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Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems

Irena Pawłow, Antoni Żochowski (2003)

Banach Center Publications

A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.

Existence of a solution for a nonlinearly elastic plane membrane “under tension”

Daniel Coutand (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A justification of the two-dimensional nonlinear “membrane” equations for a plate made of a Saint Venant-Kirchhoff material has been given by Fox et al. [9] by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of ℝ 3 , is equivalent to finding the critical points...

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