A Generalized Shear Lag Model for the “Brick-Mortar” Staggered Composite With Arbitrary Soft Phase Contents

Abstract Although the mechanical mechanisms of staggered biological composites are widely investigated, each existing model has its own application scope. In order to comprehensively characterize the mechanical properties of the staggered composite with arbitrary soft phase content, a generalized shear lag model is established, in which the soft phase may simultaneously bear the tension and shear loads. A novel approach of considering the soft phase as virtual layered composites composed of sub-soft and sub-hard phases is developed. The sub-hard phase has zero thickness and undergoes tensile load, while the sub-soft phase endures shear load. Accurate stress fields in the staggered composite can be well achieved with the new approach. Two simplified models are further proposed based on the generalized shear lag model. Comparison with the finite element results shows that the shear stress in the end soft phase has little effect on the mechanical performance of the staggered composite; while the normal stress in the interlayer soft phase and the variation of shear stress in the thickness direction of interlayer soft phase must be considered for the staggered composite with high interlayer soft phase content. Furthermore, the applicable scopes of the existing typical partition models are determined by comparing the effective Young's modulus predicted by the generalized model, the finite element calculation, and the partition models. The obtained results could be helpful for the precise design of composite materials with high mechanical properties.