Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter.

Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable.

Investigation of the optimal collagen fibre orientation in human iliac arteries.

The distribution of collagen fibres plays a significant role in the mechanical behaviour of artery walls. Experimental data show that in most artery wall layers there are two (or more) in-plane symmetrically disposed families of fibres. However, a recent investigation revealed that some artery wall layers have only one preferred fibre direction, notably in the medial layer of human common iliac arteries.

On the third- and fourth-order constants of incompressible isotropic elasticity.

Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress-strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value.

Third- and fourth-order elasticities of biological soft tissues.

In the theory of weakly nonlinear elasticity, Hamilton et al. [J. Acoust.