Elastic bounds of the coupling tensor of anisotropic composite laminates: a polar approach

TL;DR

This paper establishes bounds on the coupling tensor of anisotropic composite laminates using a polar invariants approach, revealing conditions for its components based on relations with in- and out-of-plane tensors.

Contribution

It introduces a polar invariants method to determine bounds for the coupling tensor in anisotropic laminates, linking it to in- and out-of-plane behavior tensors.

Findings

Derived bounds for the coupling tensor invariants.

Established relations between A, B, and D tensors.

Identified special cases relevant for applications.

Abstract

In the equivalent single layer theories of anisotropic laminates, the coupling tensor B describes the relation between the in- and out-of plane behavior of the plate. This tensor has some peculiar characteristics and in particular it is not defined, so it is normally considered as an unbounded tensor. We show in this paper a way to determine some relations between the polar invariants of B and those of the tensors describing the in- and out-of- plane behaviors of the laminate, A and D respectively. These relations constitute a set of bounds for the invariants of all the tensors of the laminate, A,B and D. It is hence shown that also the components of B must satisfy some conditions. Some peculiar cases, interesting for applications, are also considered.