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Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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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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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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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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A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
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A Phase-Field Approach to Continuum Damage Mechanics.

Angelo Morro1

  • 1DIBRIS, Università di Genova, 16145 Genova, Italy.

Materials (Basel, Switzerland)
|November 11, 2022
PubMed
Summary

This study introduces a phase-field method for modeling continuum mechanics damage. The approach integrates mechanical and thermal effects, enhancing models for hysteretic behavior and material degradation.

Area of Science:

  • Continuum mechanics
  • Thermodynamics
  • Material science

Background:

  • Damage modeling is crucial for predicting material failure.
  • Existing models often struggle with complex phenomena like hysteresis and coupled thermal-mechanical effects.
  • A unified framework is needed for comprehensive damage description.

Purpose of the Study:

  • To develop a novel phase-field approach for describing damage in continuum mechanics.
  • To incorporate non-stationary heat conduction and mechanical hysteretic effects.
  • To ensure thermodynamic consistency within the developed framework.

Main Methods:

  • Utilizing a phase-field variable governed by a constitutive equation.
  • Applying the Clausius-Duhem inequality from Rational Thermodynamics.
Keywords:
agingdamageentropy productionphase field

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  • Treating entropy production as a constitutive function, decomposed into two terms.

    • Main Results:

    • The phase-field approach successfully models macroscopic damage.
    • The framework accommodates non-stationary heat conduction and mechanical hysteresis.
    • Thermodynamic consistency is rigorously maintained.

    Conclusions:

    • The proposed phase-field method offers a versatile tool for damage analysis in continuum mechanics.
    • The model's ability to capture coupled phenomena enhances its predictive power.
    • This approach provides a robust foundation for advanced material behavior simulation.