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Related Concept Videos

Stress: General Loading Conditions01:15

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 Stress01:23

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...
General State of Stress01:21

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...
Transformation of Plane Stress01:18

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
Principal Stresses: Problem Solving01:15

Principal Stresses: Problem Solving

When analyzing two planes intersecting at right angles under the influence of shearing, tensile, and compressive stresses, it is essential to identify principal planes, maximum shearing stress, and principal stresses. To find the principal planes, apply a formula that equates them to twice the shearing stress divided by the difference between tensile and compressive stresses.
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...

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Related Experiment Video

Updated: Jun 22, 2026

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
10:36

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction

Published on: May 20, 2018

Subparticle stress fields in granular solids.

Vincent Topin1, Farhang Radjai, Jean-Yves Delenne

  • 1LMGC, CNRS-Université Montpellier 2, UMR 5508, Pl. E. Bataillon, 34095 Montpellier Cedex 5, France.

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

This study shows that stress distributions in granular solids with interstitial matrices, like concrete, mirror those in simpler granular materials. This extends known properties of force distributions to complex, real-world materials.

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10:36

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Published on: May 20, 2018

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Area of Science:

  • Geomechanics
  • Materials Science
  • Computational Mechanics

Background:

  • Granular solids with interstitial matrices are common in engineering materials.
  • Understanding stress distribution at subparticle scales is crucial for material behavior.
  • Existing models often simplify granular media, lacking interstitial phases.

Purpose of the Study:

  • To simulate and analyze stress fields at subparticle scales in 2D granular solids.
  • To investigate the influence of particle stiffness and interstitial matrix volume fraction.
  • To compare subscale stress analysis with particle-scale discrete element methods.

Main Methods:

  • Utilized the lattice element method for subparticle scale simulations.
  • Modeled 2D granular solids with variable particle stiffness and matrix volume fractions.
  • Analyzed contact force and stress distributions.

Main Results:

  • Subscale stress analysis yields contact force distributions similar to discrete element methods.
  • Stress distributions are exponential at contact zones.
  • Particle phase dominates compression, matrix phase dominates tension.
  • Tension stress distributions broaden with decreasing matrix fraction; compression is stiffness-dependent.

Conclusions:

  • Well-known granular media properties extend to complex materials like concrete and sandstone.
  • The lattice element method effectively captures stress field behavior in heterogeneous granular solids.
  • Findings provide insights into the mechanical behavior of composite materials.