Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics

Abstract

Some fundamental issues in the formulation of constitutive theories of material response based on the multiplicative decomposition of the deformation gradient are reviewed, with focus on finite deformation thermoelasticity, elastoplasticity, and biomechanics. The constitutive theory of isotropic thermoelasticity is first considered. The stress response and the entropy expression are derived in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. Basic kinematic and kinetic aspects of the phenomenological and single crystal elastoplasticity within the framework of the multiplicative decomposition are presented. Attention is given to additive decompositions of the stress and strain rates into their elastic and plastic parts. The constitutive analysis of the stress-modulated growth of pseudo-elastic soft tissues is then presented. The elastic and growth parts of the deformation gradient and the rate of deformation tensor are defined and used to construct the corresponding rate-type biomechanic theory. The structure of the evolution equation for growth-induced stretch ratio is discussed. There are 112 references cited in this review article.

Cell Migration with Multiple Pseudopodia: Temporal and Spatial Sensing Models

“…As in previous works (Allena et al 2010;Balan and Tsakmakis 2002;Bonet 2001;Lubarda 2004;Muñoz et al 2007), the decomposition of the deformation gradient is employed to define both F s and F f as follows:…”

Covariance in plasticity

“…11 The differenceẏ − Fw is a velocity relative to w. The push-forward of w through F is motivated by the membership ofẏ and w to two different geometric environments. If we impose that P rel b (ẏ, w) be invariant under changes in observers in class 2 above, namely…”

On the Mechanical Interplay Between Intra- and Inter-Synchronization During Collective Cell Migration: A Numerical Investigation

“…The decomposition of the deformation gradient (Allena et al 2010;Lubarda 2004) is used to describe the solid deformation tensor F a,s which is then equal to…”

“…The cohort includes approximately hundred cells; − as in previous works (Borisy and Svitkina 2000;Carlier and Pantaloni 1997;Condeelis 1993;Mogilner and Rubinstein 2005;Theriot and Mitchison 1991), the oscillating protrusion-contraction movement of the motile cells is assumed to be controlled by the cyclic polymerization-depolymerization process of the actin network inside the cytoskeleton; − the decomposition of the deformation gradient (Allena et al 2010;Lubarda 2004) is employed to take into account the active elementary deformations undergone by the motile cells (i.e. protrusion and contraction) as well as the elastic deformations generated by the interaction of the cells with the ECM (Allena 2013;Allena and Aubry 2012); − large deformations of the motile cells are considered and the cells are able to form one pseudopod at a time at their leading edge (Allena and Aubry 2012); − inside each motile cell the intra-synchronization between the active strains and the adhesion forces to the ECM is described (Allena 2013; Allena and Aubry 2012); − finally, different modes of collective migration are investigated.…”