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Related Concept Videos

Thermal Sigmatropic Reactions: Overview01:16

Thermal Sigmatropic Reactions: Overview

Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred to as...
Cranial Bones: Lateral View01:27

Cranial Bones: Lateral View

The lateral view of the cranium is dominated by temporal, sphenoid, and ethmoid bones.
The temporal bone forms the lower lateral side of the skull. The temporal bone is subdivided into several regions. The flattened upper portion is the squamous portion of the temporal bone. Below this area and projecting anteriorly is the zygomatic process of the temporal bone, which forms the posterior portion of the zygomatic arch. Posteriorly is the mastoid portion of the temporal bone. Projecting...
Thermal expansion and Thermal stress: Problem Solving01:27

Thermal expansion and Thermal stress: Problem Solving

San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
Generalized Hooke's Law01:22

Generalized Hooke's Law

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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Thermal Strain

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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Cranial Bones: Superior and Posterior View

The superior view of the cranium shows the frontal and paired parietal bones.
The frontal bone is the single bone that forms the forehead. At its anterior midline, between the eyebrows, there is a slight depression called the glabella. The frontal bone also forms the supraorbital margin of the orbit. Near the middle of this margin is the supraorbital foramen, the opening that provides passage for a sensory nerve to the forehead. The frontal bone is thickened just above each supraorbital margin,...

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A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
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An efficient method of modeling material properties using a thermal diffusion analogy: an example based on

Julian L Davis1, Elizabeth R Dumont, David S Strait

  • 1Department of Engineering, University of Southern Indiana, Evansville, Indiana, United States of America. jldavis2@usi.edu

Plos One
|February 25, 2011
PubMed
Summary

Researchers developed a novel finite element method using thermal diffusion to accurately model bone

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Area of Science:

  • Biomechanics
  • Computational modeling
  • Materials science

Background:

  • Finite element models (FEM) enable detailed analysis of skeletal components' morphology and material properties.
  • Incorporating complex material models (e.g., orthotropic) into bone FEM is challenging due to spatially varying material properties.

Purpose of the Study:

  • To present a novel, simplified method for incorporating spatially varying material properties into bone finite element models.
  • To improve the accuracy of bone mechanical response simulations.

Main Methods:

  • Utilized a finite element program's thermal-structural analysis capabilities.
  • Employed a thermal diffusion analogy to spatially propagate material modulus based on seeded temperatures.
  • Solved for the mechanical response of the model under applied loads and constraints.

Main Results:

  • The thermal diffusion analogy effectively and simply controlled spatially varying modulus in bone FEM.
  • Simulation results showed favorable comparison with experimental data.
  • Results also aligned well with a traditional FEM using complex orthotropic material models.

Conclusions:

  • The thermal diffusion analogy offers an accessible method for integrating complex material property data into bone FEM.
  • This approach enhances the accuracy and applicability of computational models in skeletal research.