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

Strain and Elastic Modulus01:15

Strain and Elastic Modulus

The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
Thermal Strain01:19

Thermal Strain

Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
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

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.
Thermal Expansion01:22

Thermal Expansion

The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surrounding air, which then exerts an upward force on the hot air to, for example, make steam and smoke rise, and hot air balloons float. The same behavior happens in all liquids and gases,...
Generalized Hooke's Law01:22

Generalized Hooke's Law

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...
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...

You might also read

Related Articles

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

Sort by
Same author

Soft matrix: probing local mechanical properties in amorphous solids.

Soft matter·2026
Same author

Influence of Particle Size Polydispersity on Dynamical Heterogeneities in Dense Particle Packings.

Chemphyschem : a European journal of chemical physics and physical chemistry·2026
Same author

Role of fragility of the glass formers in the yielding transition under oscillatory shear.

Nature communications·2026
Same author

Tuning fragility in sodium lead borate glasses: Unveiling the interplay between compositions, Stokes-Einstein breakdown, and dynamical heterogeneity.

The Journal of chemical physics·2026
Same author

Aging of amorphous materials under cyclic strain.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Yielding and Memory in a Driven Mean-Field Model of Glasses.

Physical review letters·2026

Related Experiment Video

Updated: Jun 8, 2026

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
07:44

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

Published on: April 27, 2016

Athermal nonlinear elastic constants of amorphous solids.

Smarajit Karmakar1, Edan Lerner, Itamar Procaccia

  • 1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary

We derived expressions for nonlinear elastic constants in amorphous solids under athermal conditions. These constants are crucial for understanding plastic flow, fracture, and plasticity-induced memory in these materials.

More Related Videos

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
08:58

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid

Published on: December 2, 2022

Related Experiment Videos

Last Updated: Jun 8, 2026

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
07:44

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

Published on: April 27, 2016

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
08:58

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid

Published on: December 2, 2022

Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Solid Mechanics

Background:

  • Amorphous solids exhibit unique mechanical behaviors, including plastic flow and fracture, particularly under athermal conditions.
  • Nonlinear elastic properties are critical for understanding the response of these materials beyond the linear elastic regime.

Purpose of the Study:

  • To derive expressions for the lowest nonlinear elastic constants (up to third order) of amorphous solids in athermal conditions.
  • To elucidate the role of these constants in material instabilities and elastoplasticity.
  • To connect athermal nonlinear elastic theories with existing thermal theories.

Main Methods:

  • Derivation of analytical expressions for nonlinear elastic constants based on inter-particle potentials.
  • Analysis of the convergence of athermal expressions with thermal theories at zero temperature.
  • Development of a differential equation for Hessian eigenvalues near mechanical instabilities.

Main Results:

  • Expressions for the lowest nonlinear elastic constants of amorphous solids were derived.
  • The significance of these constants in athermal plastic flow, fracture, and plasticity-induced memory (e.g., Bauschinger effect) was demonstrated.
  • A differential equation predicting the vanishing of Hessian eigenvalues at mechanical instability was obtained.

Conclusions:

  • Nonlinear elastic constants are essential for describing the behavior of amorphous solids near mechanical instabilities.
  • The derived expressions provide a foundation for predicting material failure and plasticity.
  • The study bridges the gap between athermal and thermal theories of nonlinear elasticity.