## Gurtin, Morton Edward

Compute Distance To:
 Author ID: gurtin.morton-e Published as: Gurtin, Morton E.; Gurtin, M. E.; Gurtin, Mortin E.; Gurtin, Morton more...less External Links: MGP · Wikidata · IdRef
 Documents Indexed: 230 Publications since 1959, including 6 Books 2 Contributions as Editor Biographic References: 3 Publications Co-Authors: 75 Co-Authors with 160 Joint Publications 1,626 Co-Co-Authors
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### Co-Authors

 72 single-authored 19 Fried, Eliot 16 Williams, William O. 10 Coleman, Bernard David 9 Anand, Lallit 9 Cermelli, Paolo 8 Chen, Peter J. 8 MacCamy, Richard C. 7 Bertsch, Michiel 7 Guidugli, Paolo Podio 6 Hilhorst, Danielle 6 Murphy, Lea F. 5 Sternberg, Eli 4 Peletier, Lambertus Adrianus 3 Angenent, Sigurd Bernardus 3 Herrera, Ismael 3 Hrusa, William J. 3 Levine, Daniel S. 3 Murdoch, A. Ian 3 Reddy, B. Dayanand 3 Spector, Scott J. 2 Benthien, George W. 2 Browning, Richard V. 2 Carr, Jack 2 Edelstein, Warren S. 2 Giga, Yoshikazu 2 Lele, Suvrat P. 2 Cardoso Matias, José Carlos Pedro 2 McFadden, Geoffrey Bey 2 Mizel, Victor J. 2 Needleman, Alan 2 Pipkin, Allen C. 2 Ralston, Terrance D. 2 Reynolds, David W. 2 Shvartsman, Mikhail M. 2 Slemrod, Marshall 2 Soner, Halil Mete 2 Struthers, Allan A. 2 van der Giessen, Erik 1 Almgren, Frederick Justin jun. 1 Anderson, Daniel M. 1 Bittencourt, Eduardo 1 Daví, Fabrizio 1 Day, William Alan 1 de la Penha, Guilherme M. 1 DiCarlo, Antonıo 1 Fisher, G. M. C. 1 Fix, George J. 1 Gething, C. 1 Greenberg, James M. 1 Herrera R., I. 1 Hutter, Kolumban 1 Jabbour, Michel E. 1 Leoni, Giovanni 1 Lusk, Mark T. 1 Martins, Luiz Carlos 1 Nicola, Lucia 1 Ohno, Nobutada 1 Oliver, Marion L. 1 Paslay, Paul R. 1 Polignone, Debra A. 1 Socolovsky, Eduardo A. 1 Souganidis, Panagiotis E. 1 Spear, Kathleen 1 Suliciu, Ion 1 Temam, Roger Meyer 1 Toupin, Richard A. 1 Truesdell, Clifford Ambrose III 1 Vargas, Antonio S. 1 Vianello, Maurizio 1 Villaggio, Piero 1 Viñals, Jorge 1 Voorhees, Peter W. 1 Walsh, Edward K. 1 Yatomi, Chikayoshi 1 Ziemer, William Paul
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### Serials

 56 Archive for Rational Mechanics and Analysis 27 Quarterly of Applied Mathematics 23 Journal of the Mechanics and Physics of Solids 12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 International Journal of Solids and Structures 8 Journal of Elasticity 6 Mathematical Biosciences 5 International Journal of Plasticity 5 Journal of Applied Mechanics 5 Physica D 3 Journal of Fluid Mechanics 3 Journal of Mathematical Biology 3 Journal of Differential Equations 3 Continuum Mechanics and Thermodynamics 2 Journal of Mathematical Analysis and Applications 2 Theoretical and Computational Fluid Dynamics 2 Meccanica 2 Note di Matematica 2 SIAM Journal on Applied Mathematics 2 Journal of the Society for Industrial & Applied Mathematics 1 International Journal of Engineering Science 1 Journal of the Acoustical Society of America 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Physics of Fluids 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal für die Reine und Angewandte Mathematik 1 Le Matematiche 1 Numerische Mathematik 1 Journal of Integral Equations and Applications 1 Japan Journal of Industrial and Applied Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Mathematical Analysis 1 Interfaces and Free Boundaries 1 Journal of the Aerospace Sciences 1 Applied Mathematical Sciences 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 The IMA Volumes in Mathematics and its Applications 1 Mathematics in Science and Engineering 1 Nonlinear Analysis. Theory, Methods & Applications 1 Oxford Mathematical Monographs
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### Fields

 130 Mechanics of deformable solids (74-XX) 41 Classical thermodynamics, heat transfer (80-XX) 39 Fluid mechanics (76-XX) 35 Partial differential equations (35-XX) 22 Biology and other natural sciences (92-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 4 Numerical analysis (65-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX)

### Citations contained in zbMATH Open

208 Publications have been cited 7,950 times in 5,208 Documents Cited by Year
A continuum theory of elastic material surfaces. Zbl 0326.73001
Gurtin, Morton E.; Murdoch, A. Ian
1975
An introduction to continuum mechanics. Zbl 0559.73001
Gurtin, Morton E.
1981
A general theory of heat conduction with finite wave speeds. Zbl 0164.12901
Gurtin, M. E.; Pipkin, A. C.
1968
Non-linear age-dependent population dynamics. Zbl 0286.92005
Gurtin, Morton E.; MacCamy, Richard C.
1974
Surface stress in solids. Zbl 0377.73001
Gurtin, Morton E.; Murdoch, A. Ian
1978
On a theory of heat conduction involving two temperature. Zbl 0159.15103
Chen, P. J.; Gurtin, M. E.
1968
Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Zbl 0885.35121
Gurtin, Morton E.
1996
Two-phase binary fluids and immiscible fluids described by an order parameter. Zbl 0857.76008
Gurtin, Morton E.; Polignone, Debra; Viñals, Jorge
1996
On the diffusion of biological populations. Zbl 0362.92007
Gurtin, Morton E.; MacCamy, Richard C.
1977
A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. Zbl 1043.74007
Gurtin, Morton E.
2002
Configuration forces as basic concepts of continuum physics. Zbl 0951.74003
Gurtin, Morton E.
2000
On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients. Zbl 0988.74021
Gurtin, Morton E.
2000
Thermomechanics of evolving phase boundaries in the plane. Zbl 0787.73004
Gurtin, Morton E.
1993
On the linear theory of viscoelasticity. Zbl 0107.41007
Gurtin, M. E.; Sternberg, E.
1962
Structured phase transitions on a finite interval. Zbl 0564.76075
Carr, Jack; Gurtin, Morton E.; Slemrod, Marshall
1984
Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface. Zbl 0723.73017
Angenent, Sigurd; Gurtin, Morton E.
1989
A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. I: small deformations. Zbl 1120.74353
Gurtin, Morton E.; Anand, Lallit
2005
On the thermodynamics of elastic materials and of reacting fluid mixtures. Course held at the Department of Mechanics of Solids, June 1971. Zbl 0317.73002
Gurtin, Morton E.
1972
Variational principles for linear elastodynamics. Zbl 0124.40001
Gurtin, M. E.
1964
The nature of configurational forces. Zbl 0836.73002
Gurtin, Morton E.
1995
On the characterization of geometrically necessary dislocations in finite plasticity. Zbl 0989.74013
Cermelli, Paolo; Gurtin, Morton E.
2001
Continuum theory of thermally induced phase transitions based on an order parameter. Zbl 0793.35049
Fried, Eliot; Gurtin, Morton E.
1993
On the thermodynamics of non-simple elastic materials with two temperatures. Zbl 0164.26104
Chen, P. J.; Gurtin, M. E.; Williams, W. O.
1969
Multiphase thermomechanics with interfacial structure. III: Evolving phase boundaries in the presence of bulk deformation. Zbl 0723.73018
Gurtin, Morton E.; Struthers, Allan
1990
Dynamic solid-solid transitions with phase characterized by an order parameter. Zbl 0812.35164
Fried, E.; Gurtin, M. E.
1994
Some simple models for nonlinear age-dependent population dynamics. Zbl 0397.92025
Gurtin, Morton E.; MacCamy, Richard C.
1979
Two-phase deformations of elastic solids. Zbl 0525.73054
Gurtin, Morton E.
1983
Variational principles in the linear theory of viscoelasticity. Zbl 0123.40803
Gurtin, M. E.
1963
A comparison of nonlocal continuum and discrete dislocation plasticity predictions. Zbl 1100.74530
Bittencourt, E.; Needleman, A.; Gurtin, M. E.; Van der Giessen, E.
2003
Variational principles for linear initial-value problems. Zbl 0173.37602
Gurtin, M. E.
1964
Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector. Zbl 1084.74009
Gurtin, Morton E.; Needleman, Alan
2005
Waves in materials with memory. II: On the growth and decay of one- dimensional acceleration waves. Zbl 0244.73017
Coleman, Bernard D.; Gurtin, Morton E.
1965
An axiomatic foundation for continuum thermodynamics. Zbl 0144.48302
Gurtin, M. E.; Williams, W. O.
1967
Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales. Zbl 1104.74006
Fried, Eliot; Gurtin, Morton E.
2006
Thermodynamics applied to gradient theories involving the accumulated plastic strain: the theories of Aifantis and Fleck and Hutchinson and their generalization. Zbl 1170.74311
Gurtin, Morton E.; Anand, Lallit
2009
On the optimal harvesting of persistent age-structured populations. Zbl 0466.92021
Gurtin, Morton E.; Murphy, Lea F.
1981
A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. Zbl 1084.74008
Gurtin, Morton E.
2004
On the optimal harvesting of age-structured populations: Some simple models. Zbl 0467.92017
Gurtin, Morton E.; Murphy, Lea F.
1981
A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results. Zbl 1120.74350
Anand, L.; Gurtin, M. E.; Lele, S. P.; Gething, C.
2005
On a framework for small-deformation viscoplasticity: Free energy, microforces, strain gradients. Zbl 1032.74521
Gurtin, Morton E.
2003
On dissipation inequalities and linear viscoelasticity. Zbl 0173.52703
Gurtin, M. E.; Herrera, I.
1965
The thermodynamics of constrained materials. Zbl 0263.73004
Gurtin, Morton E.; Guidugli, Paolo Podio
1973
Multiphase thermomechanics with interfacial structure. I: Heat conduction and the capillary balance law. Zbl 0723.73016
Gurtin, Morton E.
1988
Gradient single-crystal plasticity with free energy dependent on dislocation densities. Zbl 1170.74013
Gurtin, Morton E.; Anand, Lallit; Lele, Suvrat P.
2007
On the thermodynamics of materials with memory. Zbl 0169.28002
Gurtin, M. E.
1968
On predator-prey interactions with predation dependent on age of prey. Zbl 0435.92023
Gurtin, Morton E.; Levine, Daniel S.
1979
Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films. Zbl 1053.74005
Gurtin, Morton E.; Jabbour, Michel E.
2002
Waves in materials with memory. III: Thermodynamic influences on the growth and decay of acceleration waves. Zbl 0244.73018
Coleman, Bernard D.; Gurtin, Morton E.
1968
On the structure of equilibrium phase transitions within the gradient theory of fluids. Zbl 0665.76120
Gurtin, Morton E.
1988
On interacting populations that disperse to avoid crowding: preservation of segregation. Zbl 0596.35074
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.; Peletier, L. A.
1985
Configurational forces and the basic laws for crack propagation. Zbl 1054.74508
Gurtin, Morton E.; Podio-Guidugli, Paolo
1996
Diffusion models for age-structured populations. Zbl 0459.92015
Gurtin, M. E.; MacCamy, Richard C.
1981
A theory of amorphous solids undergoing large deformations, with application to polymeric glasses. Zbl 1045.74016
Anand, Lallit; Gurtin, Morton E.
2003
A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. II: Finite deformations. Zbl 1101.74316
Gurtin, Morton E.; Anand, Lallit
2005
Thermodynamics and the possibility of spatial interaction in elastic materials. Zbl 0146.21106
Gurtin, M. E.
1965
Thermomechanics of the interface between a body and its environment. Zbl 1160.74303
Fried, Eliot; Gurtin, Morton E.
2007
Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations. Zbl 1032.74533
Cermelli, Paolo; Gurtin, Morton E.
2002
A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations. Zbl 1131.74006
Gurtin, Morton E.
2008
The decomposition $$\mathbf F = \mathbf F^{\text e}\mathbf F^{\text b}$$, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous. Zbl 1180.74009
Gurtin, Morton E.; Anand, Lallit
2005
On the anti-plane shear problem in finite elasticity. Zbl 0496.73036
Gurtin, Morton E.; Temam, Roger
1981
A regularized equation for anisotropic motion-by-curvature. Zbl 0800.73021
Di Carlo, Antonio; Gurtin, Morton E.; Podio-Guidugli, Paolo
1992
Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. Zbl 1083.76061
Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E.
2005
The dynamics of solid-solid phase transitions. I: Coherent interfaces. Zbl 0788.73017
Gurtin, Morton E.
1993
The continuum mechanics of coherent two-phase elastic solids with mass transport. Zbl 0795.73009
Gurtin, Morton E.; Voorhees, Peter W.
1993
A generalization of the Beltrami stress functions in continuum mechanics. Zbl 0203.26802
Gurtin, M. E.
1963
On populations that cannibalize their young. Zbl 0501.92021
Gurtin, Morton E.; Levine, Daniel S.
1982
A note on interacting populations that disperse to avoid crowding. Zbl 0534.92021
Gurtin, Morton E.; Pipkin, A. C.
1984
Theorems in linear elastostatics for exterior domains. Zbl 0101.17001
Gurtin, M. E.; Sternberg, Eli
1961
On the two-phase Stefan problem with interfacial energy and entropy. Zbl 0654.73008
Gurtin, Morton E.
1986
On the relationship between the logarithmic strain rate and the stretching tensor. Zbl 0525.73048
Gurtin, Morton E.; Spear, Kathleen
1983
Thermodynamics and stability. Zbl 0341.73003
Gurtin, Morton E.
1975
Cauchy’s theorem in classical physics. Zbl 0347.73001
Gurtin, Morton E.; Martins, Luiz C.
1976
Coherent solid-state phase transitions with atomic diffusion: A thermomechanical treatment. Zbl 0952.74053
Fried, Eliot; Gurtin, Morton E.
1999
Geometric measure theory and the axioms of continuum thermodynamics. Zbl 0599.73002
Gurtin, Morton E.; Williams, William O.; Ziemer, William P.
1986
Addenda to our paper: A continuum theory of elastic material surfaces. Zbl 0349.73008
Gurtin, Morton E.; Murdoch, A. Ian
1975
Waves in materials with memory. V: On the amplitude of acceleration waves and mild discontinuities. Zbl 0247.73022
Coleman, Bernard D.; Greenberg, James M.; Gurtin, Morton E.
1966
The Burgers vector and the flow of screw and edge dislocations in finite-deformation single-crystal plasticity. Zbl 1120.74394
Gurtin, Morton E.
2006
On the motion of a phase interface by surface diffusion. Zbl 0850.76680
Davì, Fabrizio; Gurtin, Morton E.
1990
A transport theorem for moving interfaces. Zbl 0686.73004
Gurtin, Morton E.; Struthers, Allan; Williams, William O.
1989
Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving. Zbl 0955.74004
Gurtin, Morton E.; Podio-Guidugli, Paolo
1998
Waves in materials with memory. I: The velocity of one-dimensional shock and acceleration waves. Zbl 0138.22006
Coleman, B. D.; Gurtin, M. E.; Herrera, I.
1965
A comparison theorem for crystalline evolution in the plane. Zbl 0862.35047
Giga, Yoshikazu; Gurtin, Morton E.
1996
On the stability against shear waves of steady flows of non-linear viscoelastic fluids. Zbl 0207.25302
Coleman, B. D.; Gurtin, M. E.
1968
On interacting populations that disperse to avoid crowding: The effect of a sedentary colony. Zbl 0538.92020
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.; Peletier, L. A.
1984
On a degenerate diffusion equation of the form $$c(z)_ t=\phi (z_ x)_ x$$ with application to population dynamics. Zbl 0624.35049
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.
1987
Thermal effects in the superelasticity of crystalline shape-memory materials. Zbl 1032.74019
Anand, Lallit; Gurtin, Morton E.
2003
On the growth of one-dimensional shock waves in materials with memory. Zbl 0202.25305
Chen, P. J.; Gurtin, M. E.
1970
On the thermodynamics of chemically reacting fluid mixtures. Zbl 0227.76012
Gurtin, Morton E.
1971
A continuum mechanical theory for turbulence: a generalized Navier-Stokes-$$\alpha$$ equation with boundary conditions. Zbl 1161.76485
Fried, Eliot; Gurtin, Morton E.
2008
On stability and uniqueness in finite elasticity. Zbl 0426.73038
Gurtin, Morton E.; Spector, Scott J.
1979
A coordinate transformation for the porous media equation that renders the free-boundary stationary. Zbl 0574.76093
Gurtin, Morton E.; MacCamy, Richard C.; Socolovsky, Eduardo A.
1984
On interacting populations that disperse to avoid crowding: The case of equal dispersal velocities. Zbl 0646.92018
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.
1987
Growth and decay of one-dimensional shock waves in fluids with internal state variables. Zbl 0216.53102
Chen, P. J.; Gurtin, M. E.
1971
Nanocrystalline grain boundaries that slip and separate: A gradient theory that accounts for grain-boundary stress and conditions at a triple-junction. Zbl 1162.74335
Gurtin, Morton E.; Anand, Lallit
2008
Effect of defect energy on strain-gradient predictions of confined single-crystal plasticity. Zbl 1120.74358
Nicola, Lucia; Van der Giessen, Erik; Gurtin, Morton E.
2005
Toward a nonequilibrium thermodynamics of two-phase materials. Zbl 0673.73007
Gurtin, Morton E.
1988
On the thermodynamics of mixtures. I: Mixtures of rigid heat conductors. Zbl 0209.40302
Gurtin, M. E.; de la Penha, G. M.
1970
Population dynamics with age dependence. Zbl 0398.92023
Gurtin, M. E.; Maccamy, Richard C.
1979
Alternative formulations of isotropic hardening for Mises materials, and associated variational inequalities. Zbl 1179.74013
Gurtin, Morton E.; Reddy, B. Daya
2009
On a nonequilibrium thermodynamics of capillarity and phase. Zbl 0704.35129
Gurtin, Morton E.
1989
Some issues associated with the intermediate space in single-crystal plasticity. Zbl 1482.74041
Gurtin, Morton E.; Reddy, B. Daya
2016
Gradient single-crystal plasticity within a Mises-Hill framework based on a new formulation of self- and latent-hardening. Zbl 1328.74021
Gurtin, Morton E.; Reddy, B. Daya
2014
A gradient theory of small-deformation, single-crystal plasticity that accounts for GND-induced interactions between slip systems. Zbl 1270.74041
2011
Corrigendum to “A continuum mechanical theory for turbulence: a generalized Navier-Stokes-$$\alpha$$ equation with boundary conditions”. Zbl 1272.76138
Fried, Eliot; Gurtin, Morton E.
2011
A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on the accumulation of geometrically necessary dislocations. Zbl 1432.74047
Gurtin, Morton E.
2010
Corrigendum to “Gradient nanoscale polycrystalline elasticity: intergrain interactions and triple-junction conditions”: [Journal of the Mechanics and Physics of Solids 57 (2009), 1749-1779]. Zbl 1200.74022
Fried, Eliot; Gurtin, Morton E.
2010
Thermodynamics applied to gradient theories involving the accumulated plastic strain: the theories of Aifantis and Fleck and Hutchinson and their generalization. Zbl 1170.74311
Gurtin, Morton E.; Anand, Lallit
2009
Alternative formulations of isotropic hardening for Mises materials, and associated variational inequalities. Zbl 1179.74013
Gurtin, Morton E.; Reddy, B. Daya
2009
Gradient nanoscale polycrystalline elasticity: intergrain interactions and triple-junction conditions. Zbl 1200.74021
Fried, Eliot; Gurtin, Morton E.
2009
A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations. Zbl 1131.74006
Gurtin, Morton E.
2008
A continuum mechanical theory for turbulence: a generalized Navier-Stokes-$$\alpha$$ equation with boundary conditions. Zbl 1161.76485
Fried, Eliot; Gurtin, Morton E.
2008
Nanocrystalline grain boundaries that slip and separate: A gradient theory that accounts for grain-boundary stress and conditions at a triple-junction. Zbl 1162.74335
Gurtin, Morton E.; Anand, Lallit
2008
A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation. Zbl 1171.74314
Gurtin, Morton E.
2008
Gradient single-crystal plasticity with free energy dependent on dislocation densities. Zbl 1170.74013
Gurtin, Morton E.; Anand, Lallit; Lele, Suvrat P.
2007
Thermomechanics of the interface between a body and its environment. Zbl 1160.74303
Fried, Eliot; Gurtin, Morton E.
2007
General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids. Zbl 1119.76066
Anderson, Daniel M.; Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E.; McFadden, Geoffrey B.
2007
On a continuum-mechanical theory for turbulence. Zbl 1195.76194
Fried, Eliot; Gurtin, Morton
2007
Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales. Zbl 1104.74006
Fried, Eliot; Gurtin, Morton E.
2006
The Burgers vector and the flow of screw and edge dislocations in finite-deformation single-crystal plasticity. Zbl 1120.74394
Gurtin, Morton E.
2006
A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. I: small deformations. Zbl 1120.74353
Gurtin, Morton E.; Anand, Lallit
2005
Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector. Zbl 1084.74009
Gurtin, Morton E.; Needleman, Alan
2005
A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results. Zbl 1120.74350
Anand, L.; Gurtin, M. E.; Lele, S. P.; Gething, C.
2005
A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. II: Finite deformations. Zbl 1101.74316
Gurtin, Morton E.; Anand, Lallit
2005
The decomposition $$\mathbf F = \mathbf F^{\text e}\mathbf F^{\text b}$$, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous. Zbl 1180.74009
Gurtin, Morton E.; Anand, Lallit
2005
Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. Zbl 1083.76061
Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E.
2005
Effect of defect energy on strain-gradient predictions of confined single-crystal plasticity. Zbl 1120.74358
Nicola, Lucia; Van der Giessen, Erik; Gurtin, Morton E.
2005
The unifying nature of the configurational force balance. Zbl 1221.76039
Fried, Eliot; Gurtin, Morton E.
2005
A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. Zbl 1084.74008
Gurtin, Morton E.
2004
Sharp-interface nematic-isotropic phase transitions without flow. Zbl 1060.76011
Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E.
2004
A void-based description of compaction and segregation in flowing granular materials. Zbl 1100.74535
Fried, E.; Gurtin, M. E.; Hutter, K.
2004
A comparison of nonlocal continuum and discrete dislocation plasticity predictions. Zbl 1100.74530
Bittencourt, E.; Needleman, A.; Gurtin, M. E.; Van der Giessen, E.
2003
On a framework for small-deformation viscoplasticity: Free energy, microforces, strain gradients. Zbl 1032.74521
Gurtin, Morton E.
2003
A theory of amorphous solids undergoing large deformations, with application to polymeric glasses. Zbl 1045.74016
Anand, Lallit; Gurtin, Morton E.
2003
Thermal effects in the superelasticity of crystalline shape-memory materials. Zbl 1032.74019
Anand, Lallit; Gurtin, Morton E.
2003
The role of the configurational force balance in the nonequilibrium epitaxy of films. Zbl 1020.74022
Fried, Eliot; Gurtin, Morton E.
2003
A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. Zbl 1043.74007
Gurtin, Morton E.
2002
Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films. Zbl 1053.74005
Gurtin, Morton E.; Jabbour, Michel E.
2002
Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations. Zbl 1032.74533
Cermelli, Paolo; Gurtin, Morton E.
2002
On the characterization of geometrically necessary dislocations in finite plasticity. Zbl 0989.74013
Cermelli, Paolo; Gurtin, Morton E.
2001
Configuration forces as basic concepts of continuum physics. Zbl 0951.74003
Gurtin, Morton E.
2000
On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients. Zbl 0988.74021
Gurtin, Morton E.
2000
Coherent solid-state phase transitions with atomic diffusion: A thermomechanical treatment. Zbl 0952.74053
Fried, Eliot; Gurtin, Morton E.
1999
The motion of screw dislocations in crystalline materials undergoing antiplane shear: Glide, cross-slip, fine cross-slip. Zbl 0941.74006
Cermelli, Paolo; Gurtin, Morton E.
1999
Sharp-interface and phase-field theories of recrystallization in the plane. Zbl 0948.74042
Gurtin, Morton E.; Lusk, Mark T.
1999
Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving. Zbl 0955.74004
Gurtin, Morton E.; Podio-Guidugli, Paolo
1998
On the dynamics of crystalline motions. Zbl 1306.74038
Giga, Yoshikazu; Gurtin, Morton E.; Matias, Jose&rsquo;
1998
A note on the thermomechanics of curvature flows in $$\mathbb{R}^3$$ and on surfaces in $$\mathbb{R}^3$$. Zbl 0926.74006
Cermelli, Paolo; Gurtin, Morton E.; Shvartsman, Mikhail M.
1998
Configurational forces and the dynamics of planar cracks in three-dimensional bodies. Zbl 0903.73059
Gurtin, M. E.; Shvartsman, M. M.
1997
Dynamical theories of electromagnetism and superconductivity based on gauge invariance and energy. Zbl 0893.35124
Gurtin, Morton E.
1997
Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Zbl 0885.35121
Gurtin, Morton E.
1996
Two-phase binary fluids and immiscible fluids described by an order parameter. Zbl 0857.76008
Gurtin, Morton E.; Polignone, Debra; Viñals, Jorge
1996
Configurational forces and the basic laws for crack propagation. Zbl 1054.74508
Gurtin, Morton E.; Podio-Guidugli, Paolo
1996
A comparison theorem for crystalline evolution in the plane. Zbl 0862.35047
Giga, Yoshikazu; Gurtin, Morton E.
1996
A phase-field theory for solidification based on a general anisotropic sharp-interface theory with interfacial energy and entropy. Zbl 0885.35147
Fried, Eliot; Gurtin, Morton E.
1996
On configurational inertial forces at a phase interface. Zbl 0945.74663
Gurtin, Morton E.; Podio-Guidugli, Paolo
1996
Semi-quadratic variational problems for multiphase equilibria. Zbl 0896.73077
Fried, Eliot; Gurtin, Morton E.
1996
General contact-angle conditions with and without kinetics. Zbl 0867.53061
Angenent, Sigurd; Gurtin, Morton E.
1996
The nature of configurational forces. Zbl 0836.73002
Gurtin, Morton E.
1995
Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles. Zbl 0828.35054
Gurtin, M. E.; Soner, H. M.; Souganidis, P. E.
1995
Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces. Zbl 0841.76086
Gurtin, Morton E.; Matias, José
1995
Dynamic solid-solid transitions with phase characterized by an order parameter. Zbl 0812.35164
Fried, E.; Gurtin, M. E.
1994
The dynamics of solid-solid phase transitions. II: Incoherent interfaces. Zbl 0807.73006
Cermelli, Paolo; Gurtin, Morton E.
1994
Anisotropic motion of a phase interface. Well-posedness of the initial value problem and qualitative properties of the interface. Zbl 0784.35124
Angenent, Sigurd B.; Gurtin, Morton E.
1994
The characterization of configurational forces. Addendum to: The dynamics of solid-solid phase transions. I: Coherent interfaces. Zbl 0825.73045
Gurtin, Morton E.
1994
Thermodynamics and the supercritical Stefan equations with nucleations. Zbl 0809.35171
Gurtin, Morton E.
1994
Thermomechanics of evolving phase boundaries in the plane. Zbl 0787.73004
Gurtin, Morton E.
1993
Continuum theory of thermally induced phase transitions based on an order parameter. Zbl 0793.35049
Fried, Eliot; Gurtin, Morton E.
1993
The dynamics of solid-solid phase transitions. I: Coherent interfaces. Zbl 0788.73017
Gurtin, Morton E.
1993
The continuum mechanics of coherent two-phase elastic solids with mass transport. Zbl 0795.73009
Gurtin, Morton E.; Voorhees, Peter W.
1993
A regularized equation for anisotropic motion-by-curvature. Zbl 0800.73021
Di Carlo, Antonio; Gurtin, Morton E.; Podio-Guidugli, Paolo
1992
On the formulation of mechanical balance laws for structured continua. Zbl 0782.73067
Gurtin, Morton E.; Podio-Guidugli, Paolo
1992
Some remarks on the Stefan problem with surface structure. Zbl 0763.35110
Gurtin, Morton E.; Soner, H. Mete
1992
Evolving phase boundaries in the presence of deformation and surface stress. Zbl 0800.73022
Gurtin, Morton E.
1992
On the thermodynamics of viscoelastic materials of single-integral type. Zbl 0747.73006
Gurtin, Morton E.; Hrusa, William J.
1991
A hyperbolic theory for the evolution of plane curves. Zbl 0762.35068
Gurtin, Morton E.; Podio-Guidugli, Paolo
1991
On thermomechanical laws for the motion of a phase interface. Zbl 0754.73020
Gurtin, Morton E.
1991
Multiphase thermomechanics with interfacial structure. III: Evolving phase boundaries in the presence of bulk deformation. Zbl 0723.73018
Gurtin, Morton E.; Struthers, Allan
1990
On the motion of a phase interface by surface diffusion. Zbl 0850.76680
Davì, Fabrizio; Gurtin, Morton E.
1990
A mechanical theory for crystallization of a rigid solid in a liquid melt; Melting-freezing waves. Zbl 0850.76728
Gurtin, Morton E.
1990
Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface. Zbl 0723.73017
Angenent, Sigurd; Gurtin, Morton E.
1989
A transport theorem for moving interfaces. Zbl 0686.73004
Gurtin, Morton E.; Struthers, Allan; Williams, William O.
1989
On a nonequilibrium thermodynamics of capillarity and phase. Zbl 0704.35129
Gurtin, Morton E.
1989
On diffusion in two-phase systems: The sharp interface versus the transition layer. Zbl 0991.80500
Gurtin, Morton E.
1989
Multiphase thermomechanics with interfacial structure. I: Heat conduction and the capillary balance law. Zbl 0723.73016
Gurtin, Morton E.
1988
On the structure of equilibrium phase transitions within the gradient theory of fluids. Zbl 0665.76120
Gurtin, Morton E.
1988
Toward a nonequilibrium thermodynamics of two-phase materials. Zbl 0673.73007
Gurtin, Morton E.
1988
On energies for nonlinear viscoelastic materials of single-integral type. Zbl 0658.73026
Gurtin, Morton E.; Hrusa, William J.
1988
Corrections for the paper “On the two-phase Stefan problem with interfacial energy and entropy”. Zbl 0672.73080
Gurtin, Morton E.
1988
On a degenerate diffusion equation of the form $$c(z)_ t=\phi (z_ x)_ x$$ with application to population dynamics. Zbl 0624.35049
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.
1987
On interacting populations that disperse to avoid crowding: The case of equal dispersal velocities. Zbl 0646.92018
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.
1987
Some results and conjectures in the gradient theory of phase transitions. Zbl 0634.49019
Gurtin, Morton E.
1987
On the two-phase Stefan problem with interfacial energy and entropy. Zbl 0654.73008
Gurtin, Morton E.
1986
Geometric measure theory and the axioms of continuum thermodynamics. Zbl 0599.73002
Gurtin, Morton E.; Williams, William O.; Ziemer, William P.
1986
On fluids of grade $$n$$. Zbl 0626.76010
Gurtin, Morton E.; Vianello, Maurizio; Williams, William O.
1986
On predator-prey dispersal, repulsive dispersal, and the presence of shock waves. Zbl 0621.92017
Bertsch, Michiel; Gurtin, Morton E.
1986
On a system of degenerate diffusion equations. Zbl 0601.35048
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.; Peletier, L. A.
1986
On interacting populations that disperse to avoid crowding: preservation of segregation. Zbl 0596.35074
Bertsch, M.; Gurtin, M. E.; Hilhorst, D.; Peletier, L. A.
1985
One-dimensional structured phase transformations under prescribed loads. Zbl 0581.73020
Carr, Jack; Gurtin, Morton E.; Slemrod, Marshall
1985
Structured phase transitions on a finite interval. Zbl 0564.76075
Carr, Jack; Gurtin, Morton E.; Slemrod, Marshall
1984
A note on interacting populations that disperse to avoid crowding. Zbl 0534.92021
Gurtin, Morton E.; Pipkin, A. C.
1984
...and 108 more Documents
all top 5

### Cited by 5,335 Authors

 101 Gurtin, Morton Edward 45 Steinmann, Paul 39 Fabrizio, Mauro 37 Rautian, Nadegda Aleksandrovna 36 Fried, Eliot 33 Vlasov, Viktor Valentinovich 32 Miranville, Alain M. 32 Morro, Angelo 32 Quintanilla de Latorre, Ramón 29 Chen, Peter J. 28 Colli, Pierluigi 28 Eremeyev, Victor A. 28 Schiavone, Peter 26 Guidugli, Paolo Podio 24 Javili, Ali 24 Šilhavý, Miroslav 23 Anand, Lallit 23 Garcke, Harald 23 Hernández, Eduardo M. 22 Giga, Yoshikazu 22 Williams, William O. 21 Grasselli, Maurizio 20 Reddy, B. Dayanand 20 Roubíček, Tomáš 20 Wang, Xu 19 Coleman, Bernard David 19 Niordson, Christian F. 19 Spector, Scott J. 18 Fosdick, Roger L. 17 Giorgi, Claudio 17 Marin, Marin I. 16 Forest, Samuel 16 Gilardi, Gianni 16 Miehe, Christian 16 Neff, Patrizio 16 Stefanelli, Ulisse 15 Dai, Ming 15 Pata, Vittorino 15 Polizzotto, Castrenze 15 Russo, Remigio 15 Sprekels, Jürgen 15 Yang, Xiaofeng 14 Abels, Helmut 14 Ansari, Reza 14 McBride, Andrew T. 13 Bowen, Ray M. 13 Ciarletta, Michele 13 Hoger, Anne 13 Owen, David Roger Jones 13 Podio-Guidugli, Paulo 13 Tachim Medjo, Theodore 13 Tomassetti, Giuseppe 13 van der Giessen, Erik 12 Acharya, Amit 12 Bonetti, Elena 12 Cermelli, Paolo 12 Del Piero, Gianpietro 12 El-Karamany, Ahmed S. 12 Gao, Cun-Fa 12 Liu, Chun 12 Mi, Changwen 12 Novick-Cohen, Amy 12 Nunziato, Jace W. 12 Shen, Jie 12 Vianello, Maurizio 12 Willis, John Raymond 11 Bates, Peter W. 11 Bertsch, Michiel 11 Chiriţă, Stan 11 Ciarlet, Philippe Gaston 11 Cimmelli, Vito Antonio 11 Ezzinbi, Khalil 11 Fernández, Jose Ramon 11 Fleck, Norman A. 11 Fonseca, Irene 11 Grandi, Diego 11 Iannelli, Mimmo 11 Mariano, Paolo Maria 11 Mogilevskaya, Sofia G. 11 Nürnberg, Robert 11 Reddy, Junuthula Narasimha 11 Rybka, Piotr 11 Segev, Reuven 11 Svendsen, Bob 11 Truskinovsky, Lev 10 Altenbach, Holm 10 Elliott, Charles M. 10 Ezzat, Magdy A. 10 Geers, Marc G. D. 10 Gyllenberg, Mats 10 Iesan, Dorin 10 Kim, Mi-Young 10 Kružík, Martin 10 Kuhl, Ellen 10 Le Khanh Chau 10 Maugin, Gérard A. 10 Mukhopadhyay, Santwana 10 O’Regan, Donal 10 Othman, Mohamed Ibrahim Ahmed 10 Papageorgiou, Nikolaos S. ...and 5,235 more Authors
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### Cited in 416 Serials

 301 Archive for Rational Mechanics and Analysis 289 Journal of Elasticity 269 Journal of the Mechanics and Physics of Solids 252 Acta Mechanica 190 Computer Methods in Applied Mechanics and Engineering 159 International Journal of Engineering Science 152 Journal of Mathematical Analysis and Applications 135 Mathematics and Mechanics of Solids 132 ZAMP. Zeitschrift für angewandte Mathematik und Physik 117 European Journal of Mechanics. A. Solids 116 Continuum Mechanics and Thermodynamics 96 Journal of Differential Equations 87 Journal of Computational Physics 76 Applied Mathematics and Computation 75 Computers & Mathematics with Applications 72 Computational Mechanics 69 Applied Mathematical Modelling 66 Meccanica 60 Journal of Mathematical Biology 59 Mathematical Biosciences 55 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 54 International Journal of Plasticity 54 International Journal for Numerical Methods in Engineering 46 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 45 Physica D 45 Nonlinear Analysis. Real World Applications 42 International Journal of Solids and Structures 37 Mathematical Methods in the Applied Sciences 35 Applied Mathematics Letters 33 Mathematical and Computer Modelling 33 Nonlinear Analysis. Theory, Methods & Applications 30 Archive of Applied Mechanics 28 Applicable Analysis 28 Applied Mathematics and Mechanics. (English Edition) 28 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 28 Engineering Analysis with Boundary Elements 26 Calculus of Variations and Partial Differential Equations 25 Wave Motion 25 Quarterly of Applied Mathematics 25 Discrete and Continuous Dynamical Systems 24 Journal of Mathematical Physics 24 Discrete and Continuous Dynamical Systems. Series B 23 Annali di Matematica Pura ed Applicata. Serie Quarta 23 Journal of Computational and Applied Mathematics 23 Journal of Mathematical Sciences (New York) 23 Differential Equations 21 Applied Numerical Mathematics 21 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 21 International Journal of Fracture 20 Transactions of the American Mathematical Society 19 AMM. Applied Mathematics and Mechanics. (English Edition) 18 Journal of Scientific Computing 18 European Journal of Applied Mathematics 18 Communications in Partial Differential Equations 18 SIAM Journal on Mathematical Analysis 18 Acta Mechanica Sinica 18 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 17 Journal of Dynamics and Differential Equations 17 Journal of Nonlinear Science 16 Rendiconti del Seminario Matematico della Università di Padova 15 Journal of Non-Equilibrium Thermodynamics 15 Evolution Equations and Control Theory 14 Journal of Engineering Mathematics 14 Theoretical Population Biology 14 Japan Journal of Industrial and Applied Mathematics 14 Journal de Mathématiques Pures et Appliquées. Neuvième Série 14 SIAM Journal on Applied Mathematics 14 Discrete and Continuous Dynamical Systems. Series S 13 Journal of Fluid Mechanics 13 Numerische Mathematik 13 NoDEA. Nonlinear Differential Equations and Applications 13 Abstract and Applied Analysis 12 Bulletin of Mathematical Biology 12 Applied Mathematics and Optimization 12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Journal of Integral Equations and Applications 12 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 12 Boundary Value Problems 12 Waves in Random and Complex Media 11 Journal of Applied Mathematics and Mechanics 11 Rocky Mountain Journal of Mathematics 11 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 11 Mathematical Population Studies 10 Computers and Fluids 10 Soviet Applied Mechanics 10 Journal of Optimization Theory and Applications 10 Rendiconti del Circolo Matemàtico di Palermo. Serie II 10 Numerical Methods for Partial Differential Equations 10 Physics of Fluids 9 Communications in Mathematical Physics 9 Mathematics of Computation 9 Journal of Functional Analysis 9 Mathematische Zeitschrift 9 Proceedings of the American Mathematical Society 9 Acta Applicandae Mathematicae 9 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 9 Acta Mathematica Sinica. English Series 9 Journal of Evolution Equations 9 Archives of Computational Methods in Engineering 9 Communications on Pure and Applied Analysis ...and 316 more Serials
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### Cited in 53 Fields

 2,904 Mechanics of deformable solids (74-XX) 1,634 Partial differential equations (35-XX) 672 Fluid mechanics (76-XX) 568 Biology and other natural sciences (92-XX) 529 Numerical analysis (65-XX) 362 Classical thermodynamics, heat transfer (80-XX) 322 Integral equations (45-XX) 265 Calculus of variations and optimal control; optimization (49-XX) 243 Statistical mechanics, structure of matter (82-XX) 207 Ordinary differential equations (34-XX) 144 Operator theory (47-XX) 134 Differential geometry (53-XX) 107 Dynamical systems and ergodic theory (37-XX) 101 Systems theory; control (93-XX) 82 Probability theory and stochastic processes (60-XX) 54 Mechanics of particles and systems (70-XX) 54 Optics, electromagnetic theory (78-XX) 49 Real functions (26-XX) 48 Global analysis, analysis on manifolds (58-XX) 33 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 23 Geophysics (86-XX) 20 Functional analysis (46-XX) 14 Difference and functional equations (39-XX) 14 Integral transforms, operational calculus (44-XX) 14 Operations research, mathematical programming (90-XX) 13 Quantum theory (81-XX) 12 History and biography (01-XX) 10 Measure and integration (28-XX) 10 Functions of a complex variable (30-XX) 10 Information and communication theory, circuits (94-XX) 9 Computer science (68-XX) 8 Convex and discrete geometry (52-XX) 7 Special functions (33-XX) 6 Approximations and expansions (41-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistics (62-XX) 5 General and overarching topics; collections (00-XX) 5 Relativity and gravitational theory (83-XX) 4 Group theory and generalizations (20-XX) 3 Number theory (11-XX) 3 Topological groups, Lie groups (22-XX) 3 Potential theory (31-XX) 3 Manifolds and cell complexes (57-XX) 2 General topology (54-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)

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