James K. Knowles
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James K. Knowlesengineering Degrees
Engineering
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Mechanical Engineering
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James K. Knowlesmathematics Degrees
Mathematics
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Applied Mathematics
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Measure Theory
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Engineering Mathematics
James K. Knowles's Degrees
- PhD Applied Mathematics Stanford University
- Masters Mechanical Engineering Stanford University
Why Is James K. Knowles Influential?
(Suggest an Edit or Addition)James K. Knowles's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- On a class of conservation laws in linearized and finite elastostatics (1972) (606)
- Recent Developments Concerning Saint-Venant's Principle (1983) (426)
- On the driving traction acting on a surface of strain discontinuity in a continuum (1990) (397)
- Kinetic relations and the propagation of phase boundaries in solids (1991) (397)
- A continuum model of a thermoelastic solid capable of undergoing phase transitions (1993) (282)
- The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids (1977) (251)
- On the failure of ellipticity of the equations for finite elastostatic plane strain (1976) (219)
- On the ellipticity of the equations of nonlinear elastostatics for a special material (1975) (202)
- On Saint-Venant's principle in the two-dimensional linear theory of elasticity (1966) (194)
- On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics (1978) (182)
- Evolution of Phase Transitions: A Continuum Theory (2006) (175)
- Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids (1991) (155)
- Large deformations near a tip of an interface-crack between two Neo-Hookean sheets (1983) (154)
- On the Bending of an Elastic Plate Containing a Crack (1960) (149)
- An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack (1973) (148)
- Large amplitude oscillations of a tube of incompressible elastic material (1960) (124)
- A One-Dimensional Continuum Model for Shape-Memory Alloys (1994) (115)
- On the dissipation associated with equilibrium shocks in finite elasticity (1979) (114)
- On the dissipative response due to discontinuous strains in bars of unstable elastic material (1988) (106)
- On finite anti-plane shear for imcompressible elastic materials (1976) (101)
- Finite-deformation analysis of the elastostatic field near the tip of a crack: Reconsideration and higher-order results (1974) (94)
- On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics (1975) (85)
- On a Class of Oscillations in the Finite-Deformation Theory of Elasticity (1962) (81)
- Topics in finite elasticity (1981) (78)
- Finite dynamic deformations of an incompressible elastic medium containing a spherical cavity (1965) (75)
- A note on elastic surface waves (1966) (61)
- Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example (1980) (59)
- Dynamics of propagating phase boundaries: Thermoelastic solids with heat conduction (1994) (56)
- On the spatial decay of solutions of the heat equation (1971) (53)
- On the Propagation of Maximally Dissipative Phase Boundaries in Solids (1992) (52)
- A note on anti-plane shear for compressible materials in finite elastostatics (1977) (49)
- On the kinetics of an austenite → martensite phase transformation induced by impact in a CuAlNi shape-memory alloy (1997) (48)
- Dynamics of propagating phase boundaries: adiabatic theory for thermoelastic solids (1994) (45)
- Anti-plane shear fields with discontinuous deformation gradients near the tip of a crack in finite elastostatics (1981) (43)
- Nonlinear Elasticity: Strain-energy Functions with Multiple Local Minima: Modeling Phase Transformations Using Finite Thermo-elasticity (2001) (41)
- Nucleation, Kinetics and Admissibility Criteria for Propagating Phase Boundaries (1993) (41)
- On the exponential decay of stresses in circular elastic cylinders subject to axisymmetric self-equilibrated end loads☆ (1969) (39)
- Unstable kinetic relations and the dynamics of solid-solid phase transitions (1997) (38)
- Impact-Induced Tensile Waves in a Rubberlike Material (2002) (37)
- Minimum energy characterizations of Saint-Venant's solution to the relaxed Saint-Venant problem (1966) (36)
- The effect of nonlinearity on a principle of Saint-Venant type (1981) (36)
- On a shock-induced martensitic phase transition (2000) (36)
- AN ENERGY ESTIMATE FOR THE BIHARMONIC EQUATION AND ITS APPLICATION TO SAINT-VENANT'S PRINCIPLE IN PLANE ELASTOSTATICS (1983) (31)
- Uniqueness for plane crack problems in linear elastostatics (1973) (31)
- Stress-induced phase transitions in elastic solids (1999) (30)
- A nonlinear effect in mode II crack problems (1981) (30)
- On the Dynamic Response of a Beam to a Randomly Moving Load (1968) (29)
- A Saint-Venant principle for a class of second-order elliptic boundary value problems (1967) (28)
- Equilibrium shocks in plane deformations of incompressible elastic materials (1989) (27)
- A class of compressible elastic materials capable of sustaining finite anti-plane shear (1991) (27)
- Non-elliptic elastic materials and the modeling of elastic-plastic behavior for finite deformation (1987) (27)
- Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: an example (1987) (26)
- Eigenvalue problems associated with Korn's inequalities (1971) (26)
- On a class of singular perturbation problems (1964) (24)
- Strain-Energy Functions with Multiple Local Minima: Modeling Phase Transformations using Finite Thermoelasticity by (2000) (24)
- Impact–induced phase transitions in thermoelastic solids (1997) (23)
- Torsion and extension of helicoidal shells (1960) (23)
- A note on the spatial decay of a minimal surface over a semi-infinite strip (1977) (22)
- On Saint-Venant's principle and the torsion of solids of revolution (1966) (22)
- A Note on the Driving Traction Acting on a Propagating Interface: Adiabatic and Non-Adiabatic Processes of a Continuum (2000) (20)
- On the representation of the elasticity tensor for isotropic materials (1995) (20)
- Linear Vector Spaces and Cartesian Tensors (1997) (19)
- On the Stability of Thermoelastic Materials (1998) (18)
- A Derivation of the Equations of Shell Theory for General Orthogonal Coordinates (1956) (17)
- Evolution of Phase Transitions: Author Index (2006) (13)
- Note on Stress-Strain Relations for Thin Elastic Shells (1958) (13)
- Unstable Elastic Materials and the Viscoelastic Response of Bars in Tension (1988) (12)
- On the approximation of damped linear dynamical systems (2006) (12)
- Energy inequalities and error estimates for torsion of elastic shells of revolution (1970) (11)
- UNIVERSAL STATES OF FINITE ANTI-PLANE SHEAR: ERICKSEN'S PROBLEM IN MINIATURE (1979) (10)
- Wave Propagation in Linear, Bilinear and Trilinear Elastic Bars (1992) (9)
- On the relation between particle velocity and shock wave speed for thermoelastic materials (2002) (8)
- A Note on the Response of a Beam to a Randomly Moving Force (1970) (8)
- On shock waves in solids (2007) (8)
- Continuum models for irregular phase boundary motion in shape-memory tensile bars (1999) (7)
- A Note on the Energy Release Rate in Quasi-Static Elastic Crack Propagation (1981) (7)
- Reflection and Transmission of Waves from an Interface with a Phase-Transforming Solid (1992) (7)
- On the direct determination of the near-tip stress field for the scattering of SH-waves by a crack (1989) (7)
- On the existence of an elastic potential for a simple material without memory (1979) (5)
- A phenomenological model for failure waves in glass (2000) (5)
- On damped linear dynamical systems (1985) (5)
- On the Scale of the Nonlinear Effect in a Crack Problem (1986) (5)
- Effect of irreversible phase change on shock-wave propagation (1999) (4)
- On Maximally Dissipative Shock Waves in Nonlinear Elasticity (2010) (4)
- Dynamic thermoelastic phase transitions (1995) (4)
- Dynamically Induced Phase Transitions and the Modeling of Comminution in Brittle Solids (1997) (4)
- Linear dynamical systems and an approximation problem for linear transformations (1985) (4)
- Remarks on a question of ericksen concerning elastostatic fields of Saint-Venant type (1985) (3)
- Evolution of Phase Transitions: Preface (2006) (3)
- On entropy conditions and traffic flow models (2008) (3)
- Propagation of One‐Dimensional Waves from a Source in Random Motion (1968) (3)
- Sudden tensile loading of a rubberlike bar (2003) (3)
- Elastic Materials with Two Stress-Free Configurations (2002) (3)
- The Dirichlet problem for a thin rectangle (1967) (3)
- Continuum Modeling of Phase Transitions in Solids (1991) (2)
- DRIVING FORCE AND KINETIC RELATIONS FOR SCALAR CONSERVATION LAWS (2007) (2)
- On Stress-Strain Relations and Strain-Energy Expressions in the Theory of Thin Elastic Shells (1960) (2)
- On shock waves in a special class of thermoelastic solids (2005) (2)
- On a minimization problem associated with linear dynamical systems (1992) (2)
- On an integrodifferential equation arising in a theory of phase transitions in solids (1997) (1)
- Localized Shear Near The Tip of a Crack in Finite Elastostatics (1981) (1)
- Path-independent integrals for the direct determination of stress intensity factors in certain classical crack problems (1986) (1)
- Hysteresis in the Stress‐Cycling of Bars Undergoing Solid–solid Phase Transitions (2002) (1)
- Effects of Solid-Solid Phase Changes On Impact Mechanics (1999) (1)
- One-dimensional continuum model for shape-memory alloys. Technical report (1993) (1)
- On the structure of the Hugoniot relation for a shock-induced martensitic phase transition (2008) (1)
- Viscoelasticity of Polymethyl Methacrylate—an Experimental and Analytical Study (1955) (0)
- Evolution of Phase Transitions: Dynamics: Impact-Induced Transition in a CuAlNi Single Crystal (2006) (0)
- Evolution of Phase Transitions: Impact-Induced Transitions in Two-Phase Elastic Materials (2006) (0)
- A thermoelastic model for an experiment involving a solid-solid phase transition (1995) (0)
- Investigations of Non-elliptic Elastic Materials and the Modeling of Dissipative Behavior in Solids (1991) (0)
- Evolution of Phase Transitions: Multiple-Well Free Energy Potentials (2006) (0)
- Evolution of Phase Transitions: Thermoelastic Materials (2006) (0)
- Investigations of Non-Elliptic Elastic Materials and the Modeling of Phase Transformations in Solids. (1994) (0)
- Remarks on approximations for linear dynamical systems (1992) (0)
- Evolution of Phase Transitions: Introduction (2006) (0)
- Nonlinear Waves in Thermoelastic Solids Undergoing Phase Transitions (2001) (0)
- Evolution of Phase Transitions: Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile Bars (2006) (0)
- r 0 0 DTI FLE Cop ~ y Technical Report No . 1 ON THE PROPAGATION OF MAXIMALLY DISSIPATIVE PHASE BOUNDARIES IN SOLIDS by (0)
- Evolution of Phase Transitions: Statics: Geometric Compatibility (2006) (0)
- Evolution of Phase Transitions: Dynamics of Phase Transitions in Uniaxially Strained Thermoelastic Solids (2006) (0)
- A potential representation for two-dimensional waves in elastic materials of harmonic type (1971) (0)
- Evolution of Phase Transitions: Quasistatics: Kinetics of Martensitic Twinning (2006) (0)
- Mode iii stress intensity factors for an edge-crack in a circle (1984) (0)
- Closure to “Discussions of ‘Viscoelasticity of Polymethyl Methacrylate—an Experimental and Analytical Study’” (1955, Trans. ASME, 77, pp. 185–186) (1955) (0)
- Evolution of Phase Transitions: Models for Two-Phase Thermoelastic Materials in One Dimension (2006) (0)
- Evolution of Phase Transitions: Two-Well Potentials, Governing Equations and Energetics (2006) (0)
- Evolution of Phase Transitions: Equilibrium Phase Mixtures and Quasistatic Processes (2006) (0)
- Discrete and continuous scalar conservation laws (2011) (0)
- On the decay of end-effects due to self-equilibrated loads (1995) (0)
- Preface (1991) (0)
- No . 3 WAVE PROPAGATION IN LINEAR , BILINEAR 7 AND TRILINEAR ELASTIC (0)
- Evolution of Phase Transitions: The Continuum Theory of Driving Force (2006) (0)
- Eigenvalue Problems Associated with Korn ' s Inequalities 385 (2004) (0)
- Evolution of Phase Transitions: Kinetics and Nucleation (2006) (0)
- Eli Sternberg Memoriam (1989) (0)
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