Tensor-valued random fields in continuum physics

Anatoliy Malyarenko, Martin Ostoja Starzewski

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This article reports progress on homogeneous isotropic tensor random fields (TRFs) for continuum mechanics. The basic thrust is on determining most general representations of the correlation functions as well as their spectral expansions. Once this is accomplished, the second step is finding the restrictions dictated by a particular physical application. Thus, in the case of fields of material properties (like conductivity and stiffness), the restriction resides in the positive-definiteness, whereby a connection to experiments and/or computational micromechanics can be established. On the other hand, in the case of fields of dependent properties (e.g., stress, strain and displacement), restrictions are due to the respective field equations.

Original languageEnglish (US)
Title of host publicationSpringer Tracts in Mechanical Engineering
PublisherSpringer International Publishing
Pages75-87
Number of pages13
DOIs
StatePublished - Jan 1 2016

Publication series

NameSpringer Tracts in Mechanical Engineering
Volume18
ISSN (Print)2195-9862
ISSN (Electronic)2195-9870

Fingerprint

Continuum mechanics
Micromechanics
Tensors
Materials properties
constrictions
Physics
Stiffness
tensors
continuums
physics
micromechanics
continuum mechanics
Experiments
thrust
stiffness
conductivity
expansion

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Civil and Structural Engineering
  • Automotive Engineering
  • Instrumentation
  • Aerospace Engineering
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes
  • Industrial and Manufacturing Engineering

Cite this

Malyarenko, A., & Starzewski, M. O. (2016). Tensor-valued random fields in continuum physics. In Springer Tracts in Mechanical Engineering (pp. 75-87). (Springer Tracts in Mechanical Engineering; Vol. 18). Springer International Publishing. https://doi.org/10.1007/978-3-319-21494-8_6

Tensor-valued random fields in continuum physics. / Malyarenko, Anatoliy; Starzewski, Martin Ostoja.

Springer Tracts in Mechanical Engineering. Springer International Publishing, 2016. p. 75-87 (Springer Tracts in Mechanical Engineering; Vol. 18).

Research output: Chapter in Book/Report/Conference proceedingChapter

Malyarenko, A & Starzewski, MO 2016, Tensor-valued random fields in continuum physics. in Springer Tracts in Mechanical Engineering. Springer Tracts in Mechanical Engineering, vol. 18, Springer International Publishing, pp. 75-87. https://doi.org/10.1007/978-3-319-21494-8_6
Malyarenko A, Starzewski MO. Tensor-valued random fields in continuum physics. In Springer Tracts in Mechanical Engineering. Springer International Publishing. 2016. p. 75-87. (Springer Tracts in Mechanical Engineering). https://doi.org/10.1007/978-3-319-21494-8_6
Malyarenko, Anatoliy ; Starzewski, Martin Ostoja. / Tensor-valued random fields in continuum physics. Springer Tracts in Mechanical Engineering. Springer International Publishing, 2016. pp. 75-87 (Springer Tracts in Mechanical Engineering).
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