# A nonlinear couple stress-based sandwich beam theory

## TL;DR

This paper develops a nonlinear sandwich beam theory based on couple stress mechanics and Kármán kinematics, enabling accurate analysis of periodic sandwich structures with size effects and buckling predictions.

## Contribution

It introduces a novel nonlinear couple stress-based beam model for sandwich structures, incorporating micromechanical stiffness derivation and finite element implementation.

## Key findings

- Accurately predicts deflections, stresses, and buckling loads.
- Shows good agreement with detailed finite element models.
- Captures size effects in elastic sandwich beams.

## Abstract

A geometrically nonlinear sandwich beam model founded on the modified couple stress Timoshenko beam theory with K\'arm\'an kinematics is derived and employed in the analysis of periodic sandwich structures. The constitutive model is based on the mechanical behavior of sandwich beams, with the bending response split into membrane-induced and local bending modes. A micromechanical approach based on the structural analysis of a unit cell is derived and utilized to obtain the stiffness properties of selected prismatic cores. The model is shown to be equivalent to the classical thick-face sandwich theory for the same basic assumptions. A two-node finite element interpolated with linear and cubic shape functions is proposed and its stiffness and geometric stiffness matrices are derived. Three examples illustrate the model capabilities in predicting deflections, stresses and critical buckling loads of elastic sandwich beams including elastic size effects. Good agreement is obtained throughout in comparisons with more involved finite element models.