# Experimental Mechanics, Tool to Verify Continuum Mechanics Predictions

## Author ORCID Identifier

Holly Jones:https://orcid.org/0000-0002-5512-9958

## Publication Title

Conference Proceedings of the Society for Experimental Mechanics Series

## ISSN

21915644

## E-ISSN

21915652

## ISBN

9783030300081

## Document Type

Conference Proceeding

## Abstract

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.

## First Page

13

## Last Page

32

## Publication Date

1-1-2020

## DOI

10.1007/978-3-030-30009-8_3

## Keywords

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

## Recommended Citation

Sciammarella, C. A.; Lamberti, L.; and Sciammarella, F. M., "Experimental Mechanics, Tool to Verify Continuum Mechanics Predictions" (2020). *NIU Bibliography*. 630.

https://huskiecommons.lib.niu.edu/niubib/630

## Department

Department of Mechanical Engineering