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2014 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Dynamic Fracture of Piezoelectric Materials

Solution of Time-Harmonic Problems via BIEM

verfasst von: Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov

Verlag: Springer International Publishing

Buchreihe : Solid Mechanics and Its Applications

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

Dynamic Fracture of Piezoelectric Materials focuses on the Boundary Integral Equation Method as an efficient computational tool. The presentation of the theoretical basis of piezoelectricity is followed by sections on fundamental solutions and the numerical realization of the boundary value problems. Two major parts of the book are devoted to the solution of problems in homogeneous and inhomogeneous solids. The book includes contributions on coupled electro-mechanical models, computational methods, its validation and the simulation results, which reveal different effects useful for engineering design and practice. The book is self-contained and well-illustrated, and it serves as a graduate-level textbook or as extra reading material for students and researchers.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
The subject of investigation is an infinite or finite piezoelectric solid with defects. Generalizing the proposed BIEM, new results for different classes of inhomogeneous piezoelectric solids are presented and discussed.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov

Theoretical Basics

Frontmatter
Chapter 2. Piezoelectric Materials
Abstract
After some historical remarks the field equations for piezoelectric materials are presented for the 3D and the 2D case. Furthermore, the boundary value problems in bounded and unbounded cracked domains are formulated.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 3. Fundamental Solutions
Abstract
Fundamental solutions for time-harmonic 2D dynamic problems of piezoelectric materials are derived in a closed form by Radon transform. In addition the state of the art in the field is discussed.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 4. Numerical Realization by BIEM
Abstract
Non-hypersingular traction integro-differential equations are derived for the solution of the BVPs formulated in Chap. 2 for bounded and unbounded solids. The numerical realization by the BIEM is presented and a description of the programm codes is given.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov

Homogeneous PEM

Frontmatter
Chapter 5. Steady-State Problems in a Cracked Anisotropic Domain
Abstract
We start with the uncoupled homogeneous case, which actually is for a homogeneous elastic anisotropic material. The accuracy and convergence of the numerical BIEM solution for evaluation of the SIFs is studied by comparison with existing solutions for elastic isotropic and orthotropic materials. In addition a parametric study for the wave field sensitivity regarding frequency, crack geometry and material anisotropy is presented.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 6. 2D Wave Scattering by Cracks in a Piezoelectric Plane
Abstract
Scattering and diffraction of time-harmonic plane waves by a finite crack in a homogeneous piezoelectric plane under plane strain conditions is studied. The BIEM procedure is applied to straight cracks, as well as to curved cracks under incident longitudinal waves and under vertically polarized shear waves. The SIFs results are compared with those available in the literature. Furthermore, their dependence on parameters like frequency, angle of incidence, wave type, crack geometry and material properties is discussed.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 7. Piezoelectric Cracked Finite Solids Under Time-Harmonic Loading
Abstract
The time-harmonic behavior of cracked finite piezoelectric 2D solids is studied. Plane strain and generalized traction free boundary conditions along the crack are assumed. The system may be loaded at the external boundary by arbitrary mechanical and/or electrical loads. As numerical example a center cracked rectangular piezoelectric plate under uniform axial time-harmonic tension and electrical displacement is investigated. The accuracy of the proposed numerical algorithm is checked by comparison with available results obtained by other methods. Parametric studies revealing the sensitivity of the SIFs to the frequency of the applied mechanical and electrical load, to its coupled and uncoupled character and to the piezoelectric properties of the material are presented.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 8. Dynamic Crack Interaction in Piezoelectric and Anisotropic Solids
Abstract
Multiple in-plane cracks in a piezoelectric or anisotropic plane loaded by time-harmonic waves is treated. Simulations for different crack configurations such as coplanar, collinear or cracks in arbitrary position to each other are presented and discussed. They demonstrate among others the strong effect of electromechanical coupling, show the frequency dependent shielding and amplification resulting from crack interaction and reveal the sensitivity of the K-factors to the complex influence of both the wave–crack and crack–crack interaction.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 9. Different Electric Boundary Conditions
Abstract
Dynamic SIFs for a straight crack in a piezoelectric material under time-harmonic L- or SV- and SH- wave are determined for different electric boundary conditions. Compared are impermeable, permeable and limited permeable cracks. A parametric study in the frequency domain shows the dependence of the SIFs on the choice of the electrical boundary conditions at the crack faces.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov

Functionally Graded PEM

Frontmatter
Chapter 10. In-plane Crack Problems in Functionally Graded Piezoelectric Solids
Abstract
In-plane crack analysis of functionally graded piezoelectric solids under time-harmonic loading is performed by using a non-hypersingular traction BIEM. The material parameters are assumed to vary quadratically with both spatial variables. Numerical results for the SIFs are discussed for different examples. Investigated are the effects of the inhomogeneity parameters, the frequency of the applied electromechanical load and the geometry of the crack scenario on the K-factors.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 11. Functionally Graded Piezoelectric Media with a Single Anti-plane Crack
Abstract
Treated is an arbitrarily shaped anti-plane shear crack in a finite inhomogeneous piezoelectric domain under time-harmonic loading. Within a unified scheme different types of inhomogeneity are considered for which the material parameters may vary in arbitrary directions. The problem is solved by using a numerically efficient non-hypersingular traction BIEM. The fundamental solutions for the different inhomogeneity types are derived in closed form. Numerical results for the SIFs are discussed. They show the effect of the material inhomogeneity type and characteristics and the efficiency of the computational method.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 12. Multiple Anti-plane Cracks in Quadratically Inhomogeneous Piezoelectric Finite Solids
Abstract
Anti-plane cracks in finite functionally graded piezoelectric solids under time-harmonic loading are studied. The formulation allows for a quadratic variation of the material properties in arbitrary direction. The numerical solution provides the displacements and traction on the external boundary as well as the crack opening displacements from which the mechanical SIF and the EDIF are determined. Several examples for single and multiple straight and curved cracks show the influence of the different system parameters.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 13. Anti-plane Cracks in Exponentially Inhomogeneous Finite Piezoelectric Solid
Abstract
Anti-plane cracked functionally graded finite piezoelectric solids under time-harmonic elecro-mechanical load are studied by a non-hypersingular traction boundary integral equation method. Exponentially varying material properties are considered. Numerical solutions are obtained by using Mathematica. The dependence of the mechanical stress intensity factor and electrical field intensity factor on the inhomogeneous material parameters, on the type and frequency of the dynamic load and on the crack position are numerically analyzed by illustrative examples.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 14. Exponentially Inhomogeneous Piezoelectric Solid with a Circular Anti-plane Hole
Abstract
This chapter addresses the evaluation of the stress and electric field concentrations around a circular hole in a functionally graded piezoelectric plane subjected to anti-plane elastic SH-wave and in-plane time-harmonic electric load. All material parameters vary exponentially along a line of arbitrary orientation in the plane of the piezoelectric material under consideration. Numerical solutions with non-hypersingular traction BIEM for the stress and electric field concentration factors (SCF and EFCF, respectively) around the perimeter of the hole are obtained. Presented are results showing the dependence on various system parameters as e.g. the electro-mechanical coupling, the type of the dynamic load and its characteristics, the wave-hole and wave-material interaction and the magnitude and direction of the material inhomogeneity.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Chapter 15. Anti-plane Dynamic Crack–Hole Interaction in a Functionally Graded Piezoelectric Medium
Abstract
The anti-plane dynamic problem of a functionally graded piezoelectric plane containing a hole–crack system is treated. The material parameters vary exponentially in the same manner in an arbitrary direction. The system is loaded by an incident SH-type wave and impermeable boundary conditions are assumed. The numerical solution yields the dynamic SIFs and SCFs. A parametric study reveals their dependence on the hole–crack scenario and its geometry, characteristics of the dynamic load and magnitude and direction of the material gradient.
Petia Dineva, Dietmar Gross, Ralf Müller, Tsviatko Rangelov
Backmatter
Metadaten
Titel
Dynamic Fracture of Piezoelectric Materials
verfasst von
Petia Dineva
Dietmar Gross
Ralf Müller
Tsviatko Rangelov
Copyright-Jahr
2014
Electronic ISBN
978-3-319-03961-9
Print ISBN
978-3-319-03960-2
DOI
https://doi.org/10.1007/978-3-319-03961-9