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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...

Elasticity

Elasticity

Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...

Plastic Deformations

Plastic Deformations

Plastic deformation represents a fundamental concept in materials science, which explains the irreversible change in the shape of a material when it experiences stress beyond its elastic capability. This phenomenon is important in structural engineering, especially in designing and analyzing cantilever beams—structures that are securely fixed at one end and bear loads at the opposite end. When these beams are subjected to loads within their elastic range, they will return to their original...

Plastic Deformations

Plastic Deformations

It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...

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.

Residual Stresses in Bending

Residual Stresses in Bending

In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...

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Related Experiment Video

Updated: Jul 7, 2026

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

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

Published on: April 16, 2017

Reconstructive elasticity imaging for large deformations.

A R Skovoroda¹, L A Lubinski, S Y Emelianov

¹Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Russia 142292.

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|February 2, 2008

Summary

This summary is machine-generated.

This study presents a new method for reconstructing soft tissue elastic modulus using ultrasound, even with large deformations. The advanced technique ensures accurate results comparable to linear models, improving medical imaging capabilities.

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Area of Science:

Biomechanics
Medical Imaging
Materials Science

Background:

Accurate reconstruction of soft tissue elastic modulus is crucial for medical diagnosis.
Traditional methods struggle with large deformations, limiting their clinical applicability.
Nonlinear elastic models are necessary for significant tissue deformation analysis.

Purpose of the Study:

To develop and validate a novel method for reconstructing soft tissue elastic modulus from ultrasound data.
To address the limitations of linear elastic models in scenarios with large deformations.
To improve the accuracy and reliability of ultrasound-based tissue characterization.

Main Methods:

Utilizing ultrasonic displacement and strain images for reconstruction.
Implementing nonlinear displacement-strain relations to account for large deformations.
Developing numerical methods to minimize error propagation in higher-order derivative calculations.

Main Results:

Successfully reconstructed elastic modulus for soft tissues with large deformations.
Demonstrated that nonlinear algorithms yield image quality equivalent to linear models.
Validated the method using ultrasound measurements on tissue-equivalent phantoms.

Conclusions:

The presented method accurately reconstructs soft tissue elastic modulus under large deformations.
Nonlinear elastic models and advanced numerical techniques are essential for high-fidelity ultrasound-based biomechanical analysis.
This approach enhances the potential of ultrasound for quantitative tissue assessment in clinical settings.