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Stress: General Loading Conditions

Stress: General Loading Conditions

To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.

Components of Stress

Components of Stress

Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and opposite to those on the...

Elastic Strain Energy for Shearing Stresses

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...

General State of Stress

General State of Stress

The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...

Shearing Stress

Shearing Stress

Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.

Shearing Strain

Shearing Strain

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...

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Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

Viscosity, shear waves, and atomic-level stress-stress correlations.

V A Levashov¹, J R Morris, T Egami

¹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA.

Physical Review Letters

|April 8, 2011

Summary

Viscosity is a nonlocal property, not just a local one. Molecular dynamics simulations reveal shear waves propagating over distances relevant to viscosity, challenging previous assumptions.

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Area of Science:

Condensed matter physics
Chemical physics
Materials science

Background:

The Green-Kubo equation links macroscopic viscosity to microscopic stress correlations.
Understanding liquid dynamics requires accurate modeling of stress-stress correlations.

Purpose of the Study:

To investigate the spatial extent of atomic-level stress correlations in liquids.
To determine if viscosity is a local or nonlocal property.
To analyze the influence of simulation conditions on observed correlations.

Main Methods:

Utilizing molecular dynamics simulations to compute atomic-level stresses.
Analyzing space-time correlations of these stresses.
Examining the propagation of longitudinal and transverse waves.

Main Results:

Observed surprisingly long spatial extensions of stress-stress correlations.
Identified shear waves propagating over distances potentially exceeding system size.
Found the range of shear wave propagation correlates with viscosity-relevant distances.

Conclusions:

Viscosity is fundamentally a nonlocal quantity.
Periodic boundary conditions in simulations can mask the long-range nature of viscosity.
These findings necessitate re-evaluation of simulation methodologies for viscosity studies.