Applications of implicit constitutive theory for describing the elastic response of rocks and concrete

An implicit constitutive relation is proposed for elastic bodies, when the gradient of the displacement is assumed to be very small, and as a result the strains are small. The resulting constitutive relation is a non-linear relationship between the linearized strain and the stress. The model is used to fit data for rock and concrete. Some boundary value problems are studied within the context of homogeneous deformations, and also a problem with inhomogeneous deformations is analyzed, namely the inflation of a circular annulus. The predictions of this new implicit constitutive relation are compared with the predictions of the constitutive equations for linearized elastic bodies.

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The work of R. Bustamante was financed by the grant No. 1210002 provided by Fondecyt (Chile). The work of K.R. Rajagopal has been supported by the National Science Foundation and the Office of Naval Research. Both authors thank Professor Z. Grasley for providing the experimental data used in this work for the modelling of concrete.