Effects of higher-order interface stresses on the elastic states of two-dimensional composites

We propose a simple model to simulate higher-order interface stresses along the interface between two neighboring media in two dimensions. The interface behavior is modeled from a thin interphase of constant thickness by taking a proper limit process. In the formulation the deformation of the thin interphase is approximated by the Kirchhoff-Love assumption of thin shell. To incorporate the higher-order interface stresses, we consider the bending effects resulting from the non-uniform surface stress across the layer thickness. The stress equilibrium conditions is fulfilled by consideration of balance for forces as well as stress couples. Depending on the difference in stiffness and length scales of the interphase, we show that the interfaces can be classified into four different types. This findings, upon suitable definitions of material parameters, agree with a rigorous asymptotic analysis proposed by Benveniste and Miloh [Benveniste, Y., Miloh, T., 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33 309-323]. To illustrate the higher-order effects, we derive analytically the stress concentration factor of an infinite plate containing a circular cavity with interface stresses of different orders subjected to a remote transverse shear loading. The closed-form expressions show how the orders of interface stresses influence the concentration factor in a successive manner. In addition, we examine the effective shear modulus of composites with circular inclusions with higher-order interface effects. The effective transverse shear modulus is derived based on the generalized self-consistent method.