Papers by Keyword: Boundary Element Method (BEM)

Abstract: The purpose of this paper is to solve dynamic fracture problems of plates under both tension and bending using the boundary element method (BEM). The dynamic problems were solved in the Laplace-transform domain, which avoided the calculation of the domain integrals resulting from the inertial terms. The dual boundary element method, in which both displacement and traction boundary integral equations are utilized, was applied to the modelling of cracks. The dynamic fracture analysis of a plate under combined tension and bending loads was conducted using the BEM formulations for the generalized plane stress theory and Mindlin plate bending theory. Dynamic stress intensity factors were estimated based on the crack opening displacements.

Abstract: A microscale formulation for low-cycle fatigue degradation in heterogeneous materials is presented. The interface traction-separation law is modelled by a cohesive zone model for low-cycle fatigue analysis, which is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variables. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the static failure condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behaviour without any fatigue degradation for low levels of cyclic traction. The developed model is then applied to micro-structured materials whose micro-mechanics is analysed using a boundary integral formulation. Preliminary results demonstrate the potential of the developed cohesive model. The future application of the proposed technique is discussed in the framework of multiscale modelling of engineering components and design of micro-electro-mechanical devices (MEMS).

Abstract: The aim of this paper was to carry out numerical simulations of structural health monitoring applications for plate structures using the boundary element method (BEM). The fundamental symmetric Lamb mode (S0) is chosen for the SHM applications. The propagation, reflection and diffraction of the S0 mode Lamb wave are modelled using a boundary element formulation based on the plane stress theory. Piezoelectric (PZT) actuators are mounted on plate surfaces to excite the S0 mode wave. A semi-analytical method is adopted to couple the PZT actuators and the host plate. Numerical results show that BEM is a very efficient simulation method for the structural health monitoring of plates.

Abstract: Piezoelectric materials exhibit an electromechanical coupling which allows for their use assensors or energy harvesting devices (direct piezoelectric effect) or actuators and shape control de-vices (inverse piezoelectric effect). They are applied in many technological sectors of current interestsuch as the aerospace and automotive industries, and they are generally constructed in block form orin a thin laminated composite. The study of the integrity of such materials in their various forms andsmall sizes is still a challenge nowadays. To gain a better understanding of these systems, this workpresents a crack surface contact formulation which makes it possible to study the integrity of theseadvanced materials under more realistic crack surface multifield operational conditions. The formu-lation uses the BEM for computing the elastic influence coefficients and contact operators over theaugmented Lagrangian to enforce contact constraints on the crack surface, in the presence of electricfields. The capabilities of this methodology are illustrated solving a benchmark problem.

Abstract: Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electro-mechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for the design of such systems. The most popular numerical method for the analysis of micro-mechanical multi-physics problems, still in a continuum mechanics setting, is the Finite Element Method (FEM). Here we propose an alternative integral formulation for the grain-scale analysis of degradation and failure in polycrystalline piezoceramics. The formulation is developed for 3D aggregates and inter-granular failure is modelled through generalised cohesive laws.

Abstract: A grain-scale formulation for high-cycle fatigue inter-granular degradation in polycrystalline aggregates is presented. The aggregate is represented through Voronoi tessellations and the mechanics of individual bulk grains is modelled using a boundary integral formulation. The inter-granular interfaces degrade under the action of cyclic tractions and they are represented using cohesive laws embodying a local irreversible damage parameter that evolves according to high-cycle continuum damage laws. The consistence between cyclic and static damage, which plays an important role in the redistribution of inter-granular tractions upon cyclic degradation, is assessed at each fatigue solution jump, so to capture the onset of macro-failure. Few polycrystalline aggregates are tested using the developed technique, which may find application in multiscale modelling of engineering components as well as in the design of micro-electro-mechanical devices (MEMS).

Abstract: The present paper is dedicated to numerical solution of boundary-value problems for piecewise homogeneous solids in terms of linear three-dimensional poroviscoelasticity. Mathematical model of poroviscoelastic material is based on Biot's model of poroelasticity. Viscoelastic effects refer to a skeleton of porous material and are described through the correspondence principle. Standard linear solid model is employed. In order to study the boundary-value problem boundary integral equations method is applied, and to find their solutions boundary element method for obtaining numerical solutions. A direct version of the BIE method is developed. The boundary-element scheme is constructed using: regularized BIE’s, a matched element-by-element approximation, adaptive numerical integration in combination with a singularity-reducing algorithm. The solution of the original problem is constructed in Laplace transforms, with the subsequent application of the algorithm for numerical inversion. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. The problem of poroviscoelastic prismatic solid clamped from one end and free at another is considered. The solid is composed of two subdomains. Heaviside-type load is applied to a free end of the solid. Viscosity parameter influence on dynamic responses of displacements, pore pressure and tractions is studied. Numerical results for displacements and pore pressure when subdomains are modelled with different viscoelastic properties are presented.

Abstract: The problem of the effect of a normal harmonic force on a porous beam in a 3D formulation is solved using the boundary-element method. A homogeneous fully saturated elastic porous medium is described using Biot’s mathematical model. The effect of the porosity and permeability parameters on the deflection of the beam and the distribution of pore pressure over the beam thickness is investigated. The comparison of the boundary-element solution with a 2D numerical-analytical one is given.

Abstract: In this paper, a Laplace domain boundary element method is applied for transient dynamic analysis of three-dimensional multi-domain linear piezoelectric structures. Piezoelectric materials of homogeneous sub-domains may have arbitrary degree of anisotropy. The boundary element formulation is based on a weakly singular representation of the piezoelectric boundary integral equations in the Laplace domain. To compute the time-domain solutions a convolution quadrature formula is applied for the numerical inversion of Laplace transform. Presented multi-domain boundary element method is tested on a three-dimensional problem of nonhomogeneous column which is made of two dissimilar piezoelectric materials and subjected to dynamic impact loading.

Abstract: Mechanics of advanced materials, such as poro-, visco-or poroviscoelastic materials, is relevant to such disciplines as geophysics, geo-and biomechanics, seismology, constricting. Because of the complexity of the inertial viscosity and mechanical phases coupling in porous media most transient response problems can only be solved via numerical methods. The present work is dedicated to numerical modelling of a problem of a Heaviside-type impact load acting on a brittle slab situated above a fluid saturated foundation. Slab is treated as elastic or poroelastic rock. Fluid saturated foundation is a soil and modeled as a poroviscoelastic media. Poroviscoelastic formulation is based on Biot’s theory of poroelasticity in combination with elastic-viscoelastic correspondence principle. Classical models of viscoelasticity are employed, such as Kelvin-Voight model, standard linear solid model and model with weakly singular kernel. The problem is treated in Laplace domain. Direct boundary integral method approach is used to obtain solution. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. A problem of Heaviside-type vertical load acting on a slab bonded on a poroviscoelastic halfspace is considered. The comparison of dynamic responses when poroviscoelastic halfspace is described by different viscoelactic models is presented.