Experimental Mechanics, Tool to Verify Continuum Mechanics Predictions

  • C. A. SciammarellaEmail author
  • L. Lamberti
  • F. M. Sciammarella
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


This paper is devoted to the experimental verification of a very fundamental concept in the mechanics of materials, the representative volume element (RVE). This concept is a bridge between the theoretical concept of the continuum and the actual discontinuous structure of matter. We begin with reviewing the pertinent concepts of the kinematics of the continuum, the mathematical functions that relate displacement vectorial fields, the recording of these fields by a sensor as scalar fields of gray levels.

The derivative field tensors corresponding to the Eulerian description are then connected to the deformation of the continuum. The differential geometry that provides the deformation of an element of area is introduced. From this differential geometry of an element of area, the Euler-Almansi tensor is extracted. Properties of the Euler-Almansi tensor are derived. The next step is the analysis of the relationship between kinematic and dynamic variables: that is, the connection between strains and stresses in the Eulerian description between the Euler-Almansi tensor with the Cauchy stress tensor.

In the experimental part of the paper, some relationships between components of the Euler-Almansi tensor are verified. An example of an experimental verification of the concept of RVE is given. Finally, the verification for the fact that the Euler-Almansi and Cauchy stress sensor tensors are conjugate tensors in the Hill-Mandel sense is presented.


Representative volume element (RVE) Statistical volume element (SVE) Kinematical variables Derivatives of displacements Euler-Almansi strain tensor Cauchy stress tensor 


  1. 1.
    Sciammarella, C. A., Lamberti, L., & Sciammarella, F. M. (2019). The optical signal analysis (OSA) method to process fringe patterns containing displacement information. Optics and Lasers in Engineering, 115, 225–237.CrossRefGoogle Scholar
  2. 2.
    Sciammarella, C. A., & Lamberti, L. (2015). Basic models supporting experimental mechanics of deformations, geometrical representations, connections among different techniques. Meccanica, 50, 367–387.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Durelli, A. J., & Parks, V. J. (1970). Moiré analysis of strain. Englewood Cliffs, NJ: Prentice-Hall, Inc.Google Scholar
  4. 4.
    Sciammarella C.A. (1960). Theoretical and experimental study on moiré fringes. PhD dissertation, Illinois Institute of Technology, Chicago (USA).Google Scholar
  5. 5.
    Sciammarella, C. A., Sciammarella, F. M., & Kim, T. (2003). Strain measurements in the nanometer range in a particulate composite using computer-aided moiré. Experimental Mechanics, 43, 341–347.CrossRefGoogle Scholar
  6. 6.
    Sciammarella, C. A., & Nair, S. (1998). Micromechanics study of particulate composites. In Proceedings of the SEM Spring Conference on Experimental Mechanics (pp. 188–189).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  • C. A. Sciammarella
    • 1
    • 2
    Email author
  • L. Lamberti
    • 3
  • F. M. Sciammarella
    • 2
  1. 1.Department of Mechanical, Materials and Aerospace EngineeringIllinois Institute of TechnologyChicagoUSA
  2. 2.Department of Mechanical EngineeringNorthern Illinois UniversityDeKalbUSA
  3. 3.Dipartimento Meccanica, Matematica e ManagementPolitecnico di BariBariItaly

Personalised recommendations