A unified theoretical structure for modeling interstitial growth and muscle activation in soft tissues

An Eulerian formulation of inelasticity: from metal plasticity to growth of biological tissues

“…Rubin et al [37] developed a unified theoretical structure for modelling interstitial growth and muscle activation in soft tissues. Safadi & Rubin [38] used this theory to study significant differences in the mechanical modelling of confined growth predicted by Lagrangian and Eulerian formulations and Safadi & Rubin [39] used the theory to analyse stresses in arteries.…”

“…In contrast with inert materials like metals, biological tissues are living materials that have mass and energy supplies to allow them to grow and be active. The model developed in [37] where r m is the rate of mass supply per unit mass. This model uses only a single velocity field, it ignores details of relative motion of fluids and the solid matrix and it assumes that the tissue is highly vascularized so that mass can be supplied at any point inside the tissue.…”

“…Kuhl [35] discussed volumetric, fibre and area elastic measures for growth of tissues which were reconsidered in [37] within the context of the Eulerian formulation of growth. The elastic dilatation J e includes volumetric growth.…”

“…In contrast with inert materials like metals, biological tissues are living materials that have mass and energy supplies to allow them to grow and be active. The model developed in [37] considers the material as an open system with a rate of mass supply. In this model, the balance of mass is given byρ…”

“…The elastic dilatation J e includes volumetric growth. In [37], the elastic stretch λ es of a material fibre currently in the unit s direction and the elastic area growth λ en of the material surface currently normal to the unit vector n were defined by with s 1 being the current direction of a material fibre, s 3 being the current unit normal to a material surface and s 2 completing the triad of vectors. Specifically, Safadi & Rubin [40] introduced the elastic distortional strains…”