Controllable states of elastic dielectrics

Controllable states in thermoelasticity

“…In fact they have solved the problem completely for the special case when the response functions are independent of the temperature. However, not all the solutions given by these authors [2] are controllable when the response functions are allowed to depend upon the temperature. In this note we will obtain all controllable states with prescribed heat flux for temperature-dependent response functions.…”

“…While Ericksen's problem lay dormant for more than a decade, there has, of late, been renewed interest in the problem but mainly in the context of elastic dielectrics [2] and thermoelasticity [3], [4], [5]. An important by-product of the work of Singh and Pipkin [2] was the discovery [6] of a further family of deformations of elastic bodies not included in Ericksen's [1] list. This family generalized a family of solutions found by Klingbeil and Shield [7].…”

“…The statement is incorrect. An examination of the constitutive equations used by these authors shows that the results in [2] apply immediately to thermoelasticity only in the circumstance that the response functions be independent of the temperature. In this note we obtain the complete list of controllable states with prescribed heat flux for incompressible isotropic thermo elastic bodies with temperaturedependent response functions.…”

“…We say that such a pair (B, h) gives rise to a controllable state with prescribed heat flux. Singh and Pipkin [2] have gone far toward solving this problem. In fact they have solved the problem completely for the special case when the response functions are independent of the temperature.…”

“…In this note we will obtain all controllable states with prescribed heat flux for temperature-dependent response functions. We will solve the problem by listing the results of Singh and Pipkin [2] for temperature-independent response functions and showing how these results are modified when the response functions are allowed to depend upon the temperature. While the approach may not be the most elegant possible, it appears to have the attribute that it is the quickest way of solving the problem.…”