Investigations of Non-elliptic Elastic Materials and the Modeling of Dissipative Behavior in Solids
CALIFORNIA INST OF TECH PASADENA
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Our efforts have been directed primarily at the study of non-elliptic elasticthermoelastic materials. Such materials are capable of sustaining equilibrium deformations with discontinuous deformation gradients, and because of this, they provide a natural setting for the modeling within continuum theory of certain kinds of phase transformations in solids. Examples include martensitic phase transformations of the kind occurring in shape-memory alloys. In particular, non-elliptic elastic materials are appropriate for the description of isothermal processes such as quasi-static motions involving slowly moving surfaces of strain discontinuity. Such motions are dissipative in the sense that, for any portion of the body, the rate of work of the external forces differs from the rate of storage of strain energy. This energy imbalance allows one to introduce the notion of a driving traction - or Eshelby force - acting on the moving surface of discontinuity, i.e. phase boundary. This in turn permits one to model the kinetics and nucleation of phase boundaries as the body evolves quasi-statically through metastable states.