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Related Concept Videos

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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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Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
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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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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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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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The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Pseudo-bistability of viscoelastic shells.

Yuzhen Chen1,2, Tianzhen Liu2,3, Lihua Jin2

  • 1Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, People's Republic of China.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 12, 2023
PubMed
Summary

Viscoelastic shells can exhibit pseudo-bistability, temporarily staying inverted after pressure removal before snapping back. This study models and explains this time-dependent phenomenon in shells, including ellipsoidal shapes.

Keywords:
bucklingellipsoidal shellspseudo-bistabilityshell theorysnap-throughviscoelasticity

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Nonlinear Dynamics

Background:

  • Viscoelastic shells display complex time-dependent behaviors under pressure.
  • Pseudo-bistability, where shells remain inverted post-pressure removal, is a key phenomenon.
  • Understanding this requires integrated models of shell mechanics and material viscoelasticity.

Purpose of the Study:

  • To develop and validate a model for pseudo-bistability in viscoelastic shells.
  • To elucidate the underlying mechanism of delayed snap-back in these structures.
  • To investigate the influence of various parameters on pseudo-bistable behavior.

Main Methods:

  • Development of a viscoelastic shell model combining small strain, moderate rotation theory with a standard linear solid constitutive law.
  • Application to arbitrary axisymmetric shell shapes, with a focus on ellipsoidal shells.
  • Analysis of stability transitions via pressure-volume change relations over time.

Main Results:

  • Successful prediction of buckling, creeping, and delayed snap-back in viscoelastic ellipsoidal shells.
  • Demonstration of stability transitions from monostable to temporarily bistable states and back.
  • Identification of key geometric, material, and loading history effects on pseudo-bistability.

Conclusions:

  • The proposed model accurately captures the pseudo-bistability of viscoelastic shells.
  • Pseudo-bistability is a consequence of the interplay between shell deformation and viscoelastic creep.
  • The findings offer insights into the dynamic response of viscoelastic structures.