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Temperature Dependent Deformation01:12

Temperature Dependent Deformation

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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Method of Joints: Problem Solving I01:30

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The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint. Consider a truss structure with two forces of 20 N and 10 N acting at joints C and D, respectively. The method of joints can be used to determine the forces FCB, FDC,...
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Method of Joints: Problem Solving II01:30

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Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.
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Two-Dimensional Force System: Problem Solving01:29

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Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
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A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
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When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
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Bridging experiments and defects' mechanics: a data-driven toolbox for configurational force analysis.

Abdalrhaman Koko1,2, Alya Abdelnour3, Thorsten H Becker4

  • 1National Physical Laboratory, Hampton Road, Teddington, TW11 0LW UK.

Engineering with Computers
|January 19, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a MATLAB toolbox for analyzing material defects. It extracts fracture mechanics parameters directly from experimental data, enabling geometry-independent characterization of cracks and dislocations in various materials.

Keywords:
Computational toolbox; material testing 2.0Configurational forcesDigital image correlationHR-EBSDMixed-mode fractureStress intensity factors

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Area of Science:

  • Materials Science
  • Computational Mechanics
  • Solid Mechanics

Background:

  • Predicting material failure requires understanding mechanical behavior of defects.
  • Traditional fracture mechanics relies on assumptions often unmet in experimental settings.

Purpose of the Study:

  • To develop a computational toolbox for extracting configurational forces and mixed-mode stress intensity factors (SIFs) from experimental data.
  • To enable geometry-independent characterization of defect behavior in complex materials.

Main Methods:

  • A MATLAB-based toolbox implementing path-independent energy integrals (J- and M-integrals).
  • Novel mode decomposition for isolating mode I-III SIFs contributions.
  • Direct analysis of experimentally measured displacement or deformation gradient fields (e.g., DIC, H-EBSD).

Main Results:

  • Demonstrated robust, geometry-independent characterization of microcracks, dislocations, and fatigue cracks.
  • Successfully applied to anisotropic and complex materials.
  • Framework is material-agnostic and operates directly on experimental fields.

Conclusions:

  • The toolbox facilitates data-driven analysis of defect behavior, overcoming limitations of traditional methods.
  • Applicable to linear and anisotropic elastic/elastoplastic materials (metals, ceramics) under small-strain kinematics.
  • Enables advanced understanding of material failure and performance enhancement.