Papers by Author: Vladimir Sladek

Abstract: The finite element method (FEM) is developed to analyse the size effect (flexoeletricity) for 2-D crack problems in thermo-piezoelectricity. Flexoelectricity is observed in micro/nanoelectronic structures, where large strain gradients destroy the symmetric structure of atoms in crystals and thereby causing polarization, even in dielectric materials. In contrast to using classical Fourier heat conduction theory, a finite speed of the thermal wave is considered in the higher order transport equation. The variational principle is applied to derive the FEM equations and C¹-continuous elements are employed in the implementation of the FEM. An example is presented to demonstrate the effect of the characteristic time parameter on the crack opening displacement and temperature distribution.

Abstract: The finite element method (FEM) is developed to analyse 2-D crack problems where the electric field and displacement gradients exhibit a size effect penomenon. This phenomenon in micro/nanoelectronic structures is described by the strain-and electric field-gradients in constitutive equations. The governing equations are derived using variational principles with the corresponding boundary conditions. The FEM formulation with C¹-continuous elements is subsequently developed and implemented. An example is presented and discussed to demonstrate the effects of the strain-and electric intensity-gradients on the electro-mechanical behavior of cracked solids.

Abstract: A fully coupled thermo-electro-mechanical models of cylindrical and truncated conical GaN/AlN Functionally Graded Quantum Dot (FGQD) systems with and without WL are analyzed in this study to determine the effect of lattice mismatch strain grading on the electromechanical behavior of the FGQD system. This has a technological and fundamental importance because the production methodology adopted for manufacturing QDs enables the composition of the QD material to be graded in the growth direction, so the material properties as well as the induced mismatch strain between the QD and the carrier matrix are accordingly graded. The power law is used to describe the grading function. Based on the obtained results, grading of material properties and lattice mismatch strain have significant effect on the distribution of the electromechanical quantities inside the QD and can be used as another tuning parameter in the design of QD systems.

Abstract: General 2D boundary value problems of piezoelectric nanosized structures with cracks under a thermal load are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nanosized structures is described by the strain-gradient effect. The strain gradients are considered in the constitutive equations for electric displacement and the high-order stress tensor. For this model, the governing equations are derived with the corresponding boundary conditions using the variational principle. Uncoupled thermoelasticity is considered, thus, the heat conduction problem is analyzed independently of the mechanical fields in the first step. A numerical example is presented and discussed to demonstrate the effects of the strain-gradient.

Abstract: Time-harmonic crack analysis in two-dimensional piezoelectric functionally graded materials (FGMs) is presented in this paper. A frequency-domain boundary element method (BEM) is developed for this purpose. Since fundamental solutions for piezoelectric FGMs are not available, a boundary-domain integral formulation is derived. This requires only the frequency-domain fundamental solutions for homogeneous piezoelectric materials. The radial integration method is adopted to compute the resulting domain integrals. The collocation method is used for the spatial discretization of the frequency-domain boundary integral equations. Adjacent the crack-tips square-root elements are implemented to capture the local square-root-behavior of the generalized crack-opening-displacements properly. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. Numerical examples will be presented and discussed to show the influences of the material gradation and the dynamic loading on the intensity factors.

Abstract: In this paper, static and dynamic crack analysis in two-dimensional functionally graded piezoelectric composites is presented. For this purpose, a time-domain boundary element method is developed. The collocation method is used for the spatial discretization of the time-domain boundary integral equations, while the convolution quadrature is adopted for temporal discretization. Since fundamental solutions for functionally graded piezoelectric materials are not available, a boundary-domain integral formulation is derived. The Laplace transformed fundamental solutions for homogeneous piezoelectric materials are applied. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. The radial integration method is adopted to compute the resulting domain integrals. Adjacent the crack-tips are square-root elements implemented to capture the local square-root-behaviour of the generalized crack-opening-displacements properly. An explicit time-stepping scheme is obtained to compute the unknown boundary data. Numerical examples will be presented to show the influences of the material gradation, poling direction and the transient dynamic loadings on the intensity factors.

Abstract: The size-dependent features concerning the mechanical behavior of the micro/nanoelectronic structures are well known from experiments. They are described by the strain-gradient effect in this paper since the classical elasticity theory fails to capture the size effect of the nanostructures. The electric field-strain gradient coupling is considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions using the variational principle. The path independent J-integral is derived for fracture mechanics analysis of piezoelectric solids described by the gradient theory.

Abstract: A large (magistral) crack is analyzed in a voided piezoelectric solid. The representative volume element (RVE) is analyzed for determination of influence of voids on material properties. The whole domain is divided into two subdomains. At the crack tip vicinity it is considered a subdomain with the crack tip and circular voids. Material properties correspond to the piezoelectric skeleton there. The rest part of analyzed domain is modeled by effective material properties obtained from analyses on the RVE. The scaled boundary finite element method (SBFEM) is applied to solve all boundary value problems.

Abstract: In this paper, the symmetric Galerkin boundary element method (SGBEM) will be developed and applied for boundary value problems with layered and fiber reinforced piezoelectric representative volume elements (RVE) and real macroscopic structures. Mechanical and electric loadings are considered to determine the effective material properties. For this purpose, the resulting boundary value problem is formulated as boundary integral equations (BIEs). The Galerkin method is applied for the spatial discretization of the boundary to solve the BIEs numerically. The required surface derivatives of the generalized displacements are computed directly with a boundary integral equation. Numerical examples will be presented and discussed to show the efficiency of the present SGBEM and the influence of the fiber variation on the effective material properties.

Abstract: Mechanical and electric loads are considered for 2-d crack problems in conducting piezoelectric materials. The electric displacement in conducting piezoelectric materials is influenced by the electron density and it is coupled with the electric current. The coupled governing partial differential equations (PDE) for stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. Nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity. Local integral equations are derived for a unit function as the test function on circular subdomains. All field quantities are approximated by the moving least-squares (MLS) scheme.