Education.

1978 1975 1974 1970

Ph.D. in Mathematics, Carnegie Mellon University. M.S., Carnegie Mellon University. B.S., Carnegie Mellon University. White Plains High School, White Plains, NY.

Experience.

2004-date 1990-date 1984-1990 1981-1984 1982-1983 1978-1981

Distinguished Scholar, Southern Illinois University. Professor, Southern Illinois University. Associate Professor, Southern Illinois University. Assistant Professor, Southern Illinois University. Post-doctoral Fellow, IMA, University of Minnesota. Assistant Professor, University of Tennessee, Knoxville.

Professional Visits.

April 2004 June 1997           June 1997           July 1996 1995-1996 Summer 1995           July 1992           June 1992           August 1989 1988-1989           July 1988           October 1987           March 1987 May 1986           April 1986 Spring 1985 Summer 1979 December 1978

University of Bath. University of Bath. Mathematisches Forchungsinstitut Oberwolfach. Mathematisches Forchungsinstitut Oberwolfach. IMA, University of Minnesota. EPSRC Senior Fellow, University of Bath. Universität Bonn. International Centre for Mathematical Sciences. University of Bath. IMA, University of Minnesota. Mathematisches Forchungsinstitut Oberwolfach. Cornell University. Purdue University. Heriot-Watt University, Edinburgh. Mathematisches Forchungsinstitut Oberwolfach. IMA, University of Minnesota. Post-doctoral Fellow, Johns Hopkins University. Universidade Federal do Rio de Janeiro.

Editorial Board Membership.

Journal of Elasticity.

Research Interests.

Nonlinear Elasticity, Continuum Mechanics, Calculus of Variations, Partial Differential Equations.

Society Memberships.

American Academy of Mechanics American Mathematical Society Kappa Sigma Phi Kappa Phi Pi Mu Epsilon Society of Engineering Science Society for Industrial and Applied Mathematics Society for Natural Philosophy-(Secretary 1986-87, 1990-91, 1999-2004, 2007-2008, Member of the Board of Directors, 1985-date) Tau Beta Pi

Other.

Featured Review in Mathematical Reviews, August 1996, 96h:73017 1997 Outstanding Researcher, College of Science, Southern Illinois University at Carbondale 2000 Outstanding Scholar, Southern Illinois University at Carbondale

Publications.

Applications of Estimates near the Boundary to Regularity of Solutions in Linearized Elasticity,  (with  H. C. Simpson). ABSTRACT Energy Minimising Properties of the Radial Cavitation Solution in Incompressible Nonlinear Elasticity,  (with  J. Sivaloganathan). ABSTRACT On the Symmetry of Energy Minimising Deformations in Nonlinear Elasticity II: Compressible Materials,  (with  J. Sivaloganathan). ABSTRACT On the Symmetry of Energy Minimising Deformations in Nonlinear Elasticity I: Incompressible Materials,  (with  J. Sivaloganathan). ABSTRACT On Bifurcation in Finite Elasticity: Buckling of a Rectangular Rod,  (with  H. C. Simpson). To Appear: J. Elasticity. ABSTRACT  Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Anal. Non Linéaire 25 (2008), 201-213 (with  J. Sivaloganathan). ABSTRACT A Variational Approach to Modelling Initiation of Fracture in Nonlinear Elasticity,   IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics (A. B. Movchan, ed.), Springer, 2004, pp. 295-306 (with J. Sivaloganathan). ABSTRACT The convergence of regularized minimizers for cavitation problems in nonlinear elasticity. SIAM J. Appl. Math 66 (2006), 736-757 (with J. Sivaloganathan and V. Tilakraj). ABSTRACT Myriad radial cavitating equilibria in nonlinear elasticity. SIAM J. Appl. Math. 63 (2003), 1461-1473 (with J. Sivaloganathan).  On cavitation, configurational forces and implications for fracture in a nonlinearly elastic material. J. Elasticity 67 (2002), 25-49 (with J. Sivaloganathan). ABSTRACT MR 2004e:74037 A construction of infinitely many singular weak solutions to the equations of nonlinear elasticity. Proc. Royal Soc. Edinburgh 132A (2002), 985-992 (with J. Sivaloganathan). MR 2003f:74004 An explicit radial cavitation solution in nonlinear elasticity. Math. Mech. Solids 7 (2002), 87-93 (with K. A. Pericak-Spector and J. Sivaloganathan). MR 2003c:74008 On the existence of minimizers with prescribed singular points in nonlinear elasticity J. Elasticity 59 (2000), 83-113 (with J. Sivaloganathan). ABSTRACT MR 2002h:74013. On the optimal location of singularities arising in variational problems of nonlinear elasticity J. Elasticity 58 (2000), 191-224 (with J. Sivaloganathan). ABSTRACT MR 2002d:74006. The representation theorem for linear, isotropic tensor functions in even dimensions J. Elasticity 57 (1999), 157-164 (with K. A. Pericak-Spector and J. Sivaloganathan). MR 2001i:74005 An isoperimetric estimate and W1,p-quasiconvexity in nonlinear elasticity, Calc. Var. Partial Differential Equations 8 (1999), 159-176 (with S. Müller and J. Sivaloganathan). MR 2000c:74023.  Dynamic cavitation with shocks in nonlinear elasticity Proc. Royal Soc. Edinburgh. 127A (1997), 837-857 (with K. A. Pericak-Spector). MR 98j:73028  Invertibility and a topological property of Sobolev maps, SIAM J. Math. Anal. 27 (1996), 959-976 (with S. Müller and Q. Tang). MR 97e:46041.  An existence theory for nonlinear elasticity that allows for cavitation, Arch. Rational Mech. Anal. 131 (1995), 1-66 (with S. Müller). Featured Review - MR 96h:73017. On the representation theorem for linear, isotropic tensor functions, J. Elasticity 39 (1995), 181-185 (with K. A. Pericak-Spector). MR 96g:73005.  Linear deformations as global minimizers in nonlinear elasticity, Q. Appl. Math. 52 (1994), 59-64. MR 94m:73026.  Existence of singular minimizers in three-dimensional nonlinear elasticity, Workshop on the Mathematical Theory of Nonlinear and Inelastic Material Behaviour, Darmstadt, Germany, May 25-27, 1992 (ed. H.-D. Alber), Bonner Mathematische Schriften 239 (1993), 21-31 (with S. Müller). MR 95i:73029. Remarks on W1,p-quasiconvexity, interpenetration of matter, and function spaces for elasticity, Anal. Non Linéaire 9 (1992), 263-280 (with R. D. James). MR 93h:73013. The formation of filamentary voids in solids, J. Mech. Phys. Solids 39 (1991), 783-813 (with R. D. James). MR 93d:73059.  Some necessary conditions at an internal boundary for minimizers in finite elasticity, J. Elasticity 26 (1991), 203-122 (with H. C. Simpson). MR 93g:73071.  Necessary conditions at the boundary for minimizers in finite elasticity, Arch. Rational Mech. Anal. 107 (1989), 105-125 (with H. C. Simpson) MR 90i:73057.  Nonuniqueness for a hyperbolic system: Cavitation in nonlinear elastodynamics, Arch. Rational Mech. Anal. 101 (1988), 293-317 (with K. A. Pericak-Spector) MR 89e:73013. On the positivity of the second variation in finite elasticity, Arch. Rational Mech. Anal. 98 (1987), 1-30 (with H. C. Simpson). MR 88i:73033.  On the failure of the complementing condition and nonuniqueness in linear elastostatics, J. Elasticity 15 (1985), 229-231 (with H. C. Simpson). MR 86m:73011.  On the absence of bifurcation for elastic bars in uniaxial tension, Arch. Rational Mech. Anal. 85 (1984), 171-199. MR 85c:73038.  On barrelling for a special material in finite elasticity, Q. Appl. Math. 42 (1984), 99-111 (with H. C. Simpson). MR 85e:73031.  Some monotonicity results for ratios of modified Bessel functions, Q. Appl. Math. 42 (1984), 95-98 (with H. C. Simpson). MR 85d:33021.  On barrelling instabilities in finite elasticity, J. Elasticity 14 (1984), 103-125 (with H. C. Simpson). MR 85m:73028.  On copositive matrices and strong ellipticity for isotropic elastic materials, Arch. Rational Mech. Anal. 84 (1983), 55-68 (with H. C. Simpson). MR 84m:73018. On uniqueness for the traction problem in finite elasticity, J. Elasticity 12 (1982), 367-383. MR 84d:73038. On Gibbs stability in the classical theory of fluid mixtures, ZAMP 32 (1981), 286-295. MR 82i:80003. On monotonicity of the optimal strain path in linear viscoelasticity, Q. Appl. Math. 38 (1980), 369-372 MR 82c:73035. On uniqueness and bifurcation in nonlinear viscoelasticity, Arch. Rational Mech. Anal. 72 (1980), 303-313 (with M. E. Gurtin and D. W. Reynolds). MR 80k:73038. On continuous dependence in finite elasticity, Q. Appl. Math. 38 (1980), 135-138. MR 81f:73020. On uniqueness in finite elasticity with general loading, J. Elasticity 10 (1980), 145-161. MR 81g:73059. On stability and uniqueness in finite elasticity, Arch. Rational Mech. Anal. 70 (1979), 153-165 (with M. E. Gurtin). MR 80j:73022. On the sign of the specific heat, Q. J. Mech. Appl. Math. 29, (1976), 493-497 (with M. E. Gurtin). MR 55 #7142.

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