Expansion and collapse of spherically symmetric isotropic elastic bodies surrounded by vacuum

TL;DR

This paper investigates the dynamic behavior of spherically symmetric elastic bodies in vacuum, showing conditions under which they can either expand infinitely or collapse in finite time based on residual pressure.

Contribution

It introduces a class of isotropic, scale-invariant strain energy functions that model the expansion or collapse of elastic bodies with vacuum surroundings.

Findings

Bodies can expand infinitely or collapse in finite time.

The model accounts for internal elastic stress without boundary forces.

Residual pressure determines the expansion or collapse behavior.

Abstract

A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time, depending on the sign of the residual pressure. The body is surrounded by vacuum so that the boundary surface forces vanish, while the density remains strictly positive. The body is subject only to internal elastic stress.