Transformation Properties of the Lagrangian and Eulerian Strain Tensors

Abstract

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates. The Eulerian strain is a two-point tensor that transforms as a second rank tensor under transformation of spatial coordinates and transforms as a scalar under transformation of the material coordinates. The Lagrangian strain is a two-point tensor that transforms as a scalar under transformation of spatial coordinates and transforms as a second rank tensor under transformation of the material coordinates. These transformation properties are needed when transforming the strain tensors from one frame of reference to another moving frame.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2002
Accession Number
ADA400671

Entities

People

  • Thomas B. Bahder

Organizations

  • United States Army Research Laboratory

Tags

DTIC Thesaurus Topics

  • Army Aviation
  • Cartesian Coordinates
  • Coordinate Systems
  • Delta Functions
  • Displacement
  • Equations
  • Four Dimensional
  • Geometry
  • Materials
  • Military Research
  • Molecular Dynamics
  • Notation
  • Particles
  • Relative Motion
  • Three Dimensional
  • Translations
  • Transport Ships

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Materials Science (Mechanical Engineering).