Growth induced instabilities in a circular hyperelastic plate

TL;DR

This paper investigates how growth causes mechanical instabilities in a circular hyperelastic plate, deriving governing equations and analyzing buckling behavior under different growth conditions relevant to soft tissues.

Contribution

It derives two-dimensional plate equations for growth-induced instability and analyzes buckling modes under radial and combined growth, advancing understanding of soft tissue deformation.

Findings

Growth affects buckling modes and critical growth factors.

Radial and combined growth lead to different instability patterns.

Results applicable to modeling soft tissue deformation.

Abstract

In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational approach. The derived plate equations are solved using the compound matrix method for two cases of axisymmetric growth conditions - purely radial, and combined radial and circumferential growth. The effect of growth on the buckling behaviour of the plate (in particular, the critical growth factor and the associated buckling mode shapes) is investigated for different thickness values. These results are applicable to model growth induced deformation in planar soft tissues such as skin.