This work proposes a study, carried out from both theoretical and numerical point of view, on the nonlinear microscopic failure phenomena occurring in nonlinear composite metamaterials whose microstructure is obtained by a periodic assembly of layers connected by cohesive interfaces, finitely strained along combined shear-compression macro-deformation loading path. A non-proportional loading path is analyzed where shear is applied parallel to the direction of lamination while compression along the layer direction. The paper focuses on the influence of shear on the level of the critical axial compression loading factor associated to the onset of microscopic instabilities and bifurcations, determined through an advanced nonlinear homogenization approach taking into account both irreversible decohesion and contact effects at the interfaces between different layers. To address the complexities in the analysis deriving from both contact mechanics formulation and nonlinear interface cohesive constitutive model, novel methodologies able to provide lower bound estimates are established. Numerical simulations are carried out on a representative volume element via an FE approach based on a total Lagrangean framework, assuming a hyperelastic behavior for the reinforcing and matrix layers. The proposed numerical model determines the principal deformation path and, subsequently, solves the corresponding sequence of eigenvalue problems. These problems identify the eigenmodes and instability modes associated with both the nonlinear actual problem and its linear comparison counterpart. The developed parametric analyses cover different reinforcement volume fractions, considering single and double interface debonding cases and highlight the critical role of shear in microstructural failure phenomena.
Gaetano et al. (Wed,) studied this question.