Material Strain Tensor

  • Pavel A. Zhilin
  • Holm Altenbach
  • Elena A. Ivanova
  • Anton KrivtsovEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 22)


The problem of description of large inelastic deformations of solids is considered. On a simple discrete model it is shown that the classical concept of deformations used in continuum mechanics can exhibit serious difficulties due to reorganizations of the internal structure of materials. The way of construction of constitutive equations in continuum mechanics aimed to avoid these problems is proposed. A method of introduction of material strain tensor for the inelastic continuum is suggested. The paper is based on the report: P. A. Zhilin, A.  Krivtsov: Point mass simulation of inelastic extension process. It was prepared for the ICIAM 95 (Third International Congress on Industrial and Applied Mathematics, Hamburg, Germany, July 3–7, 1995), but not accepted for publication.


Strain Tensor Anisotropic Material Inelastic Deformation Cauchy Stress Tensor Logarithmic Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Authors are deeply grateful to O.T. Bruhns for helpful discussions of the final version of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pavel A. Zhilin
    • 1
    • 2
  • Holm Altenbach
    • 1
  • Elena A. Ivanova
    • 2
  • Anton Krivtsov
    • 2
    Email author
  1. 1.Faculty of Mechanical EngineeringOtto-von-Guericke UniversityMagdeburgGermany
  2. 2.Saint Petersburg State Polytechnical University, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences St. PetersburgRussia

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