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Modeling Gum Metal and other newly developed titanium alloys within a new class of constitutive relations for elastic bodies

Kulvait V., Málek J., Rajagopal K. R.

Archives of Mechanics

2017

Vol. 69, nr 3

223--241

Many titanium alloys and even materials such as concrete exhibit a nonlinear relationship between strain and stress, when the strain is small enough that the square of the norm of the displacement gradient can be ignored in comparison to the norm of the displacement gradient. Such response cannot be described within the classical theory of Cauchy elasticity wherein a linearization of the nonlinear strain leads to the classical linearized elastic response. A new framework for elasticity has been put into place in which one can justify rigorously a nonlinear relationship between the linearized strain and stress. Here, we consider one such model based on a power-law relationship. Previous attempts at describing such response have been either limited to the response of one particular material, e.g. Gum Metal, or involved a model with more material moduli, than the model considered in this work. For the uniaxial response of several metallic alloys, the model that is being considered fits experimental data exceedingly well.

Stress concentration due to an elliptic hole in a degrading linearized elastic solid

Kulvait V., Malek J., Rajagopal K. R.

International Journal of Applied Mechanics and Engineering

2010

Vol. 15, no 1

35-49

A computational analysis is carried out of boundary-value problems associated with a planar generalized linearized elastic solid body with an elliptic hole in it, with a fluid diffusing through the solid. This diffusion of fluid can either enhance or degrade the load carrying capacity of the body, based on how the material moduli of the solid depend on the concentration of the fluid, that is whether the presence of the fluid degrades or strengthens the material. We investigate the nature of the solution when the aspect ratio tends to zero, a problem relevant to the stress singularity at crack tips.