Plasticity of Pressure-Sensitive Materials by Holm Altenbach, Andreas Öchsner

By Holm Altenbach, Andreas Öchsner

Classical plasticity concept of metals is self sufficient of the hydrostatic strain. even if if the steel comprises voids or pores or if the constitution consists of cells, this classical assumption isn't any extra legitimate and the effect of the hydrostatic strain has to be included within the constitutive description. taking a look at the microlevel, steel plasticity is hooked up with the uniform planes of atoms geared up with long-range order. Planes might slip earlier one another alongside their close-packed instructions. the result's an enduring switch of form in the crystal and plastic deformation. The presence of dislocations raises the possibility of planes slipping.

Nowadays, the idea of strain delicate plasticity is effectively utilized to many different very important sessions of fabrics (polymers, concrete, bones etc.) no matter if the phenomena at the micro-level are assorted to classical plasticity of metals. The theoretical historical past of this phenomenological technique according to observations at the macro-level is defined intimately during this monograph and utilized to a variety of diverse very important fabrics within the final a part of this book.

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It depends only on the kinematical variables and the temperature: U =U (kinematic variables, θ ). If we divide a homogeneous system with the mass m into n homogeneous subsystems with the masses m i the following statement is valid 24 H. Altenbach and V. A. Eremeyev Ui = n mi U , i = 1, . . , n, m n Ui = U , i=1 mi = m (77) i=1 Intensive variables are independent of the amount of the continuum. If we divide now the system which is in an equilibrium state, into n subsystems, than the intensive state variable in each subsystem has the same value.

The data are taken from various sources and they are related to different manufacturers. They can be used as first estimates only. Note that the experiments were performed for specimens with different geometries and using different techniques. The relations d and k of the materials can be represented in Figs. 4 and 5 together with the models in order to simplify the choice of the suitable model [104]. 4 Inelastic Poisson’s Ratio In the linear theory of elasticity the Poisson’s ratio is defined as the negative ratio of the strain εII = εIII in the direction orthogonal to the applied load and the strain εI in the tension direction [20, 89]: ν el = − εII εIII =− , εI εI ν el ∈ −1, 1 .

Cosserat Theories: Shells Rods and Points. Kluwer, Dordrecht (2000) 20. : Materialtheorie. Springer, Berlin (1986) 21. : The Foundations of Mechanics and Thermodynamics. Springer, Berlin (1974) 22. : What is the general constitutive equation? In: Beiträge Festschrift zum 65 . Geburtstag von Rudolf Trostel, TU Berlin. Berlin, pp. 28–37 (1994) 23. : Phänomenologische Rheologie : eine Einführung. Springer, Berlin (1994) 24. : Rheologie. Fachbuchverlag, Leipzig (1968) 25. : A First Course in Rational Continuum Mechanics, Pure and Applied Mathematics, vol.

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