Experimental microelasticity of two porous solids

One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory.

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On generalized Cosserat-type theories of plates and shells: a short review and bibliography

Auxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio ν. Isotropic configurations with ν≈−1 have been designed and are expected to provide increased shear stiffness G. This assumes that Young's modulus and ν can be engineered independently. In this article, a micropolar-continuum model is employed to describe the behavior of a representative auxetic structural network, the chiral lattice, in an attempt to remove the indeterminacy in its constitutive law resulting from ν=−1. While this indeterminacy is successfully removed, it is found that the shear modulus is an independent parameter and, for certain configurations, it is equal to that of the triangular lattice. This is remarkable as the chiral lattice is subject to bending deformation of its internal members, and thus is more compliant than the triangular lattice which is stretch dominated. The derived micropolar model also indicates that this unique lattice has the highest characteristic length scale lc of all known lattice topologies, as well as a negative first Lame constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N=1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.

Elasto-static micropolar behavior of a chiral auxetic lattice

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.

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W. E. Jahsman

Papers

A Quest for Micropolar Elastic Constants

Bending of a Curved Bar of Micropolar Elastic Material

Reexamination of the Kolsky Technique for Measuring Dynamic Material Behavior

Reflection and Refraction of Weak Elastic-Plastic Waves