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Related Concept Videos

Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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...
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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...
Viscosity of Fluid01:19

Viscosity of Fluid

Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
Plastic Behavior01:21

Plastic Behavior

A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and reloaded.
Normal Strain under Axial Loading01:20

Normal Strain under Axial Loading

Normal strain under axial loading is an important concept in the field of mechanics of materials. Axial loading implies the application of a force along the axis of a material, like a column or bar. This force can either compress or stretch the material. In the context of axial loading, normal strain is the deformation experienced by the material in the direction of the loading force. It's calculated as the change in length divided by the original length of the material. This unitless ratio...
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.

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Related Experiment Video

Updated: Jun 18, 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

Viscoelastic subdiffusion: from anomalous to normal.

Igor Goychuk1

  • 1Institut für Physik, Universität Augsburg, Augsburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

Viscoelastic subdiffusion in complex potentials exhibits unique dynamics. Our findings reveal that transition kinetics deviate from standard theories, especially in high potential barriers, offering new insights into non-Markovian processes.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Subdiffusion is a complex transport phenomenon observed in various systems.
  • Understanding dynamics in potential landscapes is crucial for many scientific fields.
  • Generalized Langevin Equation (GLE) provides a framework for studying anomalous diffusion.

Purpose of the Study:

  • To investigate viscoelastic subdiffusion in bistable and periodic potentials using the GLE approach.
  • To analyze the transition kinetics and residence time statistics in these potentials.
  • To compare the GLE results with existing non-Markovian rate theory (NMRT).

Main Methods:

  • Utilizing the generalized Langevin equation (GLE) framework.
  • Analyzing dynamics in bistable and periodic potential landscapes.
  • Investigating the asymptotic behavior and transient dynamics of subdiffusion.

Main Results:

  • Viscoelastic subdiffusion in bistable potentials shows bursting and anticorrelated residence times.
  • Transition kinetics are asymptotically stretched exponential for high potential barriers (V0 > k(B)T).
  • NMRT approximations improve with increasing barrier height but fail to capture all dynamics.

Conclusions:

  • The study justifies a slow fluctuating rate view for bistable non-Markovian dynamics.
  • Rate descriptions are restored only above a barrier height dependent on subdiffusion exponent alpha.
  • Periodic potentials exhibit long-time insensitivity to barrier height, but transients are slow and barrier-dependent.