Developments in Theoretical and Applied Mechanics. by W. A. Shaw

By W. A. Shaw

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By W. A. Shaw

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An example of a notched bar in uniaxial tension is given. The second new concept concerns the strain energy in the slab analogy. It is shown that the strain energy of a dislocation has an analogous relation to the strain energy of a bending slab due to a concentrated moment at the geometrically similar position on the slab. The calculation of a dislocation resistance caused by vacancy clusters and the calculation of the energy increment of a dislocation due to an opening crack are given as examples to illustrate the application of the slab energy analogy.

SNYDER West Virginia University ABSTRACT The rate-type materials treated in this paper have constitutive equations given by a tensor relationship of the form stress-rate=F (strain-rate, current stress, current density) where the functions F are homogeneous of degree one in the strain-rate. A generalized tensor development of some variational, uniqueness, and extremum principles is made in terms of the Piola pseudo-stress and the absolute covariant derivative of the velocity vector. The results are then applied to linear materials and interpreted in terms of the true stress and rate-of-deformation tensors.

A2) can be transformed to 8φ - dxk = M,+^«* and integrating leads to φ=| Aifiids + (2) oikXk + oco where a 0 is a constant of integration. For a rotational dislocation around a circuit we have dco = Jd(ieuUj9i) = JSijWjjkàXk <$>£iMVj,ki+Ukji)dxk = ZijejkjdXk ( A 3 ) where \ ] { and ejk are the displacements and elastic strains, respectively, and Since Hooke's law may be written as (1 + v) 1 mm Eq. (A3) takes the following form: = -Oç,mmini ι r a (V ^)ds - i t s 2 (3) (A4) By writing Γ l and y ί )άω (see (A3)) Eq.

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