I-Shih Liu

E-mail:
liu (at) im.ufrj.br

Résumé

Research Interests

My Books

Recent Publications

Selected Publications

   Me

• B. S. from Civil Engineering Department of National Taiwan University in 1964.
• Ph. D. from Mechanics Department of the Johns Hopkins University in 1972.
• Alexander von Humboldt research fellow, Hermann Föttinger Institut,
  Technische Universität Berlin, in 1981 and 1985.
• Professor, Instituto de Matemática, Universidade Federal do Rio de Janeiro, since 1972.

Research Interests

My Books

• Continuum Mechanics

  Graduate Textbook (Table of contents and Index)
  ISBN: 3-540-43019-9
  Springer-Verlag, Berlin Heidelberg New York
  Publication: May 2002
  
  Solutions to the Exercises
  Free access to selected exercises - (click here)
          A complete version is available to instructors on request

  
  

• Introdução ao Método de Elementos Finitos
  Análise e Aplicação

  (Co-author: Mauro A. Rincon)
  ISBN: 85-87674-05-6
  Instituto de Matemática - UFRJ
  2001, 2003 Segunda Edição. (in Portuguese)
  

  
  

• Constitutive Theories: Basic Principles

  in Continuum Mechanics
  Editores: Jose Merodio e Giuseppe Saccomandi,
  in Encyclopedia of Life Support Systems (EOLSS)
  Developed under the auspices of the UNESCO Publications, Oxford, UK
  2009

  
  

• A Continuum Mechanics Primer

  Lecture Note - On Constitutive Theories of Materials
  Revised April 15, 2009

  
  

Recent Publications

• Constitutive theory of anisotropic rigid heat conductors,
  Journal of Mathematical Physics, 50, 083506 (2009), doi . Preprint-pdf.
• On entropy flux of transversely isotropic elastic bodies,
  Journal of Elasticity, 96, 97-104 (2009), doi . Preprint-pdf.
• Numerical analysis of quenching - heat conduction in metallic materials,
  Applied Mathematical Modelling, 33, 2464-2473 (2009), doi .
• Entropy flux relation for viscoelastic bodies,
  Journal of Elasticity 90, 259-270 (2008), doi . Preprint-pdf.
• A method of differential iteration for boundary value problem in extended thermodynamics,
  Nonlinear Analysis, Real World Applications, 8, 1113-1131 (2007). doi.
• Weighted iterative solutions of linear differential equations and heat conduction of ideal gases in moment theory,
  (with D. R. Vieira), Z. angew. Math. Phys. (ZAMP), 57, 1075-1091 (2006). doi.
• A nonlinear heat equation with temperature-dependent parameters,
  (with M. A. Rincon, J. Limaco), Mathematical Physics Electronic Journal (MPEJ) 12, Paper 5, 1-21 (2006). pdf-text.
• Shock structure in viscoeleasticity of relaxation type,
  (with Y. Wu), Nonlinear Analysis, Theory Methods & Applications, 65, 785-794 (2006). doi.
• Error estimates of vibrations of elastic string with moving ends,
  (with M. A. Rincon), Applied Numerical Mathematics, 56, 745-755 (2006). doi.
• Further remarks on Euclidean objectivity and the principle of material frame-indifference,
  Continuum Mech. Thermodyn. 17, 125-133 (2005). doi. pdf-file
  
• On well-posedness of classical boundary conditions in extended thermodynamics,
  Proceedings of the XIVth International Symposium (STAMM-2004), Seeheim, Germany,
  Trends in Applications of Mathematics to Mechanics, Y. Wang, K. Hutter (Eds.),
  Shaker Verlag, Aachen, 225-233 (2005). pdf-file
  
• Existence and uniqueness of solutions of elastic string with moving ends,
  (with M. A. Rincon), Mathematical Methods in the Applied Sciences, 27, 1641-1655 (2004). doi.
• On Euclidean objectivity and the principle of material frame-indifference,
  Continuum Mech. Thermodyn. 16, 177-183 (2004). doi. pdf-file
  
• A boundary value problem in extended thermodynamics - One-dimensional steady flows with heat conduction,
  (with M. A. Rincon), Continuum Mech. Thermodyn. 16, 109-124 (2004). doi.
  
• On the transformation property of the deformation gradient under a change of frame,
  Journal of Elasticity, 71, 73-80 (2003). doi.
  
• Effect of moving boundaries on the vibrating elastic string,
  (with M. A. Rincon), Applied Numerical Mathematics, 47, 159-172 (2003). doi.
  
• On numerical approximation of an optimal control problem in linear elasticity,
  (with M. A. Rincon), Divulgaciones Matemáticas, 11, 91-107 (2003). pdf-file
  
• Iterative approximation of stationary heat conduction in extended thermodynamics,
  (with M. A. Rincon; I. Müller), Continuum Mech. Thermodyn. 14, 483-493 (2002). doi.
  
• Constitutive equations of extended thermodynamics from a hybrid pair of generator functions,
  Continuum Mech. Thermodyn. 13, 25-39 (2001). doi.
  
• Instability of a square sheet under symmetric biaxial loading,
  (with W. A. das Neves), J. Braz. Soc. Mechanical Sciences, 22, 545-549 (2000). doi .
  
• Oscillation waves in Riemann problems for phase transitions,
  (with H. Frid), Quart. Appl. Math. 56, 115-135 (1998).
  
• Vanishing relaxation limit of viscoelasticity,
  (with Y. Wu), Mathematics and Mechanics of Solids 1, 227-241 (1996). doi
  
• On entropy flux-heat flux relation in thermodynamics with Lagrange multipliers,
  Continuum Mech. Thermodyn. 8, 247-256 (1996). doi .
  
• Stability of thick spherical shells,
  Continuum Mech. Thermodyn. 7, 249-258 (1995). doi
  
• Oscillation waves in Riemann problems inside elliptic regions for conservation laws of mixed type,
  (with H. Frid), ZAMP 46, 913-931 (1995). doi .
• Phase mixtures in dynamics of pseudoelasticity,
  (with H. Frid), Continuum Mech. Thermodyn. 7, 475-487 (1995). doi .

Top

Some Previous Publications

• Method of Lagrange multipliers for exploitation of entropy principle,
  Arch. Rational Mech. Anal. 46, 131-148 (1972). doi .
• On thermodynamics and thermostatics of fluids in electromagnetic fields,
  (with I. Müller) Arch. Rational Mech. Anal. 46, 149-176 (1972). doi .
• Wave propagation in fluids in electromagnetic fields,
  Arch. Rational Mech. Anal. 53, 347-358 (1974).
  
• A note on material symmetry
  (with C.-C. Wang) Arch. Rational Mech. Anal. 74, 277-296 (1980). doi .
• On chemical potential and incompressible porous media,
  Journal de Mecanique 19, 327-342 (1980).
  
• On representations of anisotropic invariants,
  Int. J. Engng Sci. 20, 1099-1109 (1982). doi .
• Decay of electromagnetic waves in fluids,
  (with G. M. Kremer) J. Non-Equilib. Thermodyn. 8, 67-74 (1983).
  
• Extended thermodynamics of classical and degenerate ideal gases,
  (with I. Müller) Arch. Rational Mech. Anal. 83, 285-332 (1983). doi .
• Relativistic thermodynamics of gases,
  (with I. Müller, T. Ruggeri) Annals of Physics, 169, 191-219 (1986). doi .
• Extended thermodynamics of viscoelastic materials,
  Continuum Mech. Thermodyn. 1, 143-164 (1989). doi .
• Hyperbolic system for viscous fluids and simulation of shock tube flows,
  (with J. A. Salvador) Continuum Mech. Thermodyn. 2, 179-197 (1990). doi .
• Energy control of numerical solutions of an elastic oscillator,
  (with I. Suliciu) Mathematics and Computers in Simulation 33, 209-221 (1991). doi .
• On interface equilibrium and inclusion problems,
  Continuum Mech. Thermodyn. 4, 177-186 (1992). doi .