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Related Concept Videos

Singularity Functions for Shear01:26

Singularity Functions for Shear

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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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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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Liquid–Solid Solutions01:29

Liquid–Solid Solutions

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The process of a solid dissolving in a liquid to form a solution is governed by the solubility limit, which is the maximum amount of the solid substance, or solute, that can be dissolved in a specific volume of the liquid or solvent. As the solute dissolves, it reaches a point where no more solute can be dissolved at a given temperature - this is known as the saturation point. However, if further solute is added and it manages to dissolve, the solution becomes supersaturated. Supersaturated...
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Singularity Functions for Bending Moment01:18

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
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A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and...
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Stress Singularities in Swelling Soft Solids.

Alain Goriely1, Johannes Weickenmeier2, Ellen Kuhl2

  • 1Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.

Physical Review Letters
|October 8, 2016
PubMed
Summary
This summary is machine-generated.

Swelling soft solids bulge through openings, creating high stresses near the edge, similar to the punch indentation problem. This research analyzes these stresses and bulging shapes, considering potential damage from high shear or fiber stretch.

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Area of Science:

  • Biomechanics
  • Materials Science
  • Surgical Innovation

Background:

  • Swelling soft solids exhibit outward bulging when confined with an opening.
  • This phenomenon is relevant to decompressive craniectomy, a neurosurgical procedure for reducing intracranial pressure.
  • Understanding stress concentrations is crucial for predicting material behavior and potential damage.

Purpose of the Study:

  • To investigate the stresses generated in a swelling soft solid constrained with a circular opening.
  • To analyze the evolution of the bulging shape during the expansion process.
  • To explore the potential for damage initiation due to high stress concentrations.

Main Methods:

  • Theoretical analysis of stress singularities in swelling solids.
  • Modeling the bulging shape and its dynamic evolution.
  • Examination of stress fields, including shear and fiber stretch.

Main Results:

  • High stresses, exhibiting singularity, develop near the opening of the constrained swelling solid.
  • The elastic energy decreases as the solid swells and bulges.
  • Identified zones of high shear stress and fiber stretch as potential damage triggers.

Conclusions:

  • The bulging of swelling soft solids under constraint generates significant stress concentrations.
  • Decompressive craniectomy may involve similar mechanics, highlighting the need to understand stress singularities.
  • Further investigation into damage mechanisms related to shear and fiber stretch is warranted.