Application of dual boundary element method in active sensing

In this paper, a boundary element method (BEM) for the dynamic analysis of 3D solid structures with bonded piezoelectric transducers is presented. The host structure is modelled with BEM and the piezoelectric transducers are formulated using a 3D semi-analytical finite element approach. The elastodynamic analysis of the entire structure is carried out in Laplace domain and the response in time domain is obtained by inverse Laplace transform. The BEM is validated against established finite element method (FEM).

A three-dimensional boundary element model for the analysis of polycrystalline materials at the microscale

A three-dimensional multi-domain anisotropic boundary element formulation is presented for the analysis of polycrystalline microstructures. The formulation is naturally expressed in terms of intergranular displacements and tractions that play an important role in polycrystalline micromechanics, micro-damage and micro-cracking. The artificial morphology is generated by Hardcore Voronoi tessellation, which embodies the main statistical features of polycrystalline microstructures. Each crystal is modeled as an anisotropic elastic region and the integrity of the aggregate is restored by enforcing interface continuity and equilibrium between contiguous grains. The developed technique has been ap…

A Grain Boundary Formulation for the Analysis of Three-Dimensional Polycrystalline Microstructures

A 3D grain boundary formulation is presented for the analysis of polycrystalline microstructures. The formulation is expressed in terms of intergranular displacements and tractions, that play an important role in polycrystalline micromechanics, micro-damage and micro-cracking. The artificial morphology is generated by Hardcore Voronoi tessellation, which embodies the main statistical features of polycrystalline microstructures. Each crystal is modeled as an anisotropic elastic region and the integrity of the aggregate is restored by enforcing interface continuity and equilibrium between contiguous grains. The developed technique has been applied to the numerical homogenization of cubic poly…

two-scale three-dimensional boundary element framework for degradation and failure in polycrystalline materials

A fully three-dimensional two-scale boundary element approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macroscale) and the material grain scale (micro-scale). The damage-induced local softening at the macroscale is modelled employing an initial stress approach. The microscopic degradation processes are explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum and employing a three-dimensional grain-boundary formulation to simulate intergranular degradation and failure in the microstructural Voronoi-type morphology through cohesive-frictional contact …

Intergranular damage and fracture in polycrystalline materials. A novel 3D microstructural grain-boundary formulation

The design of advanced materials requires a deep understanding of degradation and failure pro- cesses. It is widely recognized that the macroscopic material properties depend on the features of the microstructure. The knowledge of this link, which is the main subject of Micromechanics [1], is of relevant technological interest, as it may enable the design of materials with specific requirements by means of suitable manipulations of the microstructure. Polycrystalline materials are used in many technological applications. Their microstructure is characterized by the grains morphology, size distribution, anisotropy, crystallographic orientation, stiffness and toughness mismatch and by the phy…

A fast BEM for the analysis of plates with bonded piezoelectric patches

In this paper a fast boundary element method for the elastodynamic analysis of 3D structures with bonded piezoelectric patches is presented. The elastodynamic analysis is performed in the Laplace domain and the time history of the relevant quantities is obtained by inverse Laplace transform. The bonded patches are modelled using a semi-analytical state-space variational approach. The computational features of the technique, in terms of required storage memory and solution time, are improved by a fast solver based on the use of hierarchical matrices. The presented numerical results show the potential of the technique in the study of structural health monitoring (SHM) systems.

A fast BEM model for 3D elastic structures with attached piezoelectric sensors

A fast boundary element model for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computational…

Fast Solution of 3D Elastodynamic Boundary Element Problems by Hierarchical Matrices

In this paper a fast solver for three-dimensional elastodynamic BEM problems formulated in the Laplace transform domain is presented, implemented and tested. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix for each value of the Laplace parameter of interest and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy for speeding up the overall analysis is presented and tested. The reported numerical results demonstrate the effectiveness of the technique.

Computational modelling of brittle failure in polycrystalline materials using cohesive-frictional grain-boundary elements

A 3D grain-level formulation for the study of brittle failure in polycrystalline microstructures is presented. The microstructure is represented as a Voronoi tessellation and the boundary element method is used to model each crystal of the aggregate. The continuity of the aggregate is enforced through suitable conditions at the intergranular interfaces. The grain-boundary model takes into account the onset and evolution of damage by means of an irreversible linear cohesive law, able to address mixed-mode failure conditions. Upon interface failure, a non-linear frictional contact analysis is introduced for addressing the contact between micro-crack surfaces. An incremental-iterative algorith…

Porosity effects on elastic properties of polycrystalline materials: a three-dimensional grain boundary formulation

Polycrystalline materials are widely used in many technological applications of engineering interest. They constitute an important class of heterogeneous materials, and the investigation of the link between their macro and micro properties, main task of the micromechanics [1], is of relevant technological concern. The internal structure of a polycrystalline material is determined by the size and the shape of the grains, by their crystallographic orientation and by different type of defects within them. In this sense, the presence of internal voids, pores, is important to take into account in the determination of the polycrystalline aggregate properties. Porosity exists in almost all materia…

Dual Boundary Element Method for fatigue crack growth: implementation of the Richard’s criterion

A new criterion for fatigue crack growth, whose accuracy was previously tested in the literature with the Finite Element Method, is here adopted with a Dual Boundary Element formulation. The fatigue crack growth of an elliptical inclined crack, embedded in a three dimensional cylindrical bar, is analyzed. In this way in addition to the propagation angle estimated by the Sih’s criterion, it is possible to take into account a twist propagation angle. The two propagation criteria are compared in terms of shape of the propagated crack and in terms of SIFs along the crack front. The efficiency of the Dual Boundary Element Method in this study is highlighted.

A fast dual boundary element method for 3D anisotropic crack problems

In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …

Polycrystalline materials with pores: effective properties through a boundary element homogenization scheme

In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a formulation built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are ob…

On the accuracy of the fast hierarchical DBEM for the analysis of static and dynamic crack problems

In this paper the main features of a fast dual boundary element method based on the use of hierarchical matrices and iterative solvers are described and its effectiveness for fracture mechanics problems, both in the static and dynamic case, is demonstrated. The fast solver is built by representing the collocation matrix in hierarchical format and by using a preconditioned GMRES for the solution of the algebraic system. The preconditioner is computed in hierarchical format by LU decomposition of a coarse hierarchical representation of the collocation matrix. The method is applied to elastostatic problems and to elastodynamic cases represented in the Laplace transform domain. The application …

Fast Hierarchical Boundary Element Method for Large Scale 3-D Elastic Problems

This chapter reviews recent developments in the strategies for the fast solution of boundary element systems of equations for large scale 3D elastic problems. Both isotropic and anisotropic materials as well as cracked and uncracked solids are considered. The focus is on the combined use the hierarchical representation of the boundary element collocation matrix and iterative solution procedures. The hierarchical representation of the collocation matrix is built starting from the generation of the cluster and block trees that take into account the nature of the considered problem, i.e. the possible presence of a crack. Low rank blocks are generated through adaptive cross approximation (ACA) …

Hierarchical-ACA DBEM for anisotropic three-dimensional time-domain fracture mechanics

Nonlinear Analysis of a Reinforced Panel undergoing Large Deflection

A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems

In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…

Brittle failure in polycrystalline RVEs by a grain-scale cohesive boundary element formulation

Polycrystalline materials are commonly employed in engineering structures. For modern applica- tions a deep understanding of materials degradation is of crucial relevance. It is nowadays widely recognized that the macroscopic material properties depend on the microstructure. The polycrystalline microstructure is characterized by the features of the grains and by the phys- ical and chemical properties of the intergranular interfaces, that have a direct influence on the evolution of the microstructural damage. The experimental investigation of failure mechanisms in 3D polycrystals still remains a challenging task. A viable alternative, or complement, to the experiments is Computational Microm…

Effects of voids and flaws on the mechanical properties and on intergranular damage and fracture for polycrystalline materials

It is widely recognized that the macroscopic material properties depend on the features of the microstructure. The understanding of the links between microscopic and macroscopic material properties, main topic of Micromechanics, is of relevant technological interest, as it may enable the deep understanding of the mechanisms governing materials degradation and failure. Polycrystalline materials are used in many engineering applications. Their microstructure is determined by distribution, size, morphology, anisotropy and orientation of the crystals. It worth noting that also the physical-chemical properties of the intergranular interfaces, as well as the presence of micro-imperfections within…

A fast hierarchical BEM for 3-D anisotropic elastodynamics

Hierarchical-ACA DBEM for Anisotropic Three-Dimensional Time-Harmonic Fracture Mechanics

A hierarchical BEM solver for the analysis of three-dimensional anisotropic time-harmonic fracture mechanics problems is presented. A thorough investigation on the relations and interactions between the numerically computed anisotropic fundamental solutions and the algorithm used to approximate the blocks of the hierarchical matrix, namely Adaptive Cross Approximation, is carried out leading to the employed computational strategy. The use of the hierarchical matrices and iterative solvers is proved as an effective technique for speeding up the solution procedure and reducing the required memory storage in time-harmonic three-dimensional anisotropic fracture mechanics problems.

A hierarchical-ACA technique for large-scale acoustic simulations: complex geometries with sound adsorbent materials

In this paper a boundary element approach for acoustic simulations based on the hierarchical-matrix format coupled with the adaptive cross approximation (ACA) algorithm and a hierarchical GMRES solver is presented. The cluster tree is generated using preliminary considerations of the prescribed boundary conditions. An improved ACA algorithm, applied, separately, to Neumann, Dirichlet and mixed Robin conditions, is described. Numerical results are presented to show the new approach to be up to 50% faster than conventional ACA approach.

Hierarchical BEM for dynamic analysis of anisotropic 3-D cracked solids

Rapid acoustic boundary element method for solution of 3D problems using hierarchical adaptive cross approximation GMRES approach

This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the p…