Related Experiment Video
Updated: May 16, 2026
10:09
Fast Imaging Technique to Study Drop Impact Dynamics of Non-Newtonian Fluids
Published on: March 5, 2014
Projecting low-dimensional chaos from spatiotemporal dynamics in a model for plastic instability.
Ritupan Sarmah1, G Ananthakrishna
1Materials Research Centre, Indian Institute of Science, Bangalore 560012, India. ritupan@mrc.iisc.ernet.in
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
Summary
This study reveals low-dimensional chaos in plastic instability models. Spatiotemporal dynamics correlate with stress serrations, showing chaos even at low strain rates.
Area of Science:
- Materials Science
- Physics
- Nonlinear Dynamics
Background:
- Plastic instability in materials under constant strain rate deformation is modeled.
- Dislocation bands and stress serrations are key features of this instability.
Purpose of the Study:
- To investigate the potential for projecting low-dimensional chaos from spatiotemporal dynamics.
- To explore the relationship between dislocation band patterns and stress serrations.
- To analyze the chaotic nature of the model at varying strain rates.
Main Methods:
- Analysis of spatiotemporal patterns in a plastic instability model.
- Calculation of Lyapunov exponents and Lyapunov dimension.
- Application of a modified algorithm for correlation dimension density calculation.
Main Results:
- A one-to-one correspondence exists between dislocation density bursts and stress drops at low strain rates.
- The model equations exhibit spatiotemporal chaos, with Lyapunov exponents scaling with system size.
- Stress-strain signals at low strain rates show features of low-dimensional chaos, reducible to space-independent equations.
Conclusions:
- Low-dimensional chaos can be projected from the spatiotemporal dynamics of plastic instability models.
- Increasing strain rates reduce the correlation dimension scaling regime due to enhanced dislocation band propagation.
More Related Videos
11:51Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
06:55Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
Published on: August 5, 2016
Related Concept Videos
01:14Plastic 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...
01:19Plastic 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...
01:21Plastic Behavior
A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and reloaded.
02:17Microtubule Instability
Microtubules are hollow cylindrical filaments having a diameter of approximately 25 nm and a length that varies from 200 nm to 25 μm. GTP-bound tubulin subunits form αβ-heterodimers for microtubule assembly. These core building blocks interact longitudinally, polymerizing into protofilaments. The protofilaments then interact with one another through lateral bonding forces to form stable cylindrical microtubules. These cylindrical filaments are dynamic as they undergo repeated assembly and...
01:21Plastic Deformations of Members with a Single Plane of Symmetry
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...
00:58Plasticity
Plasticity is the property where an object loses its elasticity and undergoes irreversible deformation, even after the deformation forces are eliminated. If a material deforms irreversibly without increasing stress or load, then this is called ideal plasticity. For example, when a force is applied to an aluminum rod, it changes its shape, but it does not return to its original shape once the force is removed. Plastic deformation or ductility is thus a permanent deformation or change in the...