TABLE OF CONTENTS J.L. Ericksen
Departments of Aerospace Engineering and Mechanics and School of Mathematics University of Minnesota
Abstract: Twinning is a kind of defect, commonly observed in crystalline solids. We explore some implications of this, with respect to the theory of crystal elasticity.
When the crystallographer uses mathematics, it is more likely to he elementary algebra, geometry or group theory than sophisticated analysis. However, some of the things he or the metallurgist observes and describes can be viewed as realizations of solutions of partial differential equations of a rather unusual kind, involving deep analytical difficulties. Twinning and like phenomena are included among the defects commonly seen in crystalline solids. Nonlinear elasticity theory is being used, with some success, to analyze such phenomena. In a very formal sense, the general equations are old and well-known, Euler-Lagrange equations of a somewhat special kind, there being a great number of studies of special cases. Yet the simplest considerations of these phenomena have made clear that we need to revise our thinking about the subject. My purpose is to elaborate these vague remarks.
Here, we ponder what might be considered to be the simplest possible kind of problem in elasticity theory. Consider a homogeneous elastic body, with a shape as simple as you like, and seek to determine how it can be in stable equilibrium, when it is subject to no forces or kinematic constraints.
Recall that such theories involve a fixed configuration of a body...
