Instytut Podstawowych Problemów Techniki

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In the paper the yield condition is proposed for the most general anisotropic material. It is one of the possible generalizations of the Huber-Mises-Hencky yield condition for the case of anisotropy. The body considered is anisotropic elastically as well as plastically. It is assumed that the plastic anisotropy tensor is a definite function of the elastic anisotropy tensor. The corresponding flow function is a part of the strain energy and its value remains unchanged when all normal components of stress are increased by the same value. The theory of the eigen states for fourth order tensors is used. The plastic anisotropy tensor proposed has the same deviatoric eigen states as the elastic anisotropy tensor. The proposed yield condition reduces to that of Huber-Mises-Hencky when the anisotropy is vanishingly small. The method presented in this paper can be also applied to describe other types of plastic anisotropy tensor.

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The paper is concerned with a nonlinear description of the kinetics of crack propagation in bodies exhibiting rheological properties. The analysis is based on the concept of a time-dependent cohesion modulus for an ageing nonlinear viscoelastic material. A simple model of an infinite thin plate with a rectilinear crack is considered. The discussion is followed by some conclusions.

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The paper consists of two parts. The first part is devoted to a discussion of the constitutive equations describing the dynamic properties of soils. In the second part, the relaxation problem in an elastic/visco-plastic soil is considered.

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The lecture presents a synthetic survey on the theory of viscoplasticity (reflecting the rate-sensitive dynamic properties of materials). Some examples of its applications are also discussed (relaxation phenomena occurring in elastic/visco-plastic media as well as the propagation of stress waves in such continua). Besides, we generalize the existing theories by introducing a nonstationary yield condition (variable with time). Finally we propose a further generalization of the yield criterion based on the notion of the conserved (accumulated) as well as the dissipated energy.

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The theory of plasticity represents one of the branches of rapidly developing continuum mechanics. The progress consists of both a careful analysis of the basic equations and physical relations and an extension of the range of problems and effective solutions covered by this theory. In real media the non-homogeneity of mechanical properties may be caused by numerous phenomena and its nature may be very diverse. First, it is evident that a universal property of bodies occurring in practice is their microscopic non-homogeneity. It is well- known that there have been many successful1 attempts to include microscopic non-homogeneity in the structure of Continuum Theory. The objective of the chapter, however, is the macroscopic nonhomogeneity that is taking place in regions whose linear dimensions are comparable with the characteristic dimensions of the body under consideration. The nonhomogeneity of mechanical properties may be caused, for instance, by phenomena such as the influence of flow of elementary particles, the action of temperature gradients, a nonhomogeneous hardening of the material, different types of surface working, nonhomogeneity of the composition, and so on.

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