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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...

Temperature Dependent Deformation

Temperature Dependent Deformation

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 together...

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...

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...

Deformation of a Beam under Transverse Loading

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...

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Related Experiment Video

Updated: Jul 3, 2026

A Microfluidic Technique to Probe Cell Deformability

A Microfluidic Technique to Probe Cell Deformability

Published on: September 3, 2014

Modeling cellular deformations using the level set formalism.

Liu Yang¹, Janet C Effler, Brett L Kutscher

¹Electrical & Computer Engineering, Johns Hopkins University, Baltimore, MD 21218, USA. liuyang@jhu.edu

BMC Systems Biology

|July 26, 2008

Summary

Level set methods (LSM) simplify cell shape simulations by implicitly defining cell boundaries, avoiding complex grid updates. This approach accurately models cell deformations, aiding in understanding cellular signaling and movement.

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Measuring the Mechanical Properties of Living Cells Using Atomic Force Microscopy

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Last Updated: Jul 3, 2026

A Microfluidic Technique to Probe Cell Deformability

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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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Measuring the Mechanical Properties of Living Cells Using Atomic Force Microscopy

Measuring the Mechanical Properties of Living Cells Using Atomic Force Microscopy

Published on: June 27, 2013

Area of Science:

Biophysics
Computational Biology
Cell Biology

Background:

Cellular processes often involve significant shape changes, traditionally requiring complex grid and boundary updates in simulations.
Existing simulation methods for cell shape dynamics are computationally intensive due to the need to track evolving boundaries.

Purpose of the Study:

To demonstrate the efficacy of level set methods (LSM) for simulating cell shape changes.
To integrate a viscoelastic model of Dictyostelium cells into LSM for accurate shape change recreation.
To simulate cell responses to external stimuli, such as chemotaxis.

Main Methods:

Utilized micropipette aspiration to derive a viscoelastic model for Dictyostelium cells.
Implemented level set methods (LSM) for implicit representation of cellular shapes.
Incorporated the viscoelastic model into LSM simulations to model cell protrusion and chemotactic responses.

Main Results:

Successfully recreated observed cell protrusions into a micropipette using LSM and a viscoelastic model.
Demonstrated the simulation of cell shape changes during chemotaxis in response to an external chemoattractant gradient.
Validated LSM as an effective method for simulating dynamic cellular deformations.

Conclusions:

Level set methods offer a simplified yet effective approach for incorporating cellular deformations into mathematical simulations.
These LSM-based simulations are valuable tools for studying cell signaling, chemotaxis, and cytokinesis.
The developed methods provide a foundation for more accurate and efficient modeling of complex cellular behaviors.