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Plasticity of Pressure-Sensitive Materials pp 1–47Cite as

Basic Equations of Continuum Mechanics

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Part of the book series: Engineering Materials ((ENG.MAT.))

Abstract

The modeling of the behavior of pressure-sensitive materials is embedded in the general continuum mechanics. The basic equations of continuum mechanics can be split into the material-independent and the material-dependent equations. The starting point is the introduction of the kinematics based on pure mathematical considerations. In addition, the velocities and the accelerations of the relevant kinematical variables are presented. The next section is devoted to the introduction of the action on the continuum and the inner reaction. Starting with such properties like forces and stresses finally the static equilibrium is stated. The last part of the material-independent equations is the introduction of the balances. Limiting our discussions by thermo-mechanical actions only, the balance of mass, momentum, moment of momentum, energy and entropy are deduced. The specific properties and features of the pressure-sensitive materials are presented in the next sections. Within this chapter the general ideas of material modeling (deductive approach) are given. Finally, some examples of special constitutive equations for incompressible and compressible materials are presented. These examples are mostly related to rubber-like materials.

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Authors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universtät Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Holm Altenbach & Victor A. Eremeyev

  2. South Scientific Center of RASci and South Federal University, Milchakova St. 8a, Rostov on Don, 344090, Russia

    Victor A. Eremeyev

Authors
  1. Holm Altenbach
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  2. Victor A. Eremeyev
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Correspondence to Holm Altenbach .

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Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Griffith School of Engineering, Griffith University, Southport, Australia

    Andreas Öchsner

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Altenbach, H., Eremeyev, V.A. (2014). Basic Equations of Continuum Mechanics. In: Altenbach, H., Öchsner, A. (eds) Plasticity of Pressure-Sensitive Materials. Engineering Materials. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40945-5_1

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  • DOI: https://doi.org/10.1007/978-3-642-40945-5_1

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  • Print ISBN: 978-3-642-40944-8

  • Online ISBN: 978-3-642-40945-5

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