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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear.

Kareem Khirallah1, Botond Tyukodi1,2, Damien Vandembroucq3

  • 1Northeastern University, Boston, Massachusetts 02115, USA.

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|June 11, 2021
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Summary
This summary is machine-generated.

This study models amorphous solids under cyclic shear, revealing three steady states: elastic, limit cycles, and irreversible plasticity. Critical transitions show power-law divergences in cycles and diffusivity, indicating yielding behavior.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Modeling

Background:

  • Amorphous solids exhibit complex mechanical behaviors under cyclic loading.
  • Understanding the transitions between elastic, plastic, and chaotic regimes is crucial for material design.

Purpose of the Study:

  • To investigate the steady-state behaviors of an amorphous solid model under cyclic shear.
  • To characterize the transitions between different deformation regimes, particularly yielding.

Main Methods:

  • Utilized an automaton model to simulate amorphous solid behavior.
  • Analyzed system response across varying strain amplitudes.
  • Identified distinct steady-state regimes and transition dynamics.

Main Results:

  • Identified three steady states: pure elastic, limit cycles, and irreversible plasticity.
  • Observed power-law divergences in the number of cycles (N) and diffusivity (D) near the yielding transition.
  • Found that the average period (T) of limit cycles increases approaching the yielding point.

Conclusions:

  • The automaton model successfully captures yielding phenomena in amorphous solids.
  • Power-law scaling characterizes critical transitions, providing insights into material failure.
  • Cyclic shear reveals distinct regimes with predictable behaviors near yielding.