An Equivalent Volume Law for Anisotropic Laminated Structures

TL;DR

This paper introduces a theoretical framework called the Zor model for deriving intrinsic equivalent elastic constants of anisotropic laminated structures, clarifying conditions for their uniqueness and independence from loading.

Contribution

The Zor model provides a rigorous method to determine equivalent elastic constants solely from static equilibrium and layer properties, without additional assumptions.

Findings

Equivalent elastic constants are obtained only under all in-plane force components.

The model shows these constants are independent of applied loading.

Reciprocity naturally emerges from the solution process.

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.