Algebraic structures and operator calculus. Vol.1 by Feinsilver P., Schott R.

By Feinsilver P., Schott R.

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Additional resources for Algebraic structures and operator calculus. Vol.1

Sample text

G. g. 3 Elasticity In a micromechanical point of view, elasticity is predominantly caused by the evolution of interatomic forces in response to the impact of external forces. It can be observed for crystalline substances (where the atoms are established in regular structures) as well as for amorphous materials (where the atoms compose irregular structures), and is characterized by reversibility of the deformation processes and the absence of any hysteresis. Furthermore, it is assumed that the current stress state is uniquely defined by the current strain state, and does not depend on the strain history.

20 Granite 17. . 11. . 27 Basalt 31. . 19. . 30 Limestone 13. . 11. . g. in rock mechanics. 8 for selected soils and rocks show the large variation of material parameters, which is typical for geomaterials. 4 Elastoplasticity The phenomenon of plastic yielding can be mainly observed in crystalline solid materials. It is associated with the motion of defects (so-called dislocations, discontinuities) of the regular atomic structure during deformation. Elastoplastic material behavior is characterized by elastic material response at the beginning of the deformation process.

For instance, comparatively simple experiments can be performed to investigate if the stress-strain curves are rate-dependent, and if hysteresis phenomena occur, indicating dissipative effects. Based on these assumptions the observable material behavior can be divided into four different basic classes: • rate-independent without hysteresis, • rate-independent with hysteresis, • rate-dependent without hysteresis, and • rate-dependent with hysteresis. 16 schematically show typical cyclic stress-strain curves for these material classes.

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