Nonlinear phenomenological models of the deformation of fibrous composite materials

Structure of nonlinear elastic relationships for the highly anisotropic layer of a nonthin shell

“…The physical relations for granular and fibrous CM with an elastic reinforcement and nonlinearly elastic matrix (the nonlinearity was assumed to be a square function of the components of the strain tensor) were obtained in [8,9] by averaging methods. Composites whose reinforcing components were also nonlinearly elastic were considered, in particular, in [10].The phenomenological approach is rarely applied to the problem of establishing the relation between the static and kinematic characteristics of CM (see, for example, [4, 11,12]). One of the most widely used ways for specifying the law of nonlinearly elastic deformation is expansion of the elastic potential in a tensorial series [11].…”