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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...

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...

Bending of Members Made of Several Materials

Bending of Members Made of Several Materials

In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...

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...

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...

Mechanisms of Membrane-bending

Mechanisms of Membrane-bending

The living membranes are flexible due to their fluid mosaic nature; however, their bending into different shapes is an active process regulated by specific lipids and proteins. The membrane bending can be transient as seen in vesicles or stable for a long time as in microvilli. Cells regulate the size, location, and duration of the membrane curvature.
Membrane bending can happen due to intrinsic changes in lipid composition or extrinsic association with different proteins. The proteins involved...

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DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

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Published on: October 25, 2017

Constrained random-force model for weakly bending semiflexible polymers.

Panayotis Benetatos¹, Eugene M Terentjev

¹Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 21, 2011

Summary

This summary is machine-generated.

This study modifies the Larkin model for elastic strings under random forces. Constraints on total transverse force and torque were added, reducing random force effects but not altering strong stretching behavior.

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Area of Science:

Statistical physics
Condensed matter physics
Polymer physics

Background:

The Larkin model is a key paradigm for disordered systems, describing elastic strings under quenched random forces.
Understanding the behavior of elastic systems with quenched disorder is crucial in statistical physics.

Purpose of the Study:

To investigate a modified Larkin model with vanishing total transverse force and torque.
To analyze the impact of these constraints on the elastic string's behavior under stretching and compression.

Main Methods:

Modification of the standard Larkin model to include constraints on total transverse force and torque.
Analytical calculations to determine the linear compression coefficient.
Comparison of the constrained model with the original model in different regimes.

Main Results:

The modified model preserves the qualitative behavior in the strong stretching regime.
Constraints significantly reduce the impact of random forces via numerical prefactors.
Transverse random forces induce undulations, softening the filament to compression.

Conclusions:

The constrained Larkin model offers insights into the role of force and torque balance in disordered elastic systems.
The findings highlight how specific constraints can modulate the response of elastic filaments to external forces.
The study quantifies the softening effect of random forces on filament compression.