By Leonid M. Zubov
ISBN-10: 364208298X
ISBN-13: 9783642082986
The writer applies equipment of nonlinear elasticity to enquire the defects within the crystal constitution of solids comparable to dislocations and disclinations that signify the plastic and energy houses of many fabrics. opposite to the geometrically encouraged nonlinear conception of dislocations always dispensed over the physique, nonlinear research of remoted dislocations and disclinations is much less built; it really is given for the 1st time during this booklet, and in a sort available to either scholars and researchers. the overall concept of Volterra's dislocations in elastic media lower than huge deformations is built. a couple of special suggestions are came across. The nonlinear method of investigating the remoted defects produces effects that frequently vary qualitatively from these of the linear idea.
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Extra info for Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies
Sample text
Jr 2 Here the contour 71 consists of the curve 7 and the part of 70 between the points A41 and A4o, whereas the contour 72 consists of the part of 70 between A4o and A41 and the curve 7. The passage along 71 and 72 begins at A4o and is counter-clockwise. 14) over a closed contour 7o with the initial point A4o. 10), it follows A C°1" ~o (E + d r . H). Co = QI" Q2. 11), being a product of orthogonal tensors, is also an orthogonal tensor; we denote it by Q0, A Qo = Co 1" ~o (E + d r . H)-Co. 12), we have Qo = Q I Q2.
5D T) + tr [(C T. D ) . (A T. 5A)]. 46 2. Stressed State of Nonlinearly Elastic Bodies with Dislocations Piola stress tensor fields satisfying the equilibrium equations and the force boundary conditions will be called statically admissible. 8), are expressed in terms of the tensor of stress functions, ,~, which should meet the boundary conditions on the surface of multiply connected body n . (rot • + D*) = f. e. the vectors f and k are some given functions of Lagrangian coordinates. 8) can be transformed into the following V.
Consider now formulation of the system of equilibrium equations for a nonlinearly elastic body with continuously distributed field of translational dislocations when the density c~ is given in advance. 8), forms the full system for the unknowns C (p) and C (e). 44 2. 9) is the variation of a functional ~, called the potential of external loads, with respect to the displacement vector, ~ pk . ~Rdv + ~ f . SRda = 5E. ~,,YYdv - t~. 6) with given parameters bk, qk on the cuts 7k. Since 5u = 5R we can consider the vector field R , specifying the location of body particles in the deformed configuration, as an argument of the functional ,4 instead of the displacement field, u.
Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies by Leonid M. Zubov
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