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Path-independent integrals to identify localized plastic events in two dimensions
Mehdi Talamali1, Viljo Petäjä, Damien Vandembroucq
1Unité Mixte CNRS-Saint-Gobain Surface du Verre et Interfaces, 39 Quai Lucien Lefranc, 93303 Aubervilliers cedex, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
This study introduces a computational method to analyze elastic fields from plastic deformation. It identifies key singularities related to material strain, aiding in understanding amorphous material plasticity.
Area of Science:
- Solid Mechanics
- Materials Science
- Computational Physics
Background:
- Understanding localized plastic deformation is crucial for materials science.
- Existing models may not fully capture the complexities of amorphous material plasticity.
Purpose of the Study:
- To develop a computational framework for analyzing elastic fields induced by localized plastic deformation.
- To associate dominant elastic field singularities with specific types of plastic strain.
Main Methods:
- Utilizing a power expansion representation of complex potentials (Kolossov-Muskhelishvili method).
- Constructing holomorphic functions from displacement fields and their derivatives.
- Defining path-independent Cauchy integrals to quantify singularity amplitudes.
Main Results:
- Identified dominant first-order singularities (quadrupolar and dipolar) far from the deformation center.
- Associated these singularities with pure deviatoric and pure volumetric plastic strain, respectively.
- Presented analytical expressions and validated with finite-element data.
Conclusions:
- The developed numerical tools can identify local structural reorganizations in amorphous materials.
- These tools offer a pathway to better understand the fundamental mechanisms of plasticity in amorphous solids.
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