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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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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.
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It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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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.
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A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and...
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Modeling for strain-softening rocks with lateral damage based on statistical physics.

Xiaoming Li1,2, Mingwu Wang1, Fengqiang Shen1

  • 1School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei, Anhui, China.

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Researchers developed a new statistical damage model for rock mechanics, improving upon existing methods. This maximum entropy model accurately captures rock

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Area of Science:

  • Rock mechanics
  • Statistical physics
  • Materials science

Background:

  • Statistical physics is crucial for understanding rock's nonlinear mechanical behaviors.
  • Existing statistical damage models and the Weibull distribution have limitations.
  • There's a need for improved models to accurately represent rock behavior.

Purpose of the Study:

  • To establish a novel statistical damage model for rocks incorporating lateral damage.
  • To develop a damage variable expression using maximum entropy distribution and constraints.
  • To validate the proposed model against experimental data and existing models.

Main Methods:

  • Established a new statistical damage model with lateral damage considerations.
  • Introduced the maximum entropy distribution function for the damage variable.
  • Applied strict constraints on the damage variable.
  • Compared the model's predictions with experimental results and other statistical models.

Main Results:

  • The proposed maximum entropy statistical damage model was developed.
  • A new expression for the damage variable was derived.
  • The model demonstrated rationality when compared with experimental data.
  • The model showed better agreement with experimental results than two other models.

Conclusions:

  • The maximum entropy statistical damage model accurately reflects rock's strain-softening behavior.
  • The model effectively represents residual strength in rocks.
  • This provides a valuable theoretical reference for rock engineering and design.