The mechanics of soft solids

Jan 1, 0001

Our research focuses primarily on the study of elastic solids and the development of constitutive equations that describe the various components of these materials and their impact on forces and deformations. My work primarily centres on two main themes: stressed solids and fibre-reinforced solids.

In addition to constitutive equations, we also explore the use of waves and instabilities to characterise elastic solids and understand the origin of patterns in soft tissues.

Initially stressed solids

The driving question is how to mathematically describe the mechanical response of residually stressed solids? Our main contribution has been revealing a new symmetry, a result from conservation of energy, that restricts the possible mechanical responses.

This is what happens when you cut a residually stressed elastic rubber ball. The movement is powered by the release of the residual stress.
The arrows indicate the direction of the residual stress of a thick tube. The material is in equilibrium.

instability patterns

Most biological materials (and industrial) are reinforced with stiff fibres or are under tension. I figure out how these mechanisms influence elastic surface waves and the formation of surface wrinkles. The main reasons to do this are

  • will give us greater control over surface waves or forming textured surfaces (using surface wrinkles).
  • use these surface waves and surface wrinkles to measure biological materials.
solid-mechanics elasticity initial-stress
Avatar
Artur L Gower
Lecturer in Dynamics

Art Gower is a lecturer at the University of Sheffield and part of the Dynamics group. He uses maths to understand waves (sound and light) in materials. Sometimes computers show him that his maths is wrong.

Related

Publications

Representing the stress and strain energy of elastic solids with initial stress and transverse texture anisotropy

Real-world solids, such as rocks, soft tissues and engineering materials, are often under some form of stress. Most real materials are …
Project Paper Journal

The constitutive relations of initially stressed incompressible Mooney-Rivlin materials

Initial stresses originate in soft materials by the occurrence of misfits in the undeformed microstructure. Since the reference …
Project Paper Journal

A new restriction for initially stressed elastic solids

We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The …
Preprint Project Paper Journal

Oblique Wrinkles

We prove theoretically that when a soft solid is subjected to an extreme deformation, wrinkles can form on its surface at an angle that …
Project Slides Paper Journal

Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition

Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider …
Project Paper Journal

On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter

Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting …
Project Paper Journal

Initial stress symmetry and its applications in elasticity

An initial stress within a solid can arise to support external loads or from processes such as thermal expansion in inert matter or …
Preprint Project Paper Journal

Connecting the material parameters of soft fibre-reinforced solids with the formation of surface wrinkles

There is a need for more complete models of fibre-reinforced solids that use two anisotropic invariants. However, these models present …
PDF Project Slides Paper

Shear instability in skin tissue

We propose two toy-models to describe, predict and interpret the wrinkles appearing on the surface of skin when it is sheared. With the …
PDF Project Paper