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Related Concept Videos

Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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Stress-Strain Diagram - Brittle Materials01:24

Stress-Strain Diagram - Brittle Materials

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Brittle materials, including glass, cast iron, and stone, exhibit unique characteristics. They fracture without considerable change in their elongation rate, indicating that their breaking and ultimate strength are equivalent. Such materials also show lower strain levels at the point of rupture. The failure in brittle materials predominantly results from normal stresses, as evidenced by the rupture created along a surface perpendicular to the applied load. These materials do not display...
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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.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each...
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Flexural Stress01:16

Flexural Stress

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When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to...
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Plastic Deformations01:14

Plastic Deformations

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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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Fatigue01:21

Fatigue

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Fatigue occurs when materials rupture under repeated or fluctuating loads, even at stress levels far below their static breaking strength. It typically results in brittle failure, even for ductile materials. It is a critical consideration in designing machines and structural components subjected to repetitive or varying loads. The nature of these loadings can range from fluctuating loads like unbalanced pump impellers causing vibrations to repeatedly bending a thin steel rod wire back and forth...
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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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Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form.

C Y Fu1, Y Yang1, Y R Zhou1

  • 1Institute of Aerospace, School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China.

Materials (Basel, Switzerland)
|December 9, 2023
PubMed
Summary

The strong-form finite block method (FBM) accurately analyzes 3D fractures in functionally graded materials. This efficient method determines stress intensity factors, crucial for material performance and safety.

Keywords:
crack opening displacementsfinite block methodfunctionally graded materialsstress intensity factor

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Area of Science:

  • Computational mechanics
  • Materials science
  • Fracture mechanics

Background:

  • Functionally graded materials (FGMs) exhibit spatially varying properties, posing challenges for traditional analysis methods.
  • Accurate fracture analysis is critical for ensuring the structural integrity and safety of components made from FGMs.
  • Existing numerical methods may face limitations in handling the complex geometry and material gradients inherent in FGM fracture problems.

Purpose of the Study:

  • To present the strong-form finite block method (FBM) for three-dimensional fracture analysis of FGMs.
  • To develop frameworks for the strong-form FBM using Lagrange and Chebyshev polynomial interpolations.
  • To determine stress intensity factors in FGMs using the developed FBM approach.

Main Methods:

  • The strong-form finite block method (FBM) transforms the physical domain into a normalized one.
  • Direct collocation is employed to establish a linear system within the normalized domain.
  • Mapping techniques facilitate the direct construction of partial differential matrices of any order.

Main Results:

  • Frameworks for 3D FBM analysis were successfully developed using Lagrange and Chebyshev interpolations.
  • Stress intensity factors for FGMs were accurately determined based on crack opening displacement criteria.
  • Numerical examples demonstrated the high accuracy and computational efficiency of the strong-form FBM.

Conclusions:

  • The strong-form FBM is a robust and efficient technique for 3D fracture analysis of FGMs.
  • The method provides accurate stress intensity factors, essential for evaluating material reliability.
  • The developed FBM approach offers a valuable tool for researchers and engineers working with FGMs.