Elastic bounds for anisotropic layers

TL;DR

This paper derives comprehensive bounds for the elastic constants of anisotropic layers, plates, and laminates, applicable generally and useful for design feasibility and testing validation in elasticity.

Contribution

It introduces transformed bounds for elastic constants of anisotropic materials, extending classical elasticity knowledge to two-dimensional cases.

Findings

Bounds are valid for completely anisotropic bodies.

Bounds assist in determining feasible design domains.

Bounds serve as conditions for laboratory test validation.

Abstract

The complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously found. These bounds complete the knowledge of classical elasticity at least in the two-dimensional case and are useful in several situations, e.g., for determining the correct feasibility domain in design problems or as necessary conditions for accepting the results of laboratory tests on anisotropic layers.