Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Discrete and Continuum Thermomechanics

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_67-1



An approach for transition from discrete to continuum description of thermomechanical behavior of solids is discussed. The transition is carried out for several perfect anharmonic crystals with pair force interactions: one-dimensional crystal, quasi-one-dimensional crystal (a chain possessing longitudinal and transverse motions), two- and three-dimensional crystals with simple lattice. Macroscopic balance equations are derived from equations of motion for particles using continualization. Macroscopic parameters, such as stress, heat flux, deformation, thermal energy, etc., are represented via parameters of the discrete system. An approach for derivation of equations of state relating thermal pressure, thermal energy, and specific volume is presented. Derivation of constitutive equations for heat transfer is...

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This work was supported by the Russian Science Foundation (RSCF grant No. 17-71-10213).


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Authors and Affiliations

  1. 1.Department of Theoretical MechanicsPeter the Great Saint Petersburg Polytechnic UniversitySaint PetersburgRussia
  2. 2.Laboratory for Discrete Models in MechanicsInstitute for Problems in Mechanical Engineering RASSaint PetersburgRussia

Section editors and affiliations

  • Elena Ivanova
    • 1
  1. 1.Department of Theoretical Mechanics, Institute of Applied Mathematics and MechanicsPeter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia