Elastoplasticity Theory (Mechanical and Aerospace by Vlado A. Lubarda

By Vlado A. Lubarda

Figuring out the elastoplastic deformation of metals and geomaterials, together with the constitutive description of the fabrics and research of constitution present process plastic deformation, is a necessary a part of the history required by way of mechanical, civil, and geotechnical engineers in addition to fabrics scientists. in spite of the fact that, so much books deal with the topic at a introductory point and in the infinitesimal pressure context.

Elastoplasticity idea takes a special strategy in a sophisticated therapy awarded totally in the framework of finite deformation. This accomplished, self-contained textual content comprises an advent to nonlinear continuum mechanics and nonlinear elasticity. as well as in-depth research of the mathematical and actual theories of plasticity, it furnishes an updated examine modern subject matters, resembling plastic balance and localization, monocrystalline plasticity, micro-to-macro transition, and polycrysalline plasticity models.

Elastoplasticity thought displays contemporary developments and advances made within the concept of plasticity over the past 4 many years. it is going to not just aid stimulate additional examine within the box, yet will permit its readers to optimistically decide on definitely the right constitutive types for the fabrics or structural individuals proper to their very own purposes.

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794–858, Springer-Verlag, Berlin. Eringen, A. C. (1971), Tensor analysis, in Continuum Physics, ed. A. C. Eringen, Vol. 1, pp. 1–155, Academic Press, New York. -H. (1984), Rates of stretch tensors, J. Elasticity, Vol. 14, pp. 263– 267. Hill, R. (1965), Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, Vol. 13, pp. 89–101. Hill, R. (1978), Aspects of invariance in solid mechanics, Adv. Appl. , Vol. 18, pp. 1–75. -I. (1984), Distribution of directional data and fabric tensors, Int.

Vol. 30, pp. 2859–2877. Malvern, L. E. (1969), Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, New Jersey. Ogden, R. W. , Dover, 1997). Rivlin, R. S. (1955), Further remarks on the stress-deformation relations for isotropic materials, J. Rat. Mech. , Vol. 4, pp. 681–701. Scheidler, M. (1994), The tensor equation AX + XA = Φ(A, H), with applications to kinematics of continua, J. Elasticity, Vol. 36, pp. 117–153. Sidoroff, F. (1978), Tensor equation AX + XA = H, Comp.

18) and similarly for the other three decompositions. Its convected and corotational derivatives are ˙ − G · LT , G=G=G ∇ ˙ + G · L, G=G=G ◦ ˙ + G · W. 19) G=G The tensor B = F · G is a spatial tensor, whose convected derivatives are defined by Eqs. 11). The following connections hold B = F · G + F · G, ∇ ∇ ∇ ◦ B = F · G + F · G, ◦ ◦ B = F · G + F · G. 20) The same type of chain rule applies to B and B. Two additional identities exist, which are ∇ ∇ B = F · G + F · G, B = F · G + F · G. 21) On the other hand, the tensor C = G · F is a material tensor, unaffected by convected operations in the deformed configuration, so that ∇ ◦ ˙ C = C = C = C.

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