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

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 3, page 219-248
- ISSN: 1311-0454

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topFreed, 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 -

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