Prospects for Mathematics and Mechanics upon the 80th Birthday of Jerry Ericksen

Jerry Ericksen pioneered the development of continuum theory for complex materials and laid the groundwork for theory that bridges continuum mechanics and molecular structure.

His research on nonlinear elasticity in the 1950s and 1960s gave a deep understanding of how principles of invariance served to identify special solutions. This body of work contains a landmark paper on the explicit classification of all deformations possible in every incompressible nonlinear elastic material, no matter what its free energy function. In the 1960s and 1970s he turned attention to the theory of liquid crystals, and, with Frank Leslie, gave the now accepted dynamical theory of liquid crystals. This theory featured completely nonstandard but physically necessary ingredients: nonsymmetric stresses, unusual kinetics, and an unconventional energy equation. He returned to the latter in the 1980s with his formulation of theory for liquid crystal polymers involving a variable degree of orientation.

Ericksen's work in the 1970s to the present, beginning with his influential paper on Equilibrium of Bars, has focused largely on phase transformations in crystals. His research on the Cauchy-Born rule and the the relation between lattice instabilities and the loss of ellipticity of free energy functions launched a line of research in the mechanics of crystals that continues to be one of the most vital in science and mathematics. A major advance was the reconciliation of the use of infinite symmetry groups of crystals with the finite symmetry groups used in nonlinear elasticity, achieved by his definition of the Ericksen-Pitteri neighborhood. Another major advance was the generalization of the Landau theory of second order phase transformations to first order transformations. There remain parts of this work, notably on defects in crystals and liquid crystals, and recent work on x-ray theory (elasticity theory without reference configurations or strains) that may well lead to major lines of research in the future.

Ericksen's work often made use of, and led to the development of, new lines of thought in mathematics, especially in pde and geometry. He inspired both scientists and mathematicians, his influence reaching deeply into both pure mathematics and materials science. This forward-looking symposium celebrates his accomplishments, and seeks to identify prospects for future research on nonlinear materials.