A novel large-strain kinematic framework for fiber-reinforced laminated composites and its application in the characterization of damage

Abstract

In this paper, a novel kinematic framework for fiber-reinforced composite materials is presented. For this purpose, we use the multiple natural configurations in conjunction with the multi-continuum theory of Bedford and Stern~(1972). Keeping the underlying physics of the proposed kinematics consistent. The proposed kinematics results in a three-term decomposition of the deformation gradient i.e. $\mathbf{F}=\mathbf{F}^e\mathbf{F}^r_\alpha\mathbf{F}^d_\alpha$, where $\alpha$ represents either the matrix or the fiber. After discussing the kinematic framework in detail, we use this new kinematic framework to characterize the damage contents associated with four damage mechanisms. These damage mechanisms are matrix cracking, fiber breakage, interfacial slip or debonding, and delamination. While the first two are derived by measuring the incompatibility of the pertinent configuration occupied by individual constituents, the latter two involve a relative displacement between either the constituents or the lamin\ae. The geometric interpretation corresponding to these damage mechanisms is also presented using tools from differential geometry. The derived damage contents can be used in developing an appropriate constitutive model for laminated composites undergoing damage.