Verification of Continuum Mechanics Predictions with Experimental Mechanics
The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. Thi...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2019-12-01
|
Series: | Materials |
Subjects: | |
Online Access: | https://www.mdpi.com/1996-1944/13/1/77 |
id |
doaj-c4c58baf1b394a2a8ccb58c12f59e012 |
---|---|
record_format |
Article |
spelling |
doaj-c4c58baf1b394a2a8ccb58c12f59e0122020-11-25T01:15:22ZengMDPI AGMaterials1996-19442019-12-011317710.3390/ma13010077ma13010077Verification of Continuum Mechanics Predictions with Experimental MechanicsCesar A. Sciammarella0Luciano Lamberti1Federico M. Sciammarella2Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USADipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70126 Bari, ItalyMXD Corporation, 1415 N. Cherry Avenue, Chicago, IL 60642, USAThe general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler−Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler−Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al−SiC composite material is carried out. Furthermore, it is proven that the Euler−Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill−Mandel sense by solving an identification problem of the constitutive model of urethane rubber.https://www.mdpi.com/1996-1944/13/1/77representative volume element (rve)kinematical variablesderivatives of displacementslarge deformationsconstitutive modelsal–sic composite materialurethane rubber |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Cesar A. Sciammarella Luciano Lamberti Federico M. Sciammarella |
spellingShingle |
Cesar A. Sciammarella Luciano Lamberti Federico M. Sciammarella Verification of Continuum Mechanics Predictions with Experimental Mechanics Materials representative volume element (rve) kinematical variables derivatives of displacements large deformations constitutive models al–sic composite material urethane rubber |
author_facet |
Cesar A. Sciammarella Luciano Lamberti Federico M. Sciammarella |
author_sort |
Cesar A. Sciammarella |
title |
Verification of Continuum Mechanics Predictions with Experimental Mechanics |
title_short |
Verification of Continuum Mechanics Predictions with Experimental Mechanics |
title_full |
Verification of Continuum Mechanics Predictions with Experimental Mechanics |
title_fullStr |
Verification of Continuum Mechanics Predictions with Experimental Mechanics |
title_full_unstemmed |
Verification of Continuum Mechanics Predictions with Experimental Mechanics |
title_sort |
verification of continuum mechanics predictions with experimental mechanics |
publisher |
MDPI AG |
series |
Materials |
issn |
1996-1944 |
publishDate |
2019-12-01 |
description |
The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler−Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler−Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al−SiC composite material is carried out. Furthermore, it is proven that the Euler−Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill−Mandel sense by solving an identification problem of the constitutive model of urethane rubber. |
topic |
representative volume element (rve) kinematical variables derivatives of displacements large deformations constitutive models al–sic composite material urethane rubber |
url |
https://www.mdpi.com/1996-1944/13/1/77 |
work_keys_str_mv |
AT cesarasciammarella verificationofcontinuummechanicspredictionswithexperimentalmechanics AT lucianolamberti verificationofcontinuummechanicspredictionswithexperimentalmechanics AT federicomsciammarella verificationofcontinuummechanicspredictionswithexperimentalmechanics |
_version_ |
1725153668922081280 |