Exact solution for growth-induced large bending deformation of a hyperelastic plate

TL;DR

This paper derives an exact analytical solution for the large bending deformation of a hyperelastic plate caused by growth, providing insights into deformation features and serving as a benchmark for numerical methods.

Contribution

The paper presents the first exact solution for growth-induced bending in hyperelastic plates with linearly varying growth, enhancing understanding and validation of growth models.

Findings

Revealed key features of growth-induced bending deformation.

Analyzed effects of different growth parameters.

Provided a benchmark solution for numerical testing.

Abstract

In this paper, the growth-induced bending deformation of a thin hyperelastic plate is studied. For a plane-strain problem, the governing PDE system is formulated, which is composed of the mechanical equilibrium equations, the constraint equation and the boundary conditions. By adopting a gradient growth field with the growth value changes linearly along the thickness direction, the exact solution to the governing PDE system can be derived. With the obtained solution, some important features of the bending deformation in the plate can be found and the effects of the different growth parameters can be revealed. This exact solution can serve as a benchmark one for testing the correctness of numerical schemes and approximate plate models in growth theory.