Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

824
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
824
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

668
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
668
Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

535
The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
535
Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

726
Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
726
Residual Stresses in Bending01:18

Residual Stresses in Bending

688
In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
688
Generalized Hooke's Law01:22

Generalized Hooke's Law

3.2K
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
3.2K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

PEO-Reinforced Hydrogel-Forming PVA Nanofibrous Mats Prepared by Coaxial Electrospinning: A Physicochemical Basis for Biomedical Evaluation.

Chemical & pharmaceutical bulletin·2026
Same author

A multiscale theory for network advection- reaction-diffusion.

Journal of mathematical biology·2026
Same author

PRKAG2 Cardiomyopathy: A Case-Control Study on the Diagnostic Yield Of Histopathology and Ultrastructural Analysis from Endomyocardial Biopsy.

Arquivos brasileiros de cardiologia·2026
Same author

A universal phase-plane model for in vivo protein aggregation.

The Journal of chemical physics·2026
Same author

State-of-the-art and tomorrow's challenges and opportunities in constitutive modeling of soft biological tissues with a focus on arterial, cardiac and brain biomechanics.

Acta biomaterialia·2026
Same author

Dynamical <math><mi>A</mi> <mi>β</mi></math> -Tau-Neurodegeneration Model Predicts Alzheimer's Disease Mechanisms and Biomarker Progression.

bioRxiv : the preprint server for biology·2026
Same journal

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta.

Proceedings. Mathematical, physical, and engineering sciences·2025
Same journal

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

Proceedings. Mathematical, physical, and engineering sciences·2023
Same journal

The Elbert range of magnetostrophic convection. I. Linear theory.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Soft wetting with (a)symmetric Shuttleworth effect.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

The quantum theory of time: a calculus for q-numbers.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Integrable nonlinear evolution equations in three spatial dimensions.

Proceedings. Mathematical, physical, and engineering sciences·2022
See all related articles

Related Experiment Video

Updated: May 4, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

12.6K

Nonlinear elastic inclusions in isotropic solids.

Arash Yavari1, Alain Goriely2

  • 1School of Civil and Environmental Engineering, The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|December 20, 2013
PubMed
Summary
This summary is machine-generated.

This study presents a geometric framework for calculating residual stress and deformation in nonlinear solids with inclusions. The method maps material manifolds to Euclidean space, simplifying stress analysis for various symmetries and elastic properties.

Keywords:
geometric elasticityinclusionsresidual stresses

More Related Videos

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
09:39

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

Published on: June 28, 2024

1.9K
Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.5K

Related Experiment Videos

Last Updated: May 4, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

12.6K
Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
09:39

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

Published on: June 28, 2024

1.9K
Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.5K

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Geometric Analysis

Background:

  • Residual stresses and deformations in solids with inclusions are complex to model.
  • Eigenstrains within inclusions define different reference configurations, complicating analysis.

Purpose of the Study:

  • To introduce a novel geometric framework for calculating residual stress fields and deformations.
  • To analyze nonlinear solids containing inclusions and eigenstrains.

Main Methods:

  • Developed a geometric framework utilizing Riemannian manifolds to represent eigenstrains.
  • Reduced the residual stress calculation to a mapping problem from a material manifold to Euclidean space.
  • Applied the framework to model systems with spherical and cylindrical symmetries.

Main Results:

  • Successfully calculated residual stress fields for incompressible and compressible isotropic elastic solids.
  • Demonstrated uniform, hydrostatic stress within a spherical inclusion subjected to dilatational eigenstrain.
  • Identified stress singularities arising from mismatched eigenstrains at specific geometric locations.

Conclusions:

  • The geometric framework provides an effective method for analyzing residual stresses in solids with inclusions.
  • The approach simplifies complex problems by leveraging differential geometry.
  • The findings offer insights into stress concentrations and material behavior under specific loading conditions.