Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Freed, Alan, and Diethelm, Kai. "Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue." Fractional Calculus and Applied Analysis 10.3 (2007): 219-248. <http://eudml.org/doc/11328>.

@article{Freed2007,
abstract = {Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress- strain behavior of soft biological tissues is extended into a viscoelastic material model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a three-dimensional constitutive model that is suitable for general analysis. The model is derived in a configuration that differs from the current, or spatial, configuration by a rigid-body rotation; it being the polar configuration. Mappings for the fractional-order operators of integration and differentiation between the polar and spatial configurations are presented as a theorem. These mappings are used in the construction of the proposed viscoelastic model.},
author = {Freed, Alan, Diethelm, Kai},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 74B20; 74D10; 74L15},
language = {eng},
number = {3},
pages = {219-248},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue},
url = {http://eudml.org/doc/11328},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Freed, Alan
AU - Diethelm, Kai
TI - Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 3
SP - 219
EP - 248
AB - Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress- strain behavior of soft biological tissues is extended into a viscoelastic material model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a three-dimensional constitutive model that is suitable for general analysis. The model is derived in a configuration that differs from the current, or spatial, configuration by a rigid-body rotation; it being the polar configuration. Mappings for the fractional-order operators of integration and differentiation between the polar and spatial configurations are presented as a theorem. These mappings are used in the construction of the proposed viscoelastic model.
LA - eng
KW - 26A33; 74B20; 74D10; 74L15
UR - http://eudml.org/doc/11328
ER -