Accession Number : ADA132807

Title :   One-Dimensional Structured Phase Transformations under Prescribed Loads.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Carr,Jack ; Gurtin,Morton E ; Slemrod,Marshall

PDF Url : ADA132807

Report Date : Aug 1983

Pagination or Media Count : 20

Abstract : The authors consider a one-dimensional elastic bar acted on by end loads. To allow for the possibility of phase transitions they consider a stored-energy function of the form W(gamma) + epsilon sub 2(gamma')sub 2 with W(gamma) a nonconvex function of strain gamma, a function of the type capable of supporting two-phases. The term involving the strain gradient gamma, is added to model the region of rapidly varying strain in the vicinity of a phase transition. It is shown that this problem has smooth solutions which, for epsilon small, correspond to the single-phase and two-phase solutions of the problem with epsilon = O. It is shown further that the only stable solutions of this problem are the single-phase solutions gamma = constant. (Author)

Descriptors :   *Phase transformations, *Transformations(Mathematics), *Stress strain relations, One dimensional, Gradients, Elastic properties, Loads(Forces), Energy storage, Functions(Mathematics), Stability, Problem solving, Solutions(General)

Subject Categories : Numerical Mathematics
      Solid State Physics

Distribution Statement : APPROVED FOR PUBLIC RELEASE