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Related Concept Videos

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

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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.
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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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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.
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Members Made of Elastoplastic Material01:19

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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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.
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It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification.

Wei Wang1, Yang Liu1, Zongwu Xie1

  • 1State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150001, China.

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|August 12, 2023
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Summary

A modified hyperelastic model enhances prediction accuracy for polymer materials under multiaxial deformation. This improved Yeoh model offers wider applicability and accurate predictions even for untested deformations.

Keywords:
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Area of Science:

  • Materials Science
  • Computational Mechanics
  • Polymer Physics

Background:

  • Hyperelastic constitutive models are crucial for engineering component design.
  • Existing models often lack universal performance and accuracy for multiaxial deformation.
  • The Yeoh model is a foundational hyperelastic model with known advantages.

Purpose of the Study:

  • To propose a modified hyperelastic constitutive model based on the Yeoh model.
  • To enhance prediction performance for multiaxial deformation of hyperelastic polymeric materials.
  • To introduce an accurate parameter identification method.

Main Methods:

  • A modified Yeoh model incorporating a correction term based on principal stretches.
  • A parameter identification method utilizing a cyclic genetic-pattern search algorithm.
  • Validation against experimental datasets of diverse rubber-like materials and human brain tissue.

Main Results:

  • The modified model significantly improves prediction accuracy for multiaxial deformation.
  • Demonstrated wider material applicability, including challenging biological tissues.
  • Accurate prediction of untested equibiaxial deformation from uniaxial and shear data.

Conclusions:

  • The modified hyperelastic model offers superior predictive capabilities and broader applicability.
  • The proposed parameter identification method enhances model accuracy and convergence.
  • The model is suitable for practical engineering scenarios where specific deformation data is unavailable.