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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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.

Generalized Hooke's Law

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...

Shape and Texture of Coarse Aggregate

Shape and Texture of Coarse Aggregate

Aggregate shape is classified based on the relative sharpness or roundness of the edges and corners. This classification includes categories like rounded, angular, elongated, and flaky, each with specific characteristics. Rounded aggregates, fully shaped by attrition, are typical of river or seashore gravel, while angular aggregates, such as crushed rock, have well-defined edges. Aggregates that are elongated and flaky are less desirable, as they can reduce the workability and strength of...

Elastic Strain Energy for Shearing Stresses

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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...

Eccentric Axial Loading in a Plane of Symmetry

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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.

General Case of Eccentric Axial Loading

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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from symmetrical bending, which are essential for designing structures to withstand different loading conditions.
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical...

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Related Experiment Video

Updated: Apr 18, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Published on: September 29, 2019

Angularly anisotropic correlation in granular packings.

Chengjie Xia¹, Yixin Cao¹, Binquan Kou¹

¹Department of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 24, 2015

Summary

This summary is machine-generated.

This study reveals that random granular packings exhibit locally favored structures. These structures create an orientation-dependent correlation, highlighting the importance of higher-order structural analysis in granular materials.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

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Published on: September 29, 2019

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

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Published on: May 20, 2018

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

Physics
Materials Science
Engineering

Background:

Granular materials are ubiquitous in nature and industry.
Understanding their structural properties is crucial for predicting macroscopic behavior.
Previous studies often focused on lower-order correlations, potentially missing key structural information.

Purpose of the Study:

To investigate three-dimensional structural correlations in monodisperse granular packings.
To identify and characterize locally favored structures within these packings.
To explore the relationship between local structure and macroscopic properties.

Main Methods:

Utilizing X-ray microtomography for high-resolution 3D imaging.
Measuring an orientation-dependent pair correlation function.
Analyzing the local Minkowski tensor of Voronoi cells.

Main Results:

Discovered angularly anisotropic orientation correlations in the local structure.
Found the strongest correlation aligned with the major axis of the Voronoi cell's Minkowski tensor.
Observed that this anisotropy supports the existence of locally favored structures.

Conclusions:

Anisotropic correlations are key to understanding granular packing structures.
Locally favored structures significantly influence the arrangement of particles.
High-order structural correlations are essential for a comprehensive analysis of random granular packings.