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Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
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Creep refers to the time-dependent increase in strain under a sustained load, excluding other time-dependent deformations associated with shrinkage, swelling, and thermal expansion in concrete. The primary mechanism behind creep involves the loss of physically adsorbed water from the calcium silicate hydrate within the hydrated cement paste. This process is further exacerbated by concrete's non-linear stress-strain relationship, microcrack development in the interfacial transition zone, and...
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The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
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Related Experiment Video

Updated: May 27, 2025

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Study on nonlinear creep damage model based on fractional derivative.

Guanghe Li1, Hongjun Jia2,3

  • 1College of Mining, Liaoning Technical University, Fuxin, 123000, China. li_7118@126.com.

Scientific Reports
|February 19, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a fractional nonlinear creep damage model to simulate rock behavior under varying water content. The model accurately predicts rock creep characteristics, offering insights for slope stability analysis.

Keywords:
Accelerated creepFractional orderNonlinear creep constitutive modelParameter identification

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Area of Science:

  • Geotechnical Engineering
  • Materials Science
  • Applied Mathematics

Background:

  • Fractional calculus offers advanced methods for mechanical modeling, particularly for materials exhibiting intermediate properties between solids and fluids.
  • Understanding rock creep behavior under varying conditions is crucial for geotechnical engineering and slope stability.
  • Existing models may not fully capture the complex nonlinear creep and damage processes in rocks.

Purpose of the Study:

  • To develop and validate a fractional nonlinear creep damage model for simulating rock creep.
  • To investigate the influence of water content on rock creep characteristics using fractional calculus.
  • To provide a theoretical basis for the stability analysis and disaster prevention of soft rock slopes.

Main Methods:

  • Application of Riemann-Liouville's fractional calculus operator to model viscous and viscoplastic elements.
  • Establishment of a series connection of fractional order viscous element, nonlinear viscous element, and viscoplastic body.
  • Construction of the constitutive equation for the fractional nonlinear creep damage model.
  • Parameter identification using the principle of least squares and validation against experimental data.

Main Results:

  • The developed fractional nonlinear creep damage model demonstrated a high correlation ( > 0.98) with experimental data.
  • The model effectively simulates the nonlinear gradient process of rock creep under different water content conditions.
  • Analysis of model parameters revealed their impact on deformation, enhancing model verification and applicability.

Conclusions:

  • The fractional nonlinear creep damage model provides an accurate and effective tool for simulating rock creep behavior.
  • The research offers valuable theoretical insights for assessing the stability of soft rock slopes and preventing disasters.
  • The model's adaptability to various stress environments enhances its practical utility in geotechnical engineering.