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Related Concept Videos

Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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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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Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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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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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
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Bending of Members Made of Several Materials01:08

Bending of Members Made of Several Materials

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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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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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An Isoparametric Finite Element Model for Large-Strain Elastostatics.

David S Malkus1, E R Fuller2

  • 1Department of Mathematics, Illinois Institute of Technology, Chicago, IL 60616.

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|September 27, 2021
PubMed
Summary

A new finite element model for large-strain elastostatics was developed for nonlinear elasticity research. This computational model efficiently simulates stress concentrations in materials, aiding research into penalty techniques.

Keywords:
Checkerboard pressureMooney-Rivlin materialelastostaticsfinite elementsin-core solverisoparametricsnonlinear equation-solverspenalty methodplane-stressstrain invariantstensile-test specimen

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Area of Science:

  • Computational Mechanics
  • Solid Mechanics
  • Nonlinear Elasticity

Background:

  • Research in nonlinear elasticity requires robust computational models for testing advanced techniques.
  • Existing models may lack the flexibility or computational economy needed for specific research applications.
  • The development of specialized finite element models is crucial for advancing the field.

Purpose of the Study:

  • To describe a simple finite element model for large-strain elastostatics.
  • To create a computational tool for generating test problems in nonlinear elasticity research, focusing on penalty techniques.
  • To balance model flexibility with computational efficiency.

Main Methods:

  • Implementation of a small-scale computer code utilizing multilinear isoparametric elements.
  • Application of incremental loading combined with the Newton-Raphson method for solving symmetric, banded systems of equations.
  • Modeling of two- and three-dimensional symmetric bodies, including an example of an ASTM rubber tensile-test specimen.

Main Results:

  • The developed finite element model successfully simulates large-strain elastostatics.
  • The code provides a flexible yet computationally economical platform for research.
  • Analysis of a dogbone-shaped specimen revealed insights into stress concentrations in different dimensional models.

Conclusions:

  • The developed finite element model serves as a valuable tool for research in nonlinear elasticity, particularly for penalty techniques.
  • The model's design balances flexibility and computational economy, making it suitable for generating research test problems.
  • The study highlights the utility of the model in understanding stress concentration phenomena in specific geometries.