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In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials.


N20110023650

Publication Date 2011
Personal Author Nemeth, M. P.
Page Count 588
Abstract An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.
Keywords
  • Constitutive equations
  • Anisotropy
  • Temperature effects
  • Hookes law
  • Axes(Reference lines)
  • Symmetry
  • Rotation
  • Coordinates
Source Agency
  • National Aeronautics and Space Administration
Corporate Authors National Aeronautics and Space Administration, Hampton, VA. Langley Research Center.
Supplemental Notes Text in English. Publicly available Unlimited. CASI.
Document Type Technical Report
NTIS Issue Number 201212
In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials.
In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials.
N20110023650

  • Constitutive equations
  • Anisotropy
  • Temperature effects
  • Hookes law
  • Axes(Reference lines)
  • Symmetry
  • Rotation
  • Coordinates
  • National Aeronautics and Space Administration
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