Elastic-brittle reinforcement of flexural structures

TL;DR

This paper presents a variational framework to analyze the mechanical effects of flexural stiffening in 2D plates reinforced with elastic-brittle or elastic-plastic materials, including explicit equations for 1D beams.

Contribution

It introduces a novel variational description of reinforcement effects, encompassing elastic, brittle, and plastic behaviors, with explicit equations for beams.

Findings

Derivation of Euler equations for reinforced plates and beams.

Compliance identity for reinforcement behavior.

Framework applicable to elastic-brittle and elastic-plastic reinforcements.

Abstract

This note provides a variational description of the mechanical effects of flexural stiffening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforcement is assumed to be linear elastic outside possible free plastic yield lines or free crack. Explicit Euler equations and a compliance identity are shown for the reinforcement of a 1D beam.