Remarks on Coaxiality of Strain and Stress in Anisotropic Elasticity (original) (raw)

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A Generalized Strain Approach to Anisotropic Elasticity

2021

This work proposes a generalized Lagrangian strain function fα (that depends on modified stretches) and a volumetric strain function gα (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions fα and gα to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which...

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DIRECTIONS OF EXTREME STIFFNESS AND STRENGTH IN LINEAR ELASTIC ANISOTROPIC SOLIDS

An investigation for directions of extreme – maximum or minimum – values of the longitudinal and transverse stiffness moduli as well as of the limit uniaxial and limit shear stresses in anisotropic linear elastic solids is performed in the paper. The cases of cubic symmetry (regular crystal system) and of volumetrically isotropic cylindrical symmetry (hexagonal crystal system with additional constraints) are considered. The systems of non-linear equations for the components of the versors of investigated directions are derived with use of the spectral decomposition of the elasticity (stiffness and compliance) tensors

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On the coincidence of the principal axes of stress and strain in isotropic elastic bodies

1975

Page 1. LETTERS IN APPLIED AND ENGINEERING SCIENCE, Vol. 3, pp. 435-439. Pergamon Press, Inc. Printed in the United States. ON THE COINCIDENCE OF THE PRINCIPAL AXES OF STRESS AND STRAIN IN ISOTROPIC ELASTIC BODIES RC Batra Engineering Mechanics Department University of Missouri Rolla, Missouri 65401 ABSTRACT It is shown that for isotropic elastic materials the principal axes of stress are also the principal axes of strain provided the empirical inequalities hold. 1.

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Remarks on Coaxiality of Strain and Stress in Anisotropic Elasticity (original) (raw)

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