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Related Concept Videos

Microcracking in Concrete01:20

Microcracking in Concrete

103
Microcracking in concrete refers to the tiny cracks that can form within the material even before any external load is applied. These microcracks typically occur at the interface between the coarse aggregate and the hydrated cement paste, often as a result of differential volume changes prompted by variations in stress-strain behavior, as well as thermal and moisture movement. Initially, these microcracks remain stable and do not grow substantially until the concrete is stressed to about 30...
103
Effects of Creep01:25

Effects of Creep

99
Creep in concrete, the gradual deformation under prolonged stress, significantly impacts the integrity of structures. For reinforced concrete beams, it can be a vital design consideration, as it increases deflection, sometimes necessitating additional design measures. In columns, especially slender ones under eccentric loads, creep can cause buckling, compromising their stability. However, creep can be beneficial in indeterminate structures by mitigating stresses that arise from shrinkage,...
99
Fatigue01:21

Fatigue

174
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...
174
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

251
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.
251
Euler's Formula to Columns with Other End Conditions01:15

Euler's Formula to Columns with Other End Conditions

467
Euler's formula is very important in the field of structural engineering, providing a foundation for understanding the critical loading conditions of pin-ended columns. This formula links the modulus of elasticity, the moment of inertia of the cross-section, and the column's length, offering a precise calculation of the critical load at which a column is prone to buckling.
467
Types of Non-structural Cracks in Concrete01:28

Types of Non-structural Cracks in Concrete

130
Non-structural cracks are primarily of three types: plastic, early-age thermal, and drying shrinkage cracks. Plastic cracks are further classified into plastic shrinkage cracks and plastic settlement cracks.
Plastic shrinkage cracks typically form within hours after the concrete is poured. The concrete's surface dries faster than the bottom, creating tensile stress that the still-plastic concrete cannot withstand, leading to diagonal or randomly patterned cracks on the concrete surface.
130

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Related Experiment Video

Updated: Jun 8, 2025

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
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Improvements for the solution of crack evolution using extended finite element method.

Yuxiao Wang1, Akbar A Javadi2, Corrado Fidelibus3

  • 1Department of Engineering, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, United Kingdom.

Scientific Reports
|November 6, 2024
PubMed
Summary

The eXtended Finite Element Method (XFEM) efficiently simulates crack growth. This study enhances XFEM accuracy and efficiency by optimizing element subdivision and Gauss point distribution for crack analysis.

Keywords:
Extended finite element method, Crack evolution, Symmetric nodes, Accuracy improvement for the interaction integral method

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Area of Science:

  • Computational Mechanics
  • Materials Science
  • Fracture Mechanics

Background:

  • The eXtended Finite Element Method (XFEM) is a powerful tool for simulating crack evolution without mesh refinement.
  • However, approximations in XFEM can lead to inaccuracies in nodal displacements, particularly near crack tips.
  • Improving the computational efficiency and accuracy of XFEM remains an active area of research.

Purpose of the Study:

  • To mathematically investigate and enhance the solution efficiency of the eXtended Finite Element Method (XFEM).
  • To identify the causes of discrepancies in nodal displacements within XFEM simulations.
  • To propose and validate improvements for accurate and efficient crack analysis using XFEM.

Main Methods:

  • Comprehensive mathematical analysis of the XFEM solution process, focusing on the global stiffness matrix.
  • Development of two novel improvement strategies: element subdivision based on Gauss point distribution and optimal Gauss point determination.
  • Application of proposed improvements with the interaction integral method for stress intensity factor calculation.
  • Numerical validation against analytical and standard XFEM solutions.

Main Results:

  • Discrepancies in nodal displacements were identified and attributed to XFEM approximation.
  • The proposed methods of element subdivision and optimal Gauss point allocation significantly improved accuracy.
  • The enhanced XFEM approach, combined with the interaction integral method, reduced computational time and eliminated surface traction influence.
  • Validated numerical results showed enhanced accuracy and efficiency compared to standard XFEM.

Conclusions:

  • The proposed improvements effectively address the accuracy limitations of XFEM in crack simulation.
  • Optimizing element subdivision and Gauss point strategy enhances computational efficiency and solution precision.
  • The refined XFEM approach provides a more reliable and faster method for fracture mechanics analysis.