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Open AccessArticle

Verification of Continuum Mechanics Predictions with Experimental Mechanics

1
Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
2
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70126 Bari, Italy
3
MXD Corporation, 1415 N. Cherry Avenue, Chicago, IL 60642, USA
*
Author to whom correspondence should be addressed.
Materials 2020, 13(1), 77; https://doi.org/10.3390/ma13010077
Received: 13 September 2019 / Revised: 27 November 2019 / Accepted: 11 December 2019 / Published: 22 December 2019
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. View Full-Text
Keywords: representative volume element (RVE); kinematical variables; derivatives of displacements; large deformations; constitutive models; Al–SiC composite material; urethane rubber representative volume element (RVE); kinematical variables; derivatives of displacements; large deformations; constitutive models; Al–SiC composite material; urethane rubber
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MDPI and ACS Style

Sciammarella, C.A.; Lamberti, L.; Sciammarella, F.M. Verification of Continuum Mechanics Predictions with Experimental Mechanics. Materials 2020, 13, 77. https://doi.org/10.3390/ma13010077

AMA Style

Sciammarella CA, Lamberti L, Sciammarella FM. Verification of Continuum Mechanics Predictions with Experimental Mechanics. Materials. 2020; 13(1):77. https://doi.org/10.3390/ma13010077

Chicago/Turabian Style

Sciammarella, Cesar A.; Lamberti, Luciano; Sciammarella, Federico M. 2020. "Verification of Continuum Mechanics Predictions with Experimental Mechanics" Materials 13, no. 1: 77. https://doi.org/10.3390/ma13010077

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