EXPERIMENTAL METHODS FOR STUDY OF COSSERAT ELASTIC SOLIDS AND OTHER GENERALIZED ELASTIC CONTINUA

Abstract

The behavior of solids can be represented by a variety of continuum theories. For example, Cosserat elasticity allows the points in the continuum to rotate as well as translate, and the continuum supports couple per unit area as well as force per unit area. We examine experimental methods for determining the six Cosserat elastic constants of an isotropic elastic solid, or the six Cosserat relaxation functions of a Cosserat viscoelastic solid. We also consider other generalized continuum theories (including micromorphic elasticity, Cowin's void theory, and nonlocal elasticity). Ways of experimentall y discriminating among various generalized continuum representations are presented. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. I Introduction The classical theory of elasticity is presently used in engineering analyses of deformable objects at small strain. However there are other continuum theories for linear isotropic materials. Some have more freedom, and some have less freedom than classical elasticity. The various continuum theories are all mathematically self consistent. Therefore a discrimination among them is to be made by experiment. It is the purpose of this article to explore the physical consequences of various continuum theories, and how these consequences may be used in the design of experiments to discriminate among the theories. The constitutive equations for several theories are presented, and some of the salient consequences of each theory are stated and discussed. Some of the causal physical mechanisms associated with each theory are briefly discussed. Experimental methods for evaluating materials as generalized continua are presented, with emphasis on Cosserat elasticity. The treatment is restricted to linearly elastic behavior; study of Cosserat plasticity and related issues is presented elsewhere in this volume. A discussion of experimental aspects of generalized continua is considered particularly appropriate in view of the fact that most of the work done thus far in generalized continuum mechanics has been theoretical.