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Related Concept Videos

Temperature Dependent Deformation01:12

Temperature Dependent Deformation

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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...
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Elastic Strain Energy for Shearing Stresses01:20

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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...
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When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
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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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When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
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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.
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Related Experiment Video

Updated: Mar 21, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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Molecular dynamics at constant Cauchy stress.

Ronald E Miller1, Ellad B Tadmor2, Joshua S Gibson1

  • 1Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Ontario K1S5B6, Canada.

The Journal of Chemical Physics
|May 16, 2016
PubMed
Summary

The Parrinello-Rahman algorithm controls the second Piola-Kirchhoff stress, not the true Cauchy stress, in molecular dynamics. A modified algorithm directly controls Cauchy stress, improving simulation accuracy for materials under stress.

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Area of Science:

  • Computational materials science
  • Condensed matter physics
  • Molecular dynamics simulations

Background:

  • The Parrinello-Rahman algorithm is a standard method for applying stress in molecular dynamics.
  • This algorithm controls the second Piola-Kirchhoff stress, not the true Cauchy stress.
  • Discrepancies between these stress measures can lead to misinterpretations in simulations.

Purpose of the Study:

  • To address the limitations of the Parrinello-Rahman algorithm regarding stress control.
  • To propose a modification for directly controlling the true Cauchy stress.
  • To validate the improved algorithm's performance in simulating materials under stress.

Main Methods:

  • Modification of the Parrinello-Rahman algorithm.
  • Implementation of direct Cauchy stress control.
  • Simulation of martensitic phase transformations under applied stress.

Main Results:

  • The modified algorithm successfully controls the true Cauchy stress directly.
  • Simulation results show the impact of direct Cauchy stress control on phase transformations.
  • The proposed method offers a more accurate approach to stress application in molecular dynamics.

Conclusions:

  • The direct control of Cauchy stress is crucial for accurate molecular dynamics simulations.
  • The modified Parrinello-Rahman algorithm provides a more reliable method for imposing stress.
  • This advancement is vital for studying material behavior under mechanical load, such as phase transformations.