# An Invariant-Based Constitutive Model for Composite Laminates

## TL;DR

This paper introduces a new constitutive model for composite laminates using stiffness invariants and a quasi-Poisson’s ratio to simplify and improve predictions of their behavior.

## Contribution

The novel quasi-Poisson’s ratio and invariant-based approach reduce material constants and improve modeling efficiency for symmetric, balanced laminates.

## Key findings

- The model shows good agreement with classical laminate theory for critical buckling loads.
- Classical theory consistently predicts more conservative results compared to the new model.
- The invariant-based model slightly overestimates stability margins due to idealizations.

## Abstract

Composite laminates possess complex anisotropic behavior, motivating the development of simplified yet accurate modeling approaches. In this paper, we present a study that introduces a stiffness-invariants-based constitutive model for symmetric, balanced composite laminates, highlighting a novel “quasi-Poisson’s ratio” parameter as a key innovation. The proposed method reconstructs the laminate stiffness matrices using invariant theory (trace of stiffness tensor) and a Master Ply concept, thereby reducing the number of independent material constants. The methods and assumptions (e.g., neglecting minor bending-twisting couplings) are outlined, and the model’s predictions of critical buckling loads are compared to classical laminate theory (CLT) results. Good agreement is observed in most cases, with a consistent conservative bias of CLT. The results confirm that the invariant-based model captures the dominant stiffness characteristics of the laminates and can slightly overestimate stability margins due to its idealizations. In conclusion, this work provides an efficient constitutive modeling framework that can be integrated with finite element analysis and extended to more general laminates in future studies.