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Related Concept Videos

Generalized Hooke's Law01:22

Generalized Hooke's Law

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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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Temperature Dependent Deformation01:12

Temperature Dependent Deformation

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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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Circular Shafts - Elastoplastic Materials01:24

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The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
As torque on the...
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Viscosity of Fluid01:19

Viscosity of Fluid

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Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
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Sample Preparation in Quartz Crystal Microbalance Measurements of Protein Adsorption and Polymer Mechanics
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Human cornea thermo-viscoelastic behavior modelling using standard linear solid model.

Hassan M Ahmed1, Nancy M Salem2, Walid Al-Atabany2,3

  • 1Biomedical Engineering Department, Helwan University, Helwan, Egypt. hassan.gbr@h-eng.helwan.edu.eg.

BMC Ophthalmology
|June 5, 2023
PubMed
Summary
This summary is machine-generated.

Mathematical modeling accurately simulates human corneal viscoelasticity and thermal behavior. The Standard Linear Solid model is superior for predicting corneal response to loading, ensuring safety within FDA thermal limits.

Keywords:
Corneal biomechanicsCorneal modellingCorneal thermal behaviorCorneal viscoelasticity

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Area of Science:

  • Ophthalmology
  • Biomedical Engineering
  • Computational Mechanics

Background:

  • Corneal biomechanics is crucial for understanding corneal diseases and refractive surgery outcomes.
  • In-vivo and ex-vivo studies of corneal biomechanics face significant limitations.
  • Mathematical modeling offers a viable solution to study in-vivo corneal viscoelasticity under realistic conditions.

Purpose of the Study:

  • To simulate corneal viscoelasticity and thermal behavior using mathematical models.
  • To evaluate the efficacy of Kelvin-Voigt and Standard Linear Solid models for corneal viscoelasticity.
  • To assess the temperature rise in corneal tissue during simulated loading.

Main Methods:

  • Three mathematical models were employed: Kelvin-Voigt, Standard Linear Solid (SLS), and a bioheat transfer model.
  • Viscoelasticity was simulated under constant and transient loading conditions.
  • Thermal behavior was analyzed using the SLS model to calculate temperature rise.

Main Results:

  • The Standard Linear Solid model demonstrated superior accuracy in simulating human corneal viscoelastic behavior under both loading conditions.
  • SLS model-derived deformation amplitudes align better with clinical findings than Kelvin-Voigt.
  • Calculated corneal temperature rise was approximately 0.2°C, adhering to FDA safety regulations.

Conclusions:

  • The Standard Linear Solid model is more effective for describing human corneal responses to constant and transient loads.
  • The simulated temperature rise of ~0.2°C is well within FDA safety limits for soft tissues.
  • Mathematical modeling, particularly with the SLS model, provides a safe and accurate method for corneal biomechanical analysis.