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

Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

4.0K
Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
4.0K
Quantifying Work02:30

Quantifying Work

23.0K
As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system.
23.0K
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

26.0K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
26.0K
Second Law of Thermodynamics00:53

Second Law of Thermodynamics

66.5K
The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
66.5K
Castigliano's Theorem01:18

Castigliano's Theorem

762
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
762
Entropy01:18

Entropy

3.3K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.3K

You might also read

Related Articles

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

Sort by
Same author

Dynamics in Explicit Gradient Elasticity: Material Frame-Indifference, Boundary Conditions and Consistent Euler-Bernoulli Beam Theory.

Materials (Basel, Switzerland)·2024
See all related articles

Related Experiment Video

Updated: Nov 27, 2025

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation
11:11

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

Published on: May 2, 2016

11.4K

Non-Conventional Thermodynamics and Models of Gradient Elasticity.

Hans-Dieter Alber1, Carsten Broese2, Charalampos Tsakmakis2

  • 1Faculty of Mathematics, Technische Universität Darmstadt, Schlossgartenstraße 7, D-64289 Darmstadt, Germany.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a novel gradient elasticity theory that deviates from Toupin-Mindlin

Keywords:
boundary conditionsenergy transfer lawgradient elasticityinterstitial workingnon-equilibrium thermodynamics

More Related Videos

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

741
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

13.3K

Related Experiment Videos

Last Updated: Nov 27, 2025

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation
11:11

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

Published on: May 2, 2016

11.4K
Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

741
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

13.3K

Area of Science:

  • Continuum Mechanics
  • Thermodynamics
  • Materials Science

Background:

  • Gradient elasticity theories model material response using strain and its gradient.
  • Toupin-Mindlin's theory defines Cauchy stress tensors via Euler-Lagrange derivatives of free energy.
  • Existing theories may not encompass all possible stress tensor formulations.

Purpose of the Study:

  • To develop a non-conventional gradient elasticity theory.
  • To formulate Cauchy stress tensors not solely dependent on Euler-Lagrange derivatives.
  • To explore alternative thermodynamic frameworks for material modeling.

Main Methods:

  • Development of a new gradient elasticity framework.
  • Application of non-conventional thermodynamics.
  • Solution of a one-dimensional boundary value problem.

Main Results:

  • A novel gradient elasticity theory is established.
  • The theory allows for Cauchy stress tensors beyond Euler-Lagrange derivatives.
  • Illustrative boundary value problem highlights theoretical distinctions.

Conclusions:

  • The proposed non-Toupin-Mindlin gradient elasticity offers a broader scope.
  • This framework expands the possibilities for modeling material behavior.
  • Further research can explore advanced applications of this theory.