printers, rectangular grid.

https://doi.org/10.1177/10812865221100978

Investigating infill density and pattern effects in additive manufacturing by characterizing metamaterials along the strain-gradient theory

Metamaterials exhibit significantly different mechanical deformation than in classical “first-order” theory. One possible modeling approach is to use a “straingradient” theory by incorporating also higher gradients of displacements into the formulation. This procedure clearly brings in additional constitutive parameters. In this study, a numerical framework is presented by applying strain-gradient theory to 3-D printed structures with an infill ratio used frequently in additive manufacturing for weight reduction. This choice causes metamaterials; the additional constitutive parameters in the strain-gradient model are determined by an asymptotic homogenization. In order to demonstrate the reliability of this methodology, we verify the accuracy by computations using the finite element method. 

Strain-Gradient Modeling and Computation of 3-D Printed Metamaterials for Verifying Constitutive Parameters Determined by Asymptotic Homogenization

Duoskelion structures have been recently introduced by Barchiesi et al. (2021) as a proof-of-concept motif for a new class of metamaterials. The properties of these periodic beam-like chiral structural elements have been investigated, up to now, by means of a discrete model formulation whose predictions are obtained by numerical methods. In this paper we select a specific scaling law for micro stiffnesses aimed at deriving, via asymptotic homogenization, an internally-constrained Cosserat one-dimensional planar continuum model as the limit of a duoskelion structure. We analyze qualitatively and quantitatively the family of equilibrium configurations of the homogenized continuum when subjected to axial loading and compare the results of the analysis with those obtained by means of the discrete model formulation. 

A beam model for duoskelion structures derived by asymptotic homogenization and its application to axial loading problems

Self-consistent assessments for the effective properties of two-phase composites within strain gradient elasticity

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.

Salma Barboura

Papers

Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum.