Instantaneous baseline damage localisation using sensor mapping

In this paper an instantaneously recorded baseline method is proposed using piezoelectric transducers for damage localisation under varying temperature. This method eliminates need for baselines required when operating at different temper- atures by mapping a baseline area onto the interrogation area. Instantaneously recorded baselines and current interrogation signals are calibrated based on the sensor mapping. This allows extraction of damage scatter signal which is used to localise damage. The proposed method is used to localise actual impact damage on a composite plate under varying temperatures. The method is also applied to a stiffened fuselage panel to accurately localise impact damage

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 laws. The scales coupling is achieved downscaling macro-strains as periodic boundary conditions for the RVE, while overall macro-stresses are obtained via volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. Some attention is devoted to avoiding pathological damage localization at the macro-scale. The multiscale processing algorithm is described and some preliminary results are illustrated

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

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as three-dimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the tractionseparation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incremental-iterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo- and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads

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 Micromechanics. The present-day availability of cheaper computational power is favoring the advancement of the sub- ject. A popular approach for polycrystalline fracture problems consists in the use of cohesive sur- faces embedded in a Finite Element (FE) representation of the microstructure, so that the evolution of microcracks stems as an outcome of the simulation, without any assumptions, see e.g. [4]. An alternative to the FEM is the Boundary Element Method (BEM). A 2D cohesive BE formula- tion for intergranular failure and a 3D BE formulation for polycrystalline materials homogeniza- tion have been recently proposed [1–3]. In this work, a novel 3D grain-level model for the study of polycrystalline intergranular degra- dation and failure is presented. The microstructures are generated as Voronoi tessellations, that mimic the main statistics of polycrystals. The formulation is based on a grain-boundary integral representation of the elastic problem for the crystals, seen as anisotropic domains with random crystallographic orientation in space. The integrity of the aggregate is restored by enforcing suit- able intergranular conditions. The evolution of intergranular damage is modeled using an extrinsic irreversible mixed-mode cohesive linear law. Upon interface failure, non-linear frictional con- tact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. An incremental-iterative algorithm is used for tracking the micro-cracking evolution. Several numeri- cal tests have been performed and they demonstrated the capability of the formulation to track 3D micro-cracking, under either tensile or compressive loads

A multiscale approach to polycrystalline materials damage and failure

A two-scale three-dimensional approach for degradation and failure in polycrystalline materials is presented. The method involves the component level and the grain scale. The damageinduced softening at the macroscale is modelled employing an initial stress boundary element approach. The microscopic degradation is explicitly modelled associating Representative Volume Elements (RVEs) to relevant points of the macro continuum and employing a cohesive-frictional 3D grain-boundary formulation to simulate intergranular degradation and failure in the Voronoi morphology. Macro-strains are downscaled as RVEs' periodic boundary conditions, while overall macro-stresses are obtained upscaling the micro-stress field via volume averages. The comparison between effective macro-stresses for the damaged and undamaged RVEs allows to define a macroscopic measure of local material degradation. Some attention is devoted to avoiding pathological damage localization at the macro-scale. The multiscale processing algorithm is described and some preliminary results are illustrated

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

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 obtained through material homogenization, computing the volume averages of micro-strains and stresses and taking the ensemble average over a certain number of microstructural samples. In the proposed formulation, the volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The obtained results show the capability of the model to assess the macroscopic effects of porosity

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)