Elastic incompressibility in growing materials - a constraint that does work

•Elastically incompressible growing materials experience dilation.•The constraint response of elastic incompressibility does work.•A method Lagrange multipliers is proposed to model this constraint. The constraint of elastic incompressibility in a hyperelastic non-porous solid enforces isochoric tot...

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Bibliographic Details
Published in:Mechanics research communications 2018-10, Vol.93, p.138-140
Main Authors: Rubin, M.B., Safadi, M.M.
Format: Article
Language:English
Subjects:
Biological tissue
Constraints
Elastic incompressibility
Growth
Homeostasis
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Summary:•Elastically incompressible growing materials experience dilation.•The constraint response of elastic incompressibility does work.•A method Lagrange multipliers is proposed to model this constraint. The constraint of elastic incompressibility in a hyperelastic non-porous solid enforces isochoric total deformation with the constraint response being workless. In contrast, elastic incompressibility of a growing biological tissue allows for total volume change with the constraint response doing work. This paper shows that the method of Lagrange multipliers can be used to determine the constraint response in an elastically incompressible growing material.
ISSN:0093-6413
1873-3972
DOI:10.1016/j.mechrescom.2018.01.002