Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Generalized Hooke's Law01:22

Generalized Hooke's Law

807
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...
807
Bending of Members Made of Several Materials01:08

Bending of Members Made of Several Materials

139
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...
139
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

249
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.
249
Hooke's Law01:26

Hooke's Law

344
Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
344

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

Correction: Yu et al. High-Efficiency PDLC Smart Films Enabled by Crosslinking Agent Optimization and MoS<sub>2</sub> Nanosheets for Energy-Saving Windows. <i>Materials</i> 2025, <i>18</i>, 5139.

Materials (Basel, Switzerland)·2026
Same journal

Correction: Memon et al. Incorporation of Wheat Straw Ash as Partial Sand Replacement for Production of Eco-Friendly Concrete. <i>Materials</i> 2021, <i>14</i>, 2078.

Materials (Basel, Switzerland)·2026
Same journal

Correction: Ren et al. The Effect of Cu Content on the Microstructure and Properties of the Wire Arc Additive Manufacturing Al-Cu Alloy. <i>Materials</i> 2023, <i>16</i>, 2694.

Materials (Basel, Switzerland)·2026
Same journal

Correction: Chao, S. Influence of Crossrib Configuration on Bond-Slip Behavior for High-Strength Reinforcement in Concrete. <i>Materials</i> 2025, <i>18</i>, 3221.

Materials (Basel, Switzerland)·2026
Same journal

Feasibility Study of Diffusion Welding of Microcomposite Copper-Niobium Conductors.

Materials (Basel, Switzerland)·2026
Same journal

Multiscale Investigation of the Factors Governing Ice-Asphalt Interfacial Adhesion Strength: Insights from Pull-Off Tests and Molecular Simulations.

Materials (Basel, Switzerland)·2026

Related Experiment Video

Updated: Jun 3, 2025

A Facile and Eco-friendly Route to Fabricate PolyLactic Acid Scaffolds with Graded Pore Size
13:46

A Facile and Eco-friendly Route to Fabricate PolyLactic Acid Scaffolds with Graded Pore Size

Published on: October 17, 2016

8.6K

Numerical Homogenization of Orthotropic Functionally Graded Periodic Cellular Materials: Method Development and

Behnam Shahbazian1, Victor Bautista Katsalukha1, Mirmilad Mirsayar1

  • 1Department of Aerospace, Physics, and Space Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA.

Materials (Basel, Switzerland)
|January 8, 2025
PubMed
Summary

This study computes elastic properties of 2D functionally graded microcellular materials using numerical homogenization. Novel MATLAB codes accurately predict material behavior, accounting for orthotropy and void geometry effects.

Keywords:
2D numerical homogenizationMATLAB codeelasticity tensorisotropic materialsorthotropic materialsperiodic functionally graded cellular materials

More Related Videos

Additive Manufacturing of Functionally Graded Ceramic Materials by Stereolithography
06:53

Additive Manufacturing of Functionally Graded Ceramic Materials by Stereolithography

Published on: January 25, 2019

14.3K
Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.4K

Related Experiment Videos

Last Updated: Jun 3, 2025

A Facile and Eco-friendly Route to Fabricate PolyLactic Acid Scaffolds with Graded Pore Size
13:46

A Facile and Eco-friendly Route to Fabricate PolyLactic Acid Scaffolds with Graded Pore Size

Published on: October 17, 2016

8.6K
Additive Manufacturing of Functionally Graded Ceramic Materials by Stereolithography
06:53

Additive Manufacturing of Functionally Graded Ceramic Materials by Stereolithography

Published on: January 25, 2019

14.3K
Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.4K

Area of Science:

  • Materials Science
  • Computational Mechanics
  • Additive Manufacturing

Background:

  • Functionally graded materials (FGMs) with microcellular structures are crucial in additive manufacturing.
  • Understanding their macroscopic elastic properties is essential for design and application.
  • Existing methods may not fully capture anisotropic behavior arising from complex microstructures.

Purpose of the Study:

  • To develop and validate a computational framework for determining the macroscopic elastic properties of 2D periodic functionally graded microcellular materials.
  • To investigate the influence of material anisotropy (isotropic and orthotropic phases) and void geometry on overall material behavior.
  • To assess the impact of void pattern complexity and stochasticity on prediction accuracy.

Main Methods:

  • Numerical homogenization applied to each cell, treated as a material point.
  • Development of novel MATLAB codes (Cellular_Solid, Homogenize_test, homogenize_ortho, Homogenize_test_ortho_principal).
  • Derivation of a fitting function to map cell-level properties to macroscopic behavior based on scale separation principle.

Main Results:

  • The method accurately captures orthotropic effects and the influence of void geometry on macroscopic anisotropies.
  • The elasticity tensor correctly reflects differing E1 and E2 values, indicating anisotropy.
  • Increased complexity and stochasticity in void patterns lead to higher prediction errors.

Conclusions:

  • The developed numerical homogenization approach effectively predicts elastic properties of 2D FGMs.
  • Advanced fitting methods (e.g., Fourier series) and machine learning can enhance accuracy.
  • The framework is extensible to composite materials with multiple orthotropic phases and various void shapes.