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The insight of mixtures theory for growth and remodeling MOX-Dipartimento di Matematica, Politecnico di Milano
 

Summary: The insight of mixtures theory for growth and remodeling
D. Ambrosi
MOX-Dipartimento di Matematica, Politecnico di Milano
piazza Leonardo da Vinci, 32, 20133 Italy
L. Preziosi and G. Vitale
Dipartimento di Matematica, Politecnico di Torino
corso Duca degli Abruzzi, 24, 10123 Italy
October 20, 2009
Abstract
The emergence of residual stress as due to growth and remodeling of soft biological
tissues is considered in the framework of the mixture theory. The focus is on mixtures
composed by one elastic solid component and several fluid ones. It is shown that the stan-
dard theory is unable to predict residual stresses unless enriched by a suitable descriptor
of growth. Both the introduction of a dependence of the free energy on the density of
the solid component and the Kroner­Lee multiplicative decomposition of the gradient of
deformation are effective in this respect, with different levels of generality. When adopting
a multiplicative decomposition of the tensor gradient of deformation, thermodynamical
arguments suggest constitutive laws for the evolution of the growth tensor that point out
the role of the concentration of fluid species in driving the emergence of residual stress
thanks to inhomogeneous growth.

  

Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino
Preziosi, Luigi - Dipartimento di Matematica, Politecnico di Torino

 

Collections: Mathematics