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Journal of Elasticity manuscript No. (will be inserted by the editor)

Summary: Journal of Elasticity manuscript No.
(will be inserted by the editor)
Active stress vs. active strain in mechanobiology: constitutive
D. Ambrosi ˇ S. Pezzuto
May 30, 2011
Abstract Many biological tissues exhibit a non­standard continuum mechanics behavior:
they are able to modify their placement in absence of external loads. The activity of the
muscles is usually represented in solid mechanics in terms of an active stress, to be added
to the standard one. A less popular approach is to introduce a multiplicative decomposition
of the tensor gradient of deformation in two factors: the passive and the active one. Both
approaches should satisfy due mathematical properties, namely frame indifference and el-
lipticity of the total stress. At the same time, the constitutive laws should reproduce the ob-
served physiological behavior of the specific living tissue. In this paper we focus on cardiac
contractility. We review some constitutive examples of active stress and active strain taken
from the literature and we discuss them in terms of precise mathematical and physiological
properties. These arguments naturally suggest new possible models.
Keywords Active stress ˇ Active strain ˇ Rank­one convexity ˇ Cardiac mechanics ˇ
Frank­Starling law
Mathematics Subject Classification (2010) 74L15 ˇ 74B20 ˇ 74E10 ˇ 74F25


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


Collections: Mathematics