Modeling of Residually Stressed Materials

Abstract eng:
Stresses that are present in a material body in the absence of any applied loads (either body forces or surface tractions) are referred to as residual stresses. To effectively model the elastic response, relative to a residually stressed configuration, the residual stresses need to be incorporated into the constitutive equations. In this talk we provide an overview of the basic equations required to present a general elastic, invariant-based anisotropic constitutive formulation that includes residual stress. We summarize a three-dimensional incremental formulation appropriate for the implementation of the theory in a nonlinear finite element code. For numerical purposes the general constitutive formulation is specialized to a simple prototype model and a simple representation of the residual stress distribution is adopted. As well as possessing anisotropy associated with residual stresses in its unloaded (reference) configuration, the considered material has anisotropy corresponding to two preferred directions that are identified with the orientations of two families of fibers. To validate the theory and its implementation the wall stress distribution in an abdominal aortic aneurysm (AAA) using patient specific geometry and material model parameters is evaluated. The method presented in this talk is general and can be used, by specifying appropriate energy functions, to investigate other residually stressed biological systems.

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