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Related Concept Videos

Temperature Dependent Deformation01:12

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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...
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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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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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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Rigidity transitions in zero-temperature polygons.

M C Gandikota1,2, Amanda Parker1,3, J M Schwarz1,4

  • 1Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York, USA.

Physical Review. E
|December 23, 2022
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Summary
This summary is machine-generated.

Geometric properties predict material rigidity transitions in polygon networks. Convexity and cyclic configurations are key indicators of self-stress emergence, enabling prediction of rigidity changes in underconstrained systems.

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Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Computational Physics

Background:

  • Underconstrained systems, like spring networks, can exhibit a rigidity transition.
  • This transition is linked to the emergence of system-spanning self-stress.
  • Understanding the geometric factors influencing this transition is crucial for predicting material behavior.

Purpose of the Study:

  • To investigate the geometric clues associated with rigidity transitions in systems of polygons and spring networks.
  • To establish a connection between polygon geometry and the onset of self-stress.
  • To develop purely geometrical methods for predicting rigidity transitions and transition strain.

Main Methods:

  • Analysis of individual polygons with harmonic bond edges and area spring constraints under expansive strain.
  • Mathematical proof establishing convexity as a necessary and cyclic configuration as a sufficient condition for self-stress.
  • Examination of two-dimensional spring networks under isotropic expansive strain to identify geometric features at the rigidity transition.

Main Results:

  • Polygon convexity is a necessary condition for self-stress; cyclic configuration is sufficient.
  • The fraction of convex, non-cyclic polygons predicts the onset of the rigidity transition in networks.
  • Acyclic polygons correlate with larger tensions, forming effective force chains within the network.

Conclusions:

  • The study establishes a direct link between polygon geometry and system rigidity.
  • Geometrical analysis can accurately predict the onset and strain of rigidity transitions in underconstrained systems.
  • Findings provide a method to determine the rigidity of area-preserving polygons and networks based solely on their geometry.