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Related Concept Videos

Temperature Dependent Deformation01:12

Temperature Dependent Deformation

135
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...
135
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

146
When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
146
Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

130
Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
130
Castigliano's Theorem01:18

Castigliano's Theorem

346
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.
346
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

150
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...
150
Strain-Energy Density01:20

Strain-Energy Density

347
Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this...
347

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Updated: May 22, 2025

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Conversion between the numerical simulation and the calculation using the Deformation Energy Ratio approach.

Kirill Golubiatnikov1, František Wald1

  • 1Czech Technical University in Prague, Faculty of Civil Engineering, Thakurova 7, 166 29 Prague, Czech Republic.

Methodsx
|March 17, 2025
PubMed
Summary

This study introduces the Deformation Energy Ratio approach to accurately convert material properties between numerical simulations and calculations for steels. This method ensures precise limit adjustments by considering material conditions, with verified accuracy below 5.6%.

Keywords:
ConversionDeformation energyLimit valuesNumerical calculationNumerical simulationStructural steelThe Deformation Energy Ratio approach

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Area of Science:

  • Mechanical Engineering
  • Materials Science
  • Computational Mechanics

Background:

  • Numerical simulations and analytical calculations often define material curves differently.
  • Direct transfer of material data between these domains leads to inaccuracies.
  • Accurate transformation of key material values is crucial for reliable engineering analysis.

Purpose of the Study:

  • To develop and validate a method for accurate conversion of material properties between numerical simulations and calculations.
  • To enable precise limit adjustments in engineering analyses involving steel.
  • To provide a universally applicable approach for any steel type.

Main Methods:

  • The Deformation Energy Ratio (DER) approach was developed, integrating principles like Neuber's rule and Equivalent Strain Energy Density.
  • The method expresses deformation energy as a function of stress and strain.
  • It accounts for specific material conditions in both simulation and calculation contexts.

Main Results:

  • The DER approach allows for the conversion of material values between numerical simulation and calculation for all steel types.
  • It comprehensively considers the influence of material properties and various influencing factors.
  • Verification demonstrated high accuracy, with an average deviation of less than 5.0% and a maximum deviation of 5.6%.

Conclusions:

  • The Deformation Energy Ratio approach offers a simple yet effective solution for accurate material data conversion.
  • It enhances the precision of engineering analyses by bridging the gap between simulation and calculation.
  • The method's high accuracy and applicability to all steels make it a valuable tool for engineers.