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Single and multiple material constraints in thermoelasticity
Mehrdad Negahban
Department of Engineering Mechanics and The Center for Materials Research and Analysis University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA
Constraints on the possible forms of material response, such as incompressibility or inextensibility, have long been used to simplify constitutive response models, and have resulted in substantial progress in fields such as fluid mechanics and the mechanics of composite materials. A method of imposing these constraints for thermoelastic materials is considered that follows steps that remove the need for assuming an additive term resulting from the constraint. In the process, three methods are considered for the separation of the constitutively prescribed part of the response from the part that is in reaction to the constraints. Both the case of single and multiple constraints are considered with extensive examples including special considerations for including effects associated with isotropic or anisotropic thermal expansion.
Key Words: Thermoelastic • material constraint • internal constraint • geometric constraint • multiple constraints • thermodynamics • nonlinear elasticity • incompressibility • inextensibility • Bell constraint • isotropic constraints • anisotropic thermal expansion
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This version was published on December
1, 2007
Mathematics and Mechanics of Solids, Vol. 12, No. 6,
623-664 (2007)
DOI: 10.1177/1081286506067092
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