Aerospace Engineering and Mechanics

**The complex behavior of shape memory alloys (e.g. NiTi or AgCd) has
attracted a lot of attention over the past two decades, partially due to the
applicability of these alloys in active structures. When subjected to applied
mechanical loading, these materials undergo a martensitic phase transformation
from a high-strain parent phase, called austenite, to a low-strain martensite
phase. The solid-solid martensitic phase transition is characterized by a
lattice deformation that occurs through the correlated migration of phase
boundaries. The energy dissipation associated with the motion of phase
boundaries leads to a hysteretic behavior called pseudoelasticity. The
dynamics of phase boundaries plays an important role in the origin and size of
pseudoelastic hysteresis.**

**Following the pioneering work of Ericksen [1975], it has become common to
use a non-monotone, up-down-up stress-strain relation to model the materials
undergoing solid-solid phase transitions. The corresponding dynamic
initial-value problem possesses a family of solutions and thus is
ill-posed (James [1980]). One way to regularize the problem in the
dynamic setting is to postulate an additional kinetic relation that
expresses the jump in entropy across a phase boundary, called a driving
force, as a function of the interface velocity and temperature
(Truskinovsky [1987], Abeyaratne and Knowles [1993]). Such a relation and an
additional nucleation criterion are sufficient to obtain a unique solution of
the dynamic problem. **

**In this talk I will discuss the derivation of an explicit formula for a
kinetic relation governing the motion of a phase boundary in a bilinear
thermoelastic material. The relation was obtained by studying traveling wave
solutions of a regularized problem that includes viscosity, heat conduction and
convection. Both inertia and latent heat of transformation are taken into
account. By investigating the effect of material parameters on the kinetic
relation, one can calculate the range of parameters for which the relation
becomes non-monotone, in agreement with recent numerical and asymptotic
calculations (Ngan and Truskinovsky [1999], Turteltaub [1997]). The
non-monotone kinetic relations lead to an irregular propagation of phase
boundaries, as shown in the work of Rosakis and Knowles [1998] where such
non-monotonicity was postulated. The model predicts a nonzero resistance to
phase boundary motion and captures local self-heating, in qualitative agreement
with recent experiments on shape-memory-alloy wires (Leo, Shield and Bruno
[1993], Shaw and Kyriakides [1995]). If time permits, I will also discuss the
recent numerical simulations of phase transitions in a finite thermoelastic bar
undergoing time-dependent displacement-controlled loading.**

209 Akerman Hall

2:30-3:30 p.m.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior Secretary, 625-8000.