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Related Concept Videos

Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

291
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...
291
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

317
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...
317
Strain-Energy Density01:20

Strain-Energy Density

584
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...
584
Strain Energy01:13

Strain Energy

630
Strain energy is a fundamental concept in the field of materials science and structural engineering, describing the energy absorbed by a material or structure when it is deformed under load.
Consider a rod that is fixed at one end and subjected to an axial force at the free end. This axial force induces stress within the rod, leading to its elongation. As the axial force increases, so does the elongation of the rod, illustrating a direct relationship between the force applied and the resulting...
630
Castigliano's Theorem01:18

Castigliano's Theorem

585
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.
585
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

242
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...
242

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A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
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Damage separation model: A replaceable particle method based on strain energy field.

Yupeng Jiang1, Peter Mora2, Hans J Herrmann3

  • 1School of Civil Engineering, The University of Sydney, Sydney 2006, New South Wales, Australia.

Physical Review. E
|November 16, 2021
PubMed
Summary
This summary is machine-generated.

The damage separation model (DSM) realistically simulates particle fragmentation in granular materials by replacing broken particles with smaller ones. This advanced method overcomes limitations of prior techniques, improving accuracy and stability in simulations.

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Area of Science:

  • Computational mechanics
  • Granular physics
  • Material science

Background:

  • Simulating particle fragmentation in granular assemblies is crucial for understanding material behavior.
  • Existing methods often oversimplify particle stress and impose unrealistic geometrical constraints post-fragmentation.

Purpose of the Study:

  • To introduce a realistic and robust model for simulating particle fragmentation in granular assemblies.
  • To address the limitations of existing replaceable particle methods.

Main Methods:

  • Developed the damage separation model (DSM) comprising three modules: boundary element calculation for stress/strain fields, a strain-energy-based fragmentation framework, and the subset separation method (SSM) for post-breakage replacements.
  • The SSM allows for arbitrary numbers, locations, and orientations of fracture planes without geometrical limitations.

Main Results:

  • The DSM accurately simulates particle stress and strain fields, predicting fragmentation onset based on strain energy.
  • Validated through uniaxial compression tests, the DSM demonstrated superior stability and accuracy compared to four other methods.
  • The SSM effectively handles fragment generation without artificial constraints on fragment number or shape.

Conclusions:

  • The damage separation model (DSM) offers a significant advancement in simulating particle fragmentation.
  • It provides unprecedented numerical resolution for capturing morphological changes in particle breakage and comminution.
  • The DSM has great potential for applications in geomechanics, materials processing, and other fields involving granular materials.