Junction problem for thin elastic and volume rigid inclusions in elastic body
1Lavrentyev Institute of Hydrodynamics of RAS, and Novosibirsk State University, Novosibirsk 630090, Russia.
Summary
This study analyzes junction problems in 2D elastic bodies with thin elastic and rigid inclusions sharing a common point. It investigates interfacial crack behavior and derives junction conditions for various limit cases, including delamination and varying rigidity.
Area of Science:
- Solid Mechanics
- Continuum Mechanics
- Fracture Mechanics
Background:
- Junction problems involving inclusions in elastic bodies are complex.
- Interfacial cracks and delamination present significant challenges in material modeling.
- Understanding the behavior of rigid and elastic inclusions is crucial for structural integrity.
Purpose of the Study:
- To analyze a junction problem for a 2D elastic body with thin elastic and volume rigid inclusions.
- To investigate the formation and behavior of an interfacial crack due to delamination.
- To determine junction conditions at the common point of inclusions under various limiting scenarios.
Main Methods:
- Modeling of a 2D elastic body with a thin elastic inclusion and a volume rigid inclusion.
- Application of constraint-type boundary conditions to prevent crack face interpenetration.
- Analysis of limit transitions as damage and rigidity parameters vary.
- Investigation of limit models for the junction problem.
Main Results:
- Characterization of the connection between crack faces using a damage parameter.
- Justification of limit transitions for damage parameters tending to infinity and zero.
- Analysis of the limit transition as the rigidity parameter of the thin inclusion tends to infinity.
- Derivation of specific junction conditions at the common point for all considered cases.
Conclusions:
- The study provides a comprehensive analysis of junction problems with inclusions and interfacial cracks.
- Established limit models and derived junction conditions offer insights into material behavior under extreme parameters.
- Findings are relevant to understanding structural integrity and failure mechanisms in composite materials.
Keywords:
crackdamage parameterjunction conditionsrigid inclusionthin elastic inclusionvariational inequalityMore Related Videos
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