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Related Concept Videos

Microcracking in Concrete01:20

Microcracking in Concrete

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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...
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Generalized Hooke's Law01:22

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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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Three-Dimensional Analysis of Strain01:29

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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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Types of Non-structural Cracks in Concrete01:28

Types of Non-structural Cracks in Concrete

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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.
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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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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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Related Experiment Video

Updated: Nov 1, 2025

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
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A computational framework for crack propagation in spatially heterogeneous materials.

Karol Lewandowski1, Łukasz Kaczmarczyk1, Ignatios Athanasiadis1

  • 1Glasgow Computational Engineering Centre, The James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 21, 2021
PubMed
Summary

This study models brittle crack propagation in heterogeneous materials using configurational mechanics and the finite-element method. The model accurately predicts crack paths and energy dissipation, validated with experiments and equine bone fracture analysis.

Keywords:
configurational mechanicsfinite-element analysisfracturefunctionally graded materialsheterogeneous materials

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Area of Science:

  • Solid Mechanics
  • Computational Materials Science
  • Fracture Mechanics

Background:

  • Brittle crack propagation is critical in heterogeneous elastic solids found in nature and engineering.
  • Existing models often require assumptions for homogeneous materials, limiting their applicability.

Purpose of the Study:

  • To develop a mathematical formulation and numerical modeling framework for brittle crack propagation in heterogeneous elastic solids.
  • To validate the model against analytical and experimental data, including complex biological structures.

Main Methods:

  • Utilized configurational mechanics and the finite-element method for numerical modeling.
  • Employed the Griffith criterion and the principle of maximal energy dissipation.
  • Formulated crack propagation using exclusively nodal quantities for implicit modeling.

Main Results:

  • Successfully extended methodology for homogeneous materials to heterogeneous solids without further assumptions.
  • Predicted crack path trajectories consistently orient to Mode-I loading.
  • Demonstrated excellent agreement between numerical predictions and experimental/analytical results.

Conclusions:

  • The proposed model accurately predicts crack propagation in brittle heterogeneous materials.
  • The formulation is robust, validated, and applicable to complex scenarios like equine bone fracture.
  • This work provides a unified approach for modeling fracture in diverse material systems.