Book Section records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:48:14 +0000Localized Shear Near The Tip of a Crack in Finite Elastostatics
https://resolver.caltech.edu/CaltechAUTHORS:20141104-102743649
Authors: {'items': [{'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'James K.'}}]}
Year: 1982
DOI: 10.1007/978-94-009-7538-5_16
This paper describes some recent results concerning crack problems in finite anti-plane shear for a class of incompressible elastic materials for which the associated equilibrium equations lose ellipticity at sufficiently severe deformations. The principal feature of the elastic fields arising in these problems is the presence near a crack-tip of curves bearing discontinuities in displacement gradient and stress.https://authors.library.caltech.edu/records/dda46-z0y66Remarks on a Question of Ericksen Concerning Elastostatic Fields of Saint-Venant Type
https://resolver.caltech.edu/CaltechAUTHORS:20141117-134940318
Authors: {'items': [{'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'James K.'}}]}
Year: 1986
DOI: 10.1007/978-3-642-61634-1_35
In an effort to understand better the relationship between approximate theories —such as those for thin rods—and the three-dimensional theory of elasticity, Ericksen [1]–[3] has recently suggested a reconsideration of Saint-Venant's problem for elastic cylinders with traction-free lateral surfaces. Among the various questions raised in [1]–[3], one concerns the structure and role of the set of all possible elastostatic fields in an infinitely long cylinder in the absence of lateral loading and body force, but in the presence of a restriction on the size of a suitable cross-sectional norm of the associated strain tensor field.https://authors.library.caltech.edu/records/pmz40-frp75Continuum Modeling of Phase Transitions in Solids
https://resolver.caltech.edu/CaltechAUTHORS:20141024-135721760
Authors: {'items': [{'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'James K.'}}]}
Year: 1991
DOI: 10.1007/978-94-011-3644-0_116
In this paper, we describe a simple phenomenological thermoelastic model for stress-induced solid-solid phase transitions in a tensile bar. In this model, the bar is treated as a one-dimensional continuum, and the phase transition is assumed to take place quasi-statically and isothermally at a temperature θ. By accounting for temperature effects solely in the kinetics of the phase transition, we show that some of the qualitative features of the experimental observations in [1] can be predicted, even though the effects of temperature on the nucleation of the transition and on the stress-strain relation have been neglected. A purely mechanical counterpart of the theory described here has been given in [2]; the latter work, as well as a mechanical theory of fast phase transitions in solids, is reviewed in [3].https://authors.library.caltech.edu/records/zgyaz-pck27Nucleation, kinetics and admissibility criteria for propagating phase boundaries
https://resolver.caltech.edu/CaltechAUTHORS:20141029-093045003
Authors: {'items': [{'id': 'Abeyaratne-R', 'name': {'family': 'Abeyaratne', 'given': 'Rohan'}}, {'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'James K.'}}]}
Year: 1993
DOI: 10.1007/978-1-4613-8348-2_1
This paper reviews our recent studies on the nucleation and kinetics of propagating phase boundaries in an elastic bar and relates them to various admissibility criteria. First, we discuss how the field equations and jump conditions of the quasi-static theory of such a bar must be supplemented with additional constitutive information pertaining to the initiation and evolution of phase boundaries. The kinetic relation relates the driving traction f at a phase boundary to the phase boundary velocity ṡ; thus f = φ (ṡ), where φ is a materially-determined function. The nucleation criterion specifies a critical value of f at an incipient phase boundary. We then incorporate inertial effects, and we find in the context of the Riemann problem that, as long as phase boundary velocities are subsonic, the theory again needs — and has room for — a nucleation criterion and a kinetic relation. Finally, we describe the sense in which each of three widely studied admissibility criteria for phase boundaries is equivalent to a specific kinetic relation of the form f = φ (ṡ) for a particular choice of φ A kinetic relation based on thermal activation theory is also discussed.https://authors.library.caltech.edu/records/xj1yd-k1n84Dynamical behaviour of thermoelastic solids undergoing phase transitions
https://resolver.caltech.edu/CaltechAUTHORS:20141024-090731706
Authors: {'items': [{'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'J. K.'}}]}
Year: 1996
DOI: 10.4028/www.scientific.net/KEM.118-119.109
This paper summarizes some recent work carried out jointly by the author and R. Abeyaratne of
MIT on the continuum modeling of the macroscopic effect of stress-induced phase transitions in
thermoelastic solids. Attention is focussed on one-dimensional tensile bars composed of
two-phase thermoelastic materials, and emphasis is placed on the manner in which the notions of
kinetics and nucleation are imported into continuum mechanics from materials science. Although
the response to dynamic loading is the principal objective, the predictive capability of the model
with respect to quasi-static experiments involving shape-memory alloys is also discussed. In the
case of dynamic loading, the potential relevance of this model for the interpretation of flyer-plate
impact experiments in ceramics and in shape-memory single crystals is described.https://authors.library.caltech.edu/records/x69d2-m4s85Nonlinear Waves in Thermoelastic Solids Undergoing Phase Transitions
https://resolver.caltech.edu/CaltechAUTHORS:20141029-083903820
Authors: {'items': [{'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'James K.'}}]}
Year: 2001
DOI: 10.1142/9789812811950_0012
This paper is concerned with continuum modeling of the macroscopic
dynamical response of one-dimensional thermoelastic bars undergoing
phase transitions. The specific model considered involves a particular
"two-well" Helmholtz free energy potential governing the bulk response of
the material as well as a nucleation criterion and kinetic relation controlling
the initiation and evolution of the phase transition. Inertia is taken into
account, and the discussion is based on an adiabatic theory. In contrast to
models in which the free energy involves only a single well, the entropy
inequality at propagating strain discontinuities is not sufficient to assure the
uniqueness of solutions to the boundary-initial value problems of interest:
kinetics and nucleation must be imposed as well.https://authors.library.caltech.edu/records/0yjqs-rwq63