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Related Concept Videos

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...
Bending of Members Made of Several Materials01:11

Bending of Members Made of Several Materials

In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Bending of Material: Problem Solving01:09

Bending of Material: Problem Solving

In this lesson, determine the ratio of the maximum bending moments applied to two metal pipes, given that both pipes can withstand a maximum stress of 100 MPa. Both pipes have an outer radius of 1.8 cm. Pipe A has an inner radius of 1.5 cm, and Pipe B has an inner radius of 1 cm. The ratio of the maximum bending moment applied to two metallic pipes, each with a different inner and outer radius, is determined by considering their dimensions. The inner radius of the first pipe is 1.5 cm, and for...
Bending and Torsional Moments01:20

Bending and Torsional Moments

Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions.
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

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Related Experiment Video

Updated: Jun 2, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
09:32

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

Physical modeling with orthotropic material based on harmonic fields.

Sheng-Hui Liao1, Bei-Ji Zou, Jian-Ping Geng

  • 1School of Information Science and Engineering, Central South University, Changsha 410083, China. shliao@zju.edu.cn

Computer Methods and Programs in Biomedicine
|May 17, 2011
PubMed
Summary

This study introduces a new method for creating accurate finite element models of bone tissue, incorporating its natural orthotropic properties. This approach improves simulations of stress and strain, crucial for understanding bone mechanics.

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A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
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Published on: May 18, 2015

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Last Updated: Jun 2, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
09:32

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Published on: April 11, 2018

A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
11:28

A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials

Published on: May 18, 2015

Area of Science:

  • Biomechanics
  • Computational Solid Mechanics
  • Materials Science

Background:

  • Human bone exhibits orthotropic material properties, meaning its mechanical characteristics differ along different axes.
  • Previous physical modeling often used simplified isotropic or transversely isotropic models due to computational ease.
  • Accurate orthotropic modeling is essential for realistic simulations of bone behavior.

Purpose of the Study:

  • To present a novel and convenient methodology for constructing volumetric finite element meshes with complete orthotropic material properties for bone.
  • To integrate the inherent orthotropic nature of bone tissue into computational models.
  • To improve the accuracy of finite element analyses in biomechanics.

Main Methods:

  • Generation of surface harmonic fields to define the longitudinal axis direction aligned with maximum material stiffness.
  • Adaptive extraction and sampling of scalar iso-contours to create high-quality volumetric meshes.
  • Expansion of surface harmonic fields into volumetric harmonic fields to derive orthotropic principal axes vector fields.
  • Finite element analysis using the developed orthotropic models.

Main Results:

  • The developed methodology successfully generated volumetric finite element meshes reflecting bone's orthotropic properties.
  • Harmonic fields effectively defined principal material axes aligned with bone geometry.
  • Finite element analyses showed that elastic orthotropy significantly impacts stress and strain simulations, both in magnitude and distribution.

Conclusions:

  • The proposed harmonic field-based methodology provides a convenient way to integrate complete orthotropic material properties into bone finite element models.
  • Accurate orthotropic modeling is critical for reliable simulation of mechanical responses in bone tissues.
  • This work advances the accuracy and relevance of computational biomechanical studies of bone.