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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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Related Experiment Video

Updated: May 25, 2026

Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry
11:19

Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry

Published on: September 6, 2016

Constitutive model for brain tissue under finite compression.

Kaveh Laksari1, Mehdi Shafieian, Kurosh Darvish

  • 1Department of Mechanical Engineering, Temple University, Philadelphia, PA 19122, USA.

Journal of Biomechanics
|January 28, 2012
PubMed
Summary

This study developed a viscoelastic model for bovine brain tissue under compression, validating quasi-linear viscoelasticity and using generalized Rivlin and Ogden models to capture its mechanical behavior accurately.

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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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Last Updated: May 25, 2026

Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry
11:19

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Published on: September 6, 2016

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
  • Materials Science
  • Biomedical Engineering

Background:

  • Accurate material models for soft tissues, especially brain tissue, are crucial for computational biomechanics.
  • Most research focuses on shear loading, leaving compression behavior less understood.

Purpose of the Study:

  • To develop and validate a viscoelastic constitutive model for bovine brain tissue under uniaxial compression.
  • To investigate the applicability of quasi-linear viscoelasticity (QLV) and specific hyperelastic models for brain tissue.

Main Methods:

  • A viscoelastic constitutive model was developed for finite step-and-hold uniaxial compression (10 s⁻¹ ramp, 20 s hold).
  • Quasi-linear viscoelasticity (QLV) assumption was validated up to 35% strain.
  • Generalized Rivlin and two-parameter Ogden models were used for isochoric and volumetric deformation, respectively.
  • Hyperelastic parameters were fitted to isochronous curves (0.06 s and 14 s).

Main Results:

  • The QLV assumption was valid for strains up to 35%.
  • At least three terms (C(10), C(01), C(11)) of the generalized Rivlin model were necessary for accurate isochoric deformation.
  • The two-parameter Ogden model provided insights into the material's incompressibility.
  • Viscoelastic relaxation was characterized across various decay rates, with comparisons to existing models in compression and tension.

Conclusions:

  • The developed viscoelastic model accurately captures the behavior of bovine brain tissue under uniaxial compression.
  • The study highlights the importance of specific constitutive models and parameters for simulating soft tissue mechanics.
  • Findings contribute to improved computational models for brain injury and surgical simulations.