Research Activities

Research Interests:

Continuum Mechanics

Elasticity and Viscoelasticity

Fracture Mechanics

Nanomechanics

Mechanics of Biological Materials

Modeling in Cardio-Vascular Mechanics

Modeling in Cardio-Vascular Disease

Mathematical Ecology

Partial Differential Equations

Integral Equations

Representative Recent Publications:

T. L. Leise, J. R. Walton and Y. Gorb, A Boundary Integral Method for a Dynamic Transient Mode I Crack Problem with Viscoelastic Cohesive Zone, to appear Int. J. Frac., 2009.

T. L. Leise, J. R. Walton and Y. Gorb, Reconsidering the Boundary Conditions for a Dynamic Transient Mode I Crack Problem, J. Mech. Mat’ls & Struct., 3(9), pp. 1797-1807, 2008.

A. Ibragimov, L. R. Ritter and J. R. Walton, Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis, submitted, 2008.

T. Sendova and J. R. Walton, A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale, to appear Math. Mech. Solids, 2009.

A. I. Ibragimov, C. J. McNeal, L. R. Ritter and J. R. Walton, Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II, to appear J. Comp. & Math. Meth. Med., 2009.

E. Aulisa, A. I. Ibragimov, P. Valko and J. R. Walton, Mathematical Framework of the Well Productivity Index for Fast Forchheimer (Non-Darcy) Flows in Porous Media, Math. Mod. Meth. Appl. Sci., 19(8), DOI 10.1142/S0218202509003772, 2009.

E. Aulisa, A. I. Ibragimov, and J. R. Walton, A New Method for Evaluating the Productivity Index for Nonlinear Flows, to appear SPE Journal, 2009.

A. I. Ibragimov, C. J. McNeal, L. R. Ritter and J. R. Walton, Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach, J. Comp. & Math. Meth. Med., 9 (2), pp. 121-142, 2008.

E.-S. Oh, J. R. Walton and J. C. Slatter, A theory of fracture based upon an extension of continuum mechanics to the nanoscale, J. Appl. Mech. 73 (5), pp. 792-798, 2006.

E._S. Oh, J. R. Walton, D. C. Lagoudas and J. C. Slattery, Evolution of stresses in a simple class of oxidation problems, Acta Mechanica 181, pp. 231-255, 2006.

A. I. Ibragimov, C. J. McNeal, L. R. Ritter and J. W. Walton, A Mathematical Model of Atherogenisis as an Inflammatory Response, Math. Med. & Biol., 22 (4), pp.305-333, 2005.

Z. Wang, A. L. McIntosh, B. A. McElmurry, J. R. Walton R. R. Lucchese and J. W. Bevan, An improved morphed potential for Ar:HBr based upon scaling the experimental dissociation energy, J. Phys. Chem., 109, pp. 8168--8179, 2005.

J. D. Humphrey, G. Cote, J. R. Walton, G. A. Meininger and G. Laine, A new paradigm for graduate research and training in the biomedical sciences and engineering, Advances in Physiology Education, 29, pp.98-102, 2005.

D. Khalmanova and J. R. Walton, Dynamic, steady-state crack propagation in a transversely isotropic viscoelastic body, Int. J. Frac., 131 (2), pp. 107-129, 2005.

A. I. Ibragimov, D. Khalmanova, P. Valko and J. R. Walton, On a Mathematical Model of the Productivity Index of a Well from Reservoir Engineering, SIAM J. Appl. Math., 65, No. 6, pp.1952--1980, 2005.

T. Sendova and J. R. Walton, On Strong Ellipticity for Isotropic Hyperelastic Materials Based upon Logarithmic Strain, Int. J. Non-Linear Mech., 40, No. 2-3, pp. 195-212, 2004.

T. L. Leise and J. R. Walton, An analytical and numerical study of a dynamically accelerating semi-infinite crack in a linear viscoelastic material, Int. J. Frac., 127, No.2, pp. 101-117, 2004.

J. R. Walton and J. P. Wilber, Deformations of a neo-Hookean elastic wedge revisited, Math. Mech. of Solids, 9, pp. 307-327, 2004.

T. L. Leise and J. R. Walton, A solution method for a dynamically accelerating semi-infinite crack in a linear viscoelastic material, SIAM Appl. Math., 64, No. 1, pp. 94-107, 2003.

L-I. Palade, J. R. Walton and A. Farina, A New Constitutive Equation that Models Extensional Strain Hardening Based on Evolving Natural Configurations:\ \ Stability Analysis, Int.~J.~Non-linear Mech., 39 No.3,pp. 379-387, 2004.

J. R. Walton, Vibrations of a Neo-Hookean Elastic Wedge, Int. J. Non-Linear Mech., 38, pp. 1285-1296, 2003.