An Equivalent Volume Law for Anisotropic Laminated Structures

Abstract

The problem of representing laminated structures by an equivalent volume and determining the elastic constants of this equivalent volume from the layer properties is a fundamental issue in the analysis of composite and multilayered systems. In the literature, the most widely used approach for this purpose is the Voigt-type volume-weighted averaging method. Although this method is widely accepted in practice, the uniqueness (as a material characteristic) of the equivalent elastic constants, their independence from the applied loading, and the mathematical conditions under which they can be defined have not been made explicit. This issue is particularly unclear for structures with asymmetric stacking sequences and general anisotropic behavior, including triclinic cases. In this study, a theoretical framework referred to as the Zor model is presented, and it is shown that the elastic constants of the equivalent volume can be obtained only under the action of all in-plane force components (Fx + Fy + Fxy), directly from static equilibrium, linear elasticity, and perfect bonding conditions between the layers. No additional assumptions are introduced in the formulation; reciprocity is not assumed at the system level, but instead emerges naturally as a result of the solution process. The resulting equivalent elastic constants are independent of the applied loading and represent the intrinsic mechanical characteristics of the laminated structure.