Experimental application of a generalized continuum model to nondestructive testing

Journal of Engineering Materials and Technology

1991

128

Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson’s ratios.

Section: Study Of Materials As Other Generalized Continuamentioning

confidence: 99%

Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua

Journal of Engineering Materials and Technology

1991

128

“…Such long range interactions occur between charged atoms or molecules in a solid. Long range forces may also be considered to propagate along fibers or laminae in a composite material [28] or in inclusions in random composites [29]. Nonlocality is often presented in a differential form that entails an approximation to the nonlocal integral [30].…”

Section: Discussionmentioning

confidence: 99%

Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

Journal of Applied Mechanics

Drugan

2015

Pure bending experiments on prismatic bars of square cross section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars' lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such foams have a non-negligible length scale compared to the bars' cross-sectional dimensions, whereas classical elasticity theory contains no inherent length scale. All these facts raise the intriguing question: is there a richer, physically sensible, yet still continuum and relatively simple elasticity theory capable of modeling the observed phenomenon in these materials? This paper reports our exploration of the hypothesis that Cosserat elasticity can. We employ the principle of minimum potential energy for homogeneous isotropic Cosserat linear elastic material in which the microrotation vector is taken to be independent of the macrorotation vector (as prior experiments indicate that it should be in general to model such materials) to obtain an approximate three-dimensional solution to pure bending of a prismatic bar having a square cross section. We show that this solution, and hence Cosserat elasticity, captures the experimentally observed nonclassical deformation feature, both qualitatively and quantitatively, for reasonable values of the Cosserat moduli. A further interesting conclusion is that a single experiment—the pure bending one—suffices to reveal directly, via the observation of surface deformation, the presence of nonclassical elastic effects describable by Cosserat elasticity.

“…The Cosserat theory of elasticity is a continuum theory that incorporates a specific kind of nonlocal [22] interaction. The stress σ jk (force per unit area) can be asymmetric.…”

Section: Introductionmentioning

confidence: 99%

“…The Cosserat theory of elasticity is a continuum theory that incorporates a specific kind of non-local [22]…”

Section: Introductionmentioning

confidence: 99%

Cosserat elasticity of negative Poisson’s ratio foam: experiment

Rueger

2016

Smart Mater. Struct.

Negative Poisson's ratio polymer foams derived from reticulated open cell foams exhibit large size effects in torsion and bending. Effective moduli increase as diameter decreases in contrast to the prediction of classical elasticity. Size effects of this sort are predicted by Cosserat (micropolar) elasticity in which points can rotate as well as translate and distributed moments are incorporated. The Cosserat coupling number N was about twice as large as that of as-received foam, leading to strong effects. The torsion characteristic length t was similar. Cosserat effects are known to enhance toughness and immunity from stress concentration.