Dynamic growth of martensitic plates in an elastic material

Abstract

Al~raet The growth of martensitic plates under conditions of anti-plane shear is considered for a particular isotropic hypcrelastic material. An asymptotic solution is prc~nted for the displacement field near the tip of a plate growing at an arbitrary velocity up to the shear wave speed of the ansteuite. An energy balance shows that the rate of energy dissipation is essentially the same as for the quasi-static motion of a normal equilibrium shock. Numerical solutions illustrate how the martensitic plates develop in an initial boundary value problem.

Computational Methods for Propagating Phase Boundaries

“…Silling used a dynamical relaxation techdeveloping computational methods is therefore an im-nique to model quasi-static phase transformation processes portant task. and the dynamic growth of martensitic plates [59,60]. We Numerical methods developed in the last 10 years for also refer to the works by Collins and Luskin [17] and classical shock waves in CFD cannot be applied directly to Nicolaides and Walkington [50].…”

On the dissipation due to wave ringing in nonelliptic elastic materials

“…Phase boundary motion is permissible in this setting and the underposedness problem remains (James 1980;Shearer 1982Shearer , i986, 1988Truskinovsky 1982Truskinovsky , 1987Truskinovsky , 1990Slemrod 1983Slemrod , 1989Hattori 1986;Pence 1986Pence , 1987Pence , 1991aPence , b, 1992Abeyaratne and Knowles 1991a, b;Fan and Slemrod 1991;Silling 1992). In fact if one considers a body at rest in equilibrium which is then dynamically disturbed, there are now two potential sources of nonuniqueness: (i) nonuniqueness in initial conditions since many equilibrium configurations may be compatible with the boundary conditions that hold at t = 0, and (ii) nonuniqueness due to the fact that the dynamical motion from afixed set of initial conditions may also admit multiple solutions for t > 0.…”

Stability of a two-phase process in an elastic solid

“…Except for the work of Silling [24], the bulk of the continuum mechanical investigations which consider dynamical processes are confined to one-dimensional bar theory and, hence, are not of direct bearing on the issue of phase boundary morphology. Silling [24] has demonstrated, through an asymptotic analysis, that a particular ~leneralized neo-Hookean material is capable of sustaining a motion which involves a steadily propagating cusped surface of discontinuity which segregates distinct elliptic phases of the relevant material. This cusped phase boundary can be thought of as a model for one which would accompany a single plate-like structure in an actual displacive solid-solid phase transformation.…”

“…This cusped phase boundary can be thought of as a model for one which would accompany a single plate-like structure in an actual displacive solid-solid phase transformation. Silling [24] also performs numerical calculations which seem to support 1Langer [16] provides an overview of such phenomena. 2See, e.g., Abeyarantne and Knowles [1][2][3][4], James [12], Pence [20] and Silling [24].…”

“…Silling [24] also performs numerical calculations which seem to support 1Langer [16] provides an overview of such phenomena. 2See, e.g., Abeyarantne and Knowles [1][2][3][4], James [12], Pence [20] and Silling [24]. 3For a discussion of this issue consult, for instance, Rosakis [21].…”