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Related Concept Videos

Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...
Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...
Deformation of Member under Multiple Loadings01:11

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...
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
Next,...
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Planar Rigid-Body Motion

Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
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Related Experiment Video

Updated: May 29, 2026

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production
07:46

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production

Published on: March 27, 2017

Packings of deformable spheres.

Shomeek Mukhopadhyay1, Jorge Peixinho

  • 1Chemistry Department, Columbia University, New York, New York 10027, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary

This study reveals how deformable spheres in disordered packings transition from yielding to withstanding stress. Force and rearrangements depend on packing fraction and velocity, with spheres deforming at higher densities.

Area of Science:

  • Soft Matter Physics
  • Materials Science
  • Rheology

Background:

  • Understanding the mechanical properties of disordered materials is crucial for various applications.
  • Deformable particle packings exhibit complex behaviors not seen in rigid systems.
  • Previous studies often focused on idealized or rigid sphere models.

Purpose of the Study:

  • To experimentally investigate the mechanical behavior of disordered packings of deformable hydrogel spheres.
  • To quantify the relationship between packing fraction, strain, velocity, and forces in these systems.
  • To observe sphere deformation and rearrangement dynamics under compression.

Main Methods:

  • Utilized fluorescent hydrogel spheres immersed in water.
  • Employed 3D tomography for imaging sphere arrangements.

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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

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Last Updated: May 29, 2026

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production
07:46

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production

Published on: March 27, 2017

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

  • Performed compression tests on single spheres and packings within a box with a moving lid.
  • Main Results:

    • Observed a transition from yielding to a stress-bearing state in the packings.
    • Quantified power-law dependencies of normal force on packing fraction and strain at varying velocities.
    • Noted sphere rearrangements during compression-decompression cycles and saturation of coordination number indicating deformation and faceting.

    Conclusions:

    • Disordered packings of deformable spheres exhibit distinct mechanical responses compared to rigid ones.
    • Sphere deformation and rearrangement are key factors governing the macroscopic mechanical properties.
    • The study provides quantitative insights into the force transmission and structural evolution in soft granular materials.