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Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
Published on: June 28, 2024
Model of plasticity of amorphous materials
V I Marchenko1, Chaouqi Misbah
1P.L. Kapitza Institute for Physical Problems, RAS, 119334, Kosugina 2, Moscow, Russia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2011
Summary
This study introduces a new dynamical model for plastic flow, extending fluid and solid mechanics. The model describes material behavior, including necking, in a Lagrangian framework.
Area of Science:
- Continuum Mechanics
- Materials Science
- Plasticity Theory
Background:
- Classical plasticity models like the Kröner-Rieder kinematic picture.
- Existing theories for simple fluids, elastic, and viscous solids.
- Inspiration from Langer and coworkers' work on shear-transformation zones.
Purpose of the Study:
- Derive dynamical equations for plastic flow using a Lagrangian formulation.
- Extend classical plasticity theories by incorporating fluid and solid mechanics principles.
- Compare the derived model with Langer's shear-transformation zones model.
Main Methods:
- Lagrangian formulation for plastic flow dynamics.
- Extension of simple fluid, elastic, and viscous solid theories.
- Mathematical derivation and comparison with existing models.
Main Results:
- A set of dynamical equations for plastic flow is derived.
- The Maxwell model is identified as a special limit of the derived equations.
- Necking is shown to manifest in straining of slabs and rods, except under constant-velocity stretching.
Conclusions:
- The derived model offers a novel framework for describing plastic flow.
- The model shares similarities and important differences with the shear-transformation zones model.
- The model provides insights into phenomena like necking in materials.
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