Theory of Micropolar Elasticity by Witold Nowacki download in ePub, pdf, iPad
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. The system they used is an assembly of elastic spheres in contact. Experimentally we have demonstrated the existence of couple stress by measuring the effect of size on apparent stiffness of compact bone in quasi-static torsion. The problem of a blunt edge notch of elliptic contour in a strip of Cosserat micropolar elastic material under tension has been analyzed via two-dimensional plane stress finite element analysis. The elastic constants used for the calculation were determined in independent measurements of size effects on wet bone.
To explore strain redistribution processes, further experiments were conducted upon notched specimens in torsion at small strain. The material exhibits a stop band of frequency. Analysis of the results is via generalized continuum mechanics and a model of surface damage. Cosserat or micropolar elasticity has the following consequences in isotropic materials.
Wet bone follows the Cosserat curve. Strain is redistributed from peak regions to regions which are classically forbidden so that stress concentration is ameliorated for bone. This is likely the first observation of elastic chirality in a material in contrast to two ply strips. Get pdf of a review article.
For the strip geometry a Cosserat solid exhibits slower stress decay than a classical solid. Poisson's ratio tends to zero as the cubes become further apart.
These show that torsional rigidity exceeds the classical elasticity value, the difference being larger for slender bars, and that cross section warp is less than the classical amount. In this study we observe size effects in quasistatic bending of compact bone.
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