Virtual configurations and constitutive equations for residually stressed bodies with material symmetry
The paper employs the concept of a virtual configuration introduced earlier by \textit{B. E. Johnson} and by the author [\textit{A. Hoger}, J. Elasticity 42, No. 2, 115-132 1996; Zbl 0868.73020)] to construct the general forms of constitutive equations for residually stressed hyperelastic bodies possessing specified symmetry. The mechanical behaviour of a residually stressed body needs a constitutive model that explicitly includes the influence of the residual stress on deformations. Constitutive equations are derived for the cases of transversely isotropic and orthotropic symmetries and these are motivated by the description of biological tissues like the heart. The method used for the derivation can also be employed for materials with any symmetry for which an integrity basis is known. The constitutive equation for the underlying unstressed material is presumed to be known, and the response function to the set of positive definite symmetric tensors is presumed to be locally invertible. The emerging constitutive models are expressed as functions of the residual stress and the deformation gradient of the residually stressed configuration. The material parameters in the constitutive equation are those of the underlying stress-free material only.
scientific article; zbMATH DE number 1176755