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Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

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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...
398
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

329
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...
329
Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

676
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,...
676
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

537
When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
537
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

782
One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
782
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

295
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...
295

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Related Experiment Video

Updated: Dec 29, 2025

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

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Deformable objects modeling with iterative updates of local positions.

Hyehyun Han1, Doo Yong Lee1

  • 1Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.

Computer Methods and Programs in Biomedicine
|February 5, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for real-time simulation of deformable objects, accurately modeling material properties like stiffness for virtual environments. The technique achieves high accuracy with less than 15% error, enabling efficient simulations.

Keywords:
Deformable-objects modelingNonlinear modelPhysics-based simulationReal-time simulation

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Related Experiment Videos

Last Updated: Dec 29, 2025

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Area of Science:

  • Computational mechanics
  • Virtual reality simulation
  • Biomedical engineering

Background:

  • Real-time simulation of deformable objects, like human soft tissues, is computationally intensive.
  • Existing methods struggle with computational overhead, hindering interactive applications.
  • Accurate modeling of material properties is crucial for realistic virtual environments.

Purpose of the Study:

  • To propose a new modeling method for deformable objects enabling real-time simulation.
  • To control the desired behavior of virtual objects using material properties.
  • To reduce computational complexity while maintaining simulation accuracy.

Main Methods:

  • Utilizes the Saint Venant-Kirchhoff model for nonlinear material behavior.
  • Combines the governing equation with a position-based dynamics iterative solver.
  • Employs local position updates to minimize element energy and a grouping method for computational order.

Main Results:

  • Simulates various dynamic behaviors corresponding to different Young's moduli.
  • Achieves relative errors below 15% compared to ANSYS for Young's modulus between 4-10 kPa.
  • Demonstrates real-time performance using a liver model with 596 tetrahedral elements.

Conclusions:

  • The proposed method successfully simulates model stiffness in real-time based on material properties.
  • Faithful representation of material properties is achieved for deformable objects.
  • Enables efficient and accurate real-time simulations for applications requiring elastic material deformation.