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Deformation of Member under Multiple Loadings

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...

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.

Temperature Dependent Deformation

Temperature Dependent Deformation

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...

Deformation of a Beam under Transverse Loading

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...

Normal Strain under Axial Loading

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...

Plastic Behavior

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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...

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Related Experiment Video

Updated: Jul 19, 2025

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

Deformation and Force Chain of Two-Dimensional Granular Systems under Continuous Loading.

Fanxiu Chen¹, Yuxin Liu¹, Yuan Wang¹

¹School of Science, Qingdao University of Technology, Qingdao 266520, China.

Materials (Basel, Switzerland)

|August 12, 2023

Summary

This study reveals how force chains evolve in granular systems under continuous loading. Granule properties and arrangement significantly influence these force chains and the material

Keywords:

contact force digital image correlation (DIC)force chain granular system soil modeling

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Last Updated: Jul 19, 2025

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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High-pressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus

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Published on: April 3, 2018

Area of Science:

Granular Mechanics
Materials Science
Physics of Complex Systems

Background:

Understanding granular material behavior under stress is crucial for engineering applications.
Force chains, paths of force transmission, are key to granular material mechanics.
Previous studies often focused on static or simplified loading conditions.

Purpose of the Study:

To investigate the dynamic evolution of force chains in a 2D granular system under continuous line loading.
To analyze the relationship between granule properties, contact forces, and force chain network development.
To correlate force chain evolution with macroscopic mechanical responses of the granular system.

Main Methods:

Continuous loading experiment on a 2D granular system.
Digital Image Correlation (DIC) for deformation field analysis.
Granule Element Method (GEM) for quantitative contact force calculation and force chain identification.

Main Results:

The deformation field and temporal changes in granule deflection angles and coordination numbers were captured.
Internal force chains within the granular system were successfully identified and analyzed.
The evolution of force chains was found to be directly influenced by granule number, geometry, and distribution at the loading interface.

Conclusions:

Force chain formation, evolution, and reconstruction are dynamic processes during granular system loading.
The network evolution of force chains significantly impacts the macroscopic mechanical properties of granular materials.
Granule characteristics at the contact with external load are primary drivers for force chain evolution.