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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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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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The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
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Stress is a quantity that describes the magnitude of a force that causes deformation, generally defined as internal force per unit area. When forces pull on an object and cause its elongation, like the stretching of an elastic band, it is called tensile stress. When forces cause the compression of an object, it is known as compressive stress. When an object is being squeezed uniformly from all sides, like a submarine in the depths of the ocean, we call this kind of stress bulk stress (or volume...
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Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry
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Shear-induced rigidity in athermal materials: A unified statistical framework.

Sumantra Sarkar1, Bulbul Chakraborty1

  • 1Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2015
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Shear-induced solidification in athermal systems like grains and suspensions is universal. A new model explains shear jamming and discontinuous shear thickening, clarifying the roles of shear forces and packing fraction.

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Area of Science:

  • Soft Matter Physics
  • Statistical Mechanics
  • Athermal Systems

Background:

  • Shear jamming in dry grains and discontinuous shear thickening in suspensions are distinct phenomena.
  • Similarities suggest underlying universal physical processes for shear-induced rigidity in athermal materials.

Purpose of the Study:

  • To present a nonequilibrium statistical mechanics model for shear-driven rigidity transitions.
  • To identify universal physical processes and clarify the roles of shear forces and packing fraction.

Main Methods:

  • Development of a nonequilibrium statistical mechanics model.
  • Analysis of phase diagrams to identify distinct phenomenological regions.
  • Investigation of shear-driven transitions.

Main Results:

  • The model successfully reproduces shear jamming and discontinuous shear thickening.
  • Identified crucial physical processes underlying shear-induced rigidity.
  • Clarified the distinct contributions of shearing forces and packing fraction.

Conclusions:

  • Shear-induced rigidity in athermal systems exhibits universal physical principles.
  • The model provides a framework for understanding these phenomena across different materials.