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Members Made of Elastoplastic Material

Members Made of Elastoplastic Material

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...

Deformations in a Transverse Cross Section

Deformations in a Transverse Cross Section

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...

Residual Stresses in Bending

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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...

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...

Plastic Deformations

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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

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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.

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Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

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Published on: June 28, 2024

Longitudinal elastic wave control by pre-deforming semi-linear materials.

Dengke Guo¹, Yi Chen¹, Zheng Chang²

¹School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China.

The Journal of the Acoustical Society of America

|October 2, 2017

Summary

This summary is machine-generated.

Pre-deforming hyper-elastic materials offers a novel method to control elastic waves. This technique allows for distinct manipulation of longitudinal and shear waves, opening avenues for new material and device designs.

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Area of Science:

Solid Mechanics
Materials Science
Wave Physics

Background:

Hyper-elastic materials exhibit large, non-linear deformations.
Controlling elastic wave propagation is crucial for advanced material applications.
Finite pre-deformation can alter the elastic properties of materials.

Purpose of the Study:

To investigate the control of elastic waves in pre-deformed hyper-elastic materials.
To explore the differential treatment of longitudinal and shear waves.
To demonstrate wave control and band structure manipulation via pre-deformation.

Main Methods:

Theoretical analysis of wave propagation in semi-linear elastic materials under symmetric pre-deformation.
Form invariance analysis for longitudinal and shear waves.
Development of a one-dimensional spring lattice model to mimic semi-linear behavior.

Main Results:

Governing equations for longitudinal waves maintain form invariance under pre-deformation, enabling transformation-based control.
Shear wave behavior does not exhibit the same form invariance, allowing for differential wave manipulation.
Demonstration of elastic wave control and band structure shifts through pre-deformation, validated by a spring lattice model.

Conclusions:

Pre-deforming semi-linear hyper-elastic materials provides a versatile platform for controlling elastic waves differently.
This approach facilitates distinct manipulation of longitudinal and shear wave propagation.
Findings may inspire the design of novel hyper-elastic microstructures and devices.