A microstructural model for homogenisation and cracking of piezoelectric polycrystals

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Abstract

Download PDFShareExportAdvancedOutlineAbstractKeywords1. Introduction2. Morphology generation and meshing3. Boundary element modelling of piezoelectric polycrystalline materials4. Numerical discretisation and non-linear system solution5. Numerical experiments6. Discussion7. ConclusionsAcknowledgementsAppendix. Anisotropic Green’s functionsReferencesShow full outlineFigures (9)Fig. 1. Different kinds of morphology can be generated and analysed within the proposed…Fig. 2. Morphology generation and meshing: (a) an individual grain is a convex…Fig. 3. Apparent (a) Young’s modulus, (b) Shear modulus and (c) relative dielectric…Fig. 4. Apparent macroscopic constitutive properties of (a,c,e) unpoled (βmax=π) and…Fig. 5. Apparent macroscopic constitutive properties of BaTiO3 piezoelectric…Fig. 6. Effect of the piezoelectric coupling on the macroscopic stress for a simple…Show all figuresTables (2)Table 1Table 2ElsevierComputer Methods in Applied Mechanics and EngineeringVolume 357, 1 December 2019, 112595Computer Methods in Applied Mechanics and EngineeringA microstructural model for homogenisation and cracking of piezoelectric polycrystalsAuthor links open overlay panelIvanoBenedettiVincenzoGulizziAlbertoMilazzoShow morehttps://doi.org/10.1016/j.cma.2019.112595Get rights and contentAbstractAn original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitable electro-mechanical terms. The boundary integral formulation allows the expression of the microstructural piezo-electric boundary value problem in terms of generalised grain boundary and intergranular displacements and tractions only, which implies some definite modelling advantages, namely: a) the natural inclusion of the intergranular cohesive laws in the formulation; b) a meaningful simplification of the analysis pre-processing stage, i.e. input data and mesh preparation; c) the reduction of the number of degrees of freedom of the overall analysis with respect to other popular numerical methods. The developed formulation has been applied to the computation of the effective properties, i.e. material homogenisation, of crystal aggregates and to the investigation of micro-cracking in PZT-4 ceramics, providing consistent results.
Lingua originaleEnglish
Numero di pagine21
RivistaComputer Methods in Applied Mechanics and Engineering
Volume357
Stato di pubblicazionePublished - 2019

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Polycrystals
polycrystals
homogenizing
formulations
Mechanics
Elastic moduli
Polycrystalline materials
Electromechanical coupling
Piezoelectric materials
Boundary value problems
Nonlinear systems
traction
Numerical methods
Materials properties
Grain boundaries
preprocessing
nonlinear systems
simplification
boundary value problems
Cracks

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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title = "A microstructural model for homogenisation and cracking of piezoelectric polycrystals",
abstract = "Download PDFShareExportAdvancedOutlineAbstractKeywords1. Introduction2. Morphology generation and meshing3. Boundary element modelling of piezoelectric polycrystalline materials4. Numerical discretisation and non-linear system solution5. Numerical experiments6. Discussion7. ConclusionsAcknowledgementsAppendix. Anisotropic Green’s functionsReferencesShow full outlineFigures (9)Fig. 1. Different kinds of morphology can be generated and analysed within the proposed…Fig. 2. Morphology generation and meshing: (a) an individual grain is a convex…Fig. 3. Apparent (a) Young’s modulus, (b) Shear modulus and (c) relative dielectric…Fig. 4. Apparent macroscopic constitutive properties of (a,c,e) unpoled (βmax=π) and…Fig. 5. Apparent macroscopic constitutive properties of BaTiO3 piezoelectric…Fig. 6. Effect of the piezoelectric coupling on the macroscopic stress for a simple…Show all figuresTables (2)Table 1Table 2ElsevierComputer Methods in Applied Mechanics and EngineeringVolume 357, 1 December 2019, 112595Computer Methods in Applied Mechanics and EngineeringA microstructural model for homogenisation and cracking of piezoelectric polycrystalsAuthor links open overlay panelIvanoBenedettiVincenzoGulizziAlbertoMilazzoShow morehttps://doi.org/10.1016/j.cma.2019.112595Get rights and contentAbstractAn original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitable electro-mechanical terms. The boundary integral formulation allows the expression of the microstructural piezo-electric boundary value problem in terms of generalised grain boundary and intergranular displacements and tractions only, which implies some definite modelling advantages, namely: a) the natural inclusion of the intergranular cohesive laws in the formulation; b) a meaningful simplification of the analysis pre-processing stage, i.e. input data and mesh preparation; c) the reduction of the number of degrees of freedom of the overall analysis with respect to other popular numerical methods. The developed formulation has been applied to the computation of the effective properties, i.e. material homogenisation, of crystal aggregates and to the investigation of micro-cracking in PZT-4 ceramics, providing consistent results.",
author = "Alberto Milazzo and Vincenzo Gulizzi and Ivano Benedetti",
year = "2019",
language = "English",
volume = "357",
journal = "Computer Methods in Applied Mechanics and Engineering",
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publisher = "Elsevier",

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TY - JOUR

T1 - A microstructural model for homogenisation and cracking of piezoelectric polycrystals

AU - Milazzo, Alberto

AU - Gulizzi, Vincenzo

AU - Benedetti, Ivano

PY - 2019

Y1 - 2019

N2 - Download PDFShareExportAdvancedOutlineAbstractKeywords1. Introduction2. Morphology generation and meshing3. Boundary element modelling of piezoelectric polycrystalline materials4. Numerical discretisation and non-linear system solution5. Numerical experiments6. Discussion7. ConclusionsAcknowledgementsAppendix. Anisotropic Green’s functionsReferencesShow full outlineFigures (9)Fig. 1. Different kinds of morphology can be generated and analysed within the proposed…Fig. 2. Morphology generation and meshing: (a) an individual grain is a convex…Fig. 3. Apparent (a) Young’s modulus, (b) Shear modulus and (c) relative dielectric…Fig. 4. Apparent macroscopic constitutive properties of (a,c,e) unpoled (βmax=π) and…Fig. 5. Apparent macroscopic constitutive properties of BaTiO3 piezoelectric…Fig. 6. Effect of the piezoelectric coupling on the macroscopic stress for a simple…Show all figuresTables (2)Table 1Table 2ElsevierComputer Methods in Applied Mechanics and EngineeringVolume 357, 1 December 2019, 112595Computer Methods in Applied Mechanics and EngineeringA microstructural model for homogenisation and cracking of piezoelectric polycrystalsAuthor links open overlay panelIvanoBenedettiVincenzoGulizziAlbertoMilazzoShow morehttps://doi.org/10.1016/j.cma.2019.112595Get rights and contentAbstractAn original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitable electro-mechanical terms. The boundary integral formulation allows the expression of the microstructural piezo-electric boundary value problem in terms of generalised grain boundary and intergranular displacements and tractions only, which implies some definite modelling advantages, namely: a) the natural inclusion of the intergranular cohesive laws in the formulation; b) a meaningful simplification of the analysis pre-processing stage, i.e. input data and mesh preparation; c) the reduction of the number of degrees of freedom of the overall analysis with respect to other popular numerical methods. The developed formulation has been applied to the computation of the effective properties, i.e. material homogenisation, of crystal aggregates and to the investigation of micro-cracking in PZT-4 ceramics, providing consistent results.

AB - Download PDFShareExportAdvancedOutlineAbstractKeywords1. Introduction2. Morphology generation and meshing3. Boundary element modelling of piezoelectric polycrystalline materials4. Numerical discretisation and non-linear system solution5. Numerical experiments6. Discussion7. ConclusionsAcknowledgementsAppendix. Anisotropic Green’s functionsReferencesShow full outlineFigures (9)Fig. 1. Different kinds of morphology can be generated and analysed within the proposed…Fig. 2. Morphology generation and meshing: (a) an individual grain is a convex…Fig. 3. Apparent (a) Young’s modulus, (b) Shear modulus and (c) relative dielectric…Fig. 4. Apparent macroscopic constitutive properties of (a,c,e) unpoled (βmax=π) and…Fig. 5. Apparent macroscopic constitutive properties of BaTiO3 piezoelectric…Fig. 6. Effect of the piezoelectric coupling on the macroscopic stress for a simple…Show all figuresTables (2)Table 1Table 2ElsevierComputer Methods in Applied Mechanics and EngineeringVolume 357, 1 December 2019, 112595Computer Methods in Applied Mechanics and EngineeringA microstructural model for homogenisation and cracking of piezoelectric polycrystalsAuthor links open overlay panelIvanoBenedettiVincenzoGulizziAlbertoMilazzoShow morehttps://doi.org/10.1016/j.cma.2019.112595Get rights and contentAbstractAn original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitable electro-mechanical terms. The boundary integral formulation allows the expression of the microstructural piezo-electric boundary value problem in terms of generalised grain boundary and intergranular displacements and tractions only, which implies some definite modelling advantages, namely: a) the natural inclusion of the intergranular cohesive laws in the formulation; b) a meaningful simplification of the analysis pre-processing stage, i.e. input data and mesh preparation; c) the reduction of the number of degrees of freedom of the overall analysis with respect to other popular numerical methods. The developed formulation has been applied to the computation of the effective properties, i.e. material homogenisation, of crystal aggregates and to the investigation of micro-cracking in PZT-4 ceramics, providing consistent results.

UR - http://hdl.handle.net/10447/369161

M3 - Article

VL - 357

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -