0000000000011039
AUTHOR
Vincenzo Gulizzi
Alternative boundary integral equations for fracture mechanics in 2D anisotropic bodies
An alternative dual boundary element formulation for generally anisotropic linear elastic twodimensional bodies is presented in this contribution. The formulation is based on the decomposition of the displacement field into the sum of a vector field satisfying the anisotropic Laplace equation and the gradient of the classic Airy stress function. By suitable manipulation of the integral representation of the anisotropic Laplace equation, a set of alternative integral equations is obtained, which can be used in combination with the displacement boundary integral equation for the solution of crack problems. Such boundary integral equations have the advantage of avoiding hyper-singular integral…
A Model for High-Cycle Fatigue in Polycrystals
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,…
Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators
In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansion…
A micro-mechanical model for grain-boundary cavitation in polycrystalline materials
In this work, the grain-boundary cavitation in polycrystalline aggregates is investigated by means of a grain-scale model. Polycrystalline aggregates are generated using Voronoi tessellations, which have been extensively shown to retain the statistical features of real microstructures. Nucleation, thickening and sliding of cavities at grain boundaries are represented by specific cohesive laws embodying the damage parameters, whose time evolution equations are coupled to the mechanical model. The formulation is presented within the framework of a grain-boundary formulation, which only requires the discretization of the grain surfaces. Some numerical tests are presented to demonstrate the fea…
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…
A microstructural model for homogenisation and cracking of piezoelectric polycrystals
Abstract An original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitab…
HIGH-ORDER ACCURATE EMBEDDED-BOUNDARY DISCONTINUOUS GALERKIN METHODS FOR INVISCID GAS DYNAMICS
This work presents a computational framework for solving the equations of inviscid gas dynamics over embedded geometries based on the discontinuous Galerkin (DG) method. The novelty of the framework is the ability to achieve high-order accuracy in the regions of smooth flow and to handle the presence of solution discontinuities via suitably introduced damping terms, which allow controlling spurious oscillations that are typical of high-order methods for first-order hyperbolic PDEs. The framework employs block structured Cartesian grids where a level set function defines implicitly the considered geometry. The domain is partitioned by intersecting the grid and the level set function, such th…
On the use of the EMI for the health monitoring of bonded elements
The low weight, robustness and fatigue resistance of adhesive joints make them suitable for structural joints. A fully developed nondestructive evaluation technique however is needed to monitor and assess the quality of bonded joints. In the present paper the application of the electromechanical impedance (EMI) technique is proposed. In the EMI method a piezoelectric transducer (PZT) is attached to the structure of interest. The high sensitivity and low power consumption make the EMI method feasible for real time structural health monitoring. In this study we investigated the sensitivity of the electromechanical response of a PZT to the curing and the quality of the adhesive used for bonded…
Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells
Abstract An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotrop…
On the use of the electromechanical impedance technique for the assessment of dental implant stability: Modeling and experimentation
We propose the electromechanical impedance technique to monitor the stability of dental implants. The technique consists of bonding one wafer-type piezoelectric transducers to the implant system. When subjected to an electric field, the transducer induces structural excitations which, in turn, affect the transducer’s electrical admittance. The hypothesis is that the health of the bone surrounding the implant affects the sensor’s admittance. A three-dimensional finite element model of a transducer bonded to the abutment of a dental implant placed in a host bone site was created to simulate the progress of the tissue healing that occurs after surgery. The healing was modeled by changing the …
High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method
Abstract A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations , while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function . The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity an…
A computational framework for low-cycle fatigue in polycrystalline materials
Abstract A three-dimensional framework for low-cycle fatigue analysis of polycrystalline aggregates is proposed in this work. First, a cohesive law coupling plasticity and damage is developed for modelling cycle-by-cycle degradation of material interfaces up to complete de-cohesion and failure. The law may model both quasi-static degradation under increasing monotonic load and degradation under cyclic loading, through a coupled plasticity-damage model whose activation and flow rules are formulated in a thermodynamically consistent framework. The proposed interface laws have been then implemented and coupled with a multi-region boundary element formulation, with the aim of analysing low-cycl…
Discontinuous Galerkin models for composite multilayered shells with higher order kinematics
Composite multilayered shells are widely employed in aerospace, automotive and civil engineering as weight-saving structural components. In multilayered shells, despite its versatility, the interplay between the curved geometry and the properties of the composite layers induces a complex distribution of the mechanical fields, which must be accurately resolved to safely employ generally curved composite shells as load-bearing structures. The problem can be addressed through the two-dimensional shell theories, which are based on suitable assumptions on the behavior of the mechanical fields throughout the thickness of the considered structures and are a viable strategy for reducing the computa…
On the repeatability of the EMI for the monitoring of bonded joints
We study the feasibility and the repeatability of the electromechanical impedance (EMI) method for the health monitoring of lightweight bonded joints. The EMI technique exploits the coupling between the displacement field and the potential field of a piezoelectric material, by attaching or embedding a piezoelectric transducer to the structure to be monitored. The sensor is excited by an external voltage and the electrical admittance which is the ratio between the electric current and the applied voltage is measured as it depends on the mechanical coupling between the transducer and the host structure. Owing to this interaction, the admittance may represent a signature for the health of the …
Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method
Abstract A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Karman's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behav…
A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates
Abstract In this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a per-layer, high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layer-level description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on a discontinuous representation of the unknown fields over the mesh elements and on the introduction of boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order mesh elements and provide …
A novel micro-mechanical model for polycrystalline inter-granular and trans-granular fracture
In this work, a novel grain boundary formulation for inter-and trans-granular cracking of polycrystalline materials is presented. The formulation is based on the use of boundary integral equations for anisotropic solids and has the advantage of expressing the considered problem in terms of grain boundary variables only. Inter-granular cracking occurs at the grain boundaries whereas trans-granular cracking is assumed to take place along specific cleavage planes, whose orientation depends on the crystallographic orientation of the grains. The evolution of inter-and trans-granular cracks is then governed by suitably defined cohesive laws, whose parameters characterize the behavior of the two f…
An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials
An enhanced three-dimensional (3D) framework for computational homogenization and intergranular cracking of polycrystalline materials is presented. The framework is aimed at reducing the computational cost of polycrystalline micro simulations, with an aim towards effective multiscale modelling. The scheme is based on a recently developed Voronoi cohesive-frictional grain-boundary formulation. A regularization scheme is used to avoid excessive mesh refinements often induced by the presence of small edges and surfaces in mathematically exact 3D Voronoi morphologies. For homogenization purposes, periodic boundary conditions are enforced on non-prismatic periodic micro representative volume ele…
A grain-scale model for high-cycle fatigue degradation in polycrystalline materials
Abstract A grain-scale three-dimensional model for the analysis of fatigue intergranular degradation in polycrystalline materials is presented. The material microstructure is explicitly represented through Voronoi tessellations, of either convex or non-convex domains, and the mechanics of individual grains is modelled using a boundary integral formulation. The intergranular interfaces degrade under the action of cyclic loads and their behaviour is represented employing a cohesive zone model embodying a local irreversible damage parameter that evolves according to high-cycle continuum damage laws. The model is based on the use of a damage decomposition into static and cyclic contributions, a…
On the use of EMI for the assessment of dental implant stability
The achievement and the maintenance of dental implant stability are prerequisites for the long-term success of the osseointegration process. Since implant stability occurs at different stages, it is clinically required to monitor an implant over time, i.e. between the surgery and the placement of the artificial tooth. In this framework, non-invasive tests able to assess the degree of osseointegration are necessary. In this paper, the electromechanical impedance (EMI) method is proposed to monitor the stability of dental implants. A 3D finite element model of a piezoceramic transducer (PZT) bonded to a dental implant placed into the bone was created, considering the presence of a bone- impla…
A discontinuous Galerkin formulation for variable angle tow composite plates higher-order theories
A discontinuous Galerkin formulation for the mechanical behaviour of Variable Angle Tow multi-layered composite plates is presented. The starting point of the formulation is the strong form of the governing equations, which are obtained by means of the Principle of Virtual Displacement, the Generalized Unified Formulation and the Equivalent Single Layer assumption for the mechanical behaviour of the whole assembly. To obtain the corresponding discontinuous Galerkin formulation, an auxiliary flux variable is introduced and the governing equations are rewritten as a first-order system of partial differential equations. To link neighbouring mesh elements, suitably defined numerical fluxes are …
A grain boundary formulation for crystal plasticity
Abstract A three-dimensional grain-boundary formulation for small strains crystal plasticity is presented for the first time. The method is developed and implemented for both single grains and polycrystalline aggregates and it is based on the use of a suitable set of boundary integral equations for modelling the individual grains, which are represented as anisotropic elasto-plastic domains. In the boundary integral framework, crystal plasticity is modelled resorting to an initial strains approach and specific aspects, related to the integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations, are discussed and suitably addressed for the first…
Electromechanical impedance method for the health monitoring of bonded joints: Numerical modelling and experimental validation
The electromechanical impedance (EMI) method is one of the many nondestructive evaluation approaches proposed for the health monitoring of aerospace, civil, and mechanical structures. The method consists of attaching or embedding one or more wafer-type piezoelectric transducers (PZTs) to the system of interest, the host structure, and measuring certain electrical characteristics of the transducers. As these characteristics are also related to the impedance of the host structure, they can be used to infer the mechanical properties of the monitored structure. In the study presented in this paper, we utilize the EMI to monitor the quality of adhesively bonded joints. A finite element formulati…
Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions
Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…
Nonlinear free vibrations analysis of cracked composite stiffened plates via X-Ritz approach
Thin and moderately thick composite multi-layered plates are widely employed in naval and aerospace structures. They can experience the presence of cracks, generated for example by corrosion, fatigue or accidental external causes, which aect their static and dynamic behaviour. As regard the dynamic characteristics of plates, many studies have focused on the linear vibration analysis of both isotropic and composite thin and thick plates, providing for a comprehensive knowledge of the plate dynamic behaviour. However, for an accurate appraisal of the plate dynamics, in some applications it is needed to investigate the nonlinear free vibration problem; a literature survey evidences that the la…
A Model for Low-Cycle Fatigue in Micro-Structured Materials
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 tra…
Modelling stress-corrosion microcracking in polycrystalline materials by the Boundary Element Method
The boundary element method is employed in this study in conjunction with the finite element method to build a multi-physics hybrid numerical model for the computational study of stress corrosion cracking related to hydrogen diffusion in polycrystalline microstructures. More specifically a boundary integral representation is used to represent the micro-mechanics of the aggregate while an explicit finite element method is used to model inter-granular hydrogen diffusion. The inter-granular interaction between contiguous grains is represented through cohesive laws, whose physical parameters depend on the concentration of inter-granular hydrogen, diffusing along the interfaces according to the …
Micro-cracking of brittle polycrystalline materials with initial damage
In this paper, the effect of pre-existing damage on brittle micro-cracking of polycrystalline materials is explored. The behaviour of single and multiple cracks randomly distributed within a grain scale polycrystalline aggregate is investigated using a recently developed grain boundary 3D computational framework. Each grain is modelled as a single crystal anisotropic domain. Opening, sliding and/or contact at grain boundaries are modelled using nonlinear cohesive-frictional laws. The polycrystalline micro-morphologies are generated using Voronoi tessellation algorithms in combination with a regularisation scheme to avoid the presence of unnecessary small geometrical entities (edges and face…
Advanced models for nonlocal magneto-electro-elastic multilayered plates based on Reissner mixed variational theorem
In the present work, nonlocal layer-wise models for the analysis of magneto-electro-elastic multilayered plates are formulated. An Eringen non-local continuum behaviour is assumed for the layers material; in particular, as usual in plate theories, partial in-plane nonlocality is assumed whereas local constitutive behaviour is considered in the thickness direction. The proposed plate theories are obtained via the Reissner Mixed Variational Theorem, assuming the generalized displacements and generalized out-of-plane stresses as primary variables, and expressing them as through-the-thickness expansions of suitably selected functions, considering the expansion order as a free parameter. In the …
Elucidating the Effect of Bimodal Grain Size Distribution on Plasticity and Fracture Behavior of Polycrystalline Materials
The refinement of grains in a polycrystalline material leads to an increase in strength but as a counterpart to a decrease in elongation to fracture. Different routes are proposed in the literature to try to overpass this strength-ductility dilemma, based on the combination of grains with highly contrasted sizes. In the simplest concept, coarse grains are used to provide relaxation locations for the highly stressed fine grains. In this work, a model bimodal polycrystalline system with a single coarse grain embedded in a matrix of fine grains is considered. Numerical full-field micro-mechanical analyses are performed to characterize the impact of this coarse grain on the stress-strain const…
A Grain-Scale Model of Inter-Granular Stress Corrosion Cracking in Polycrystals
In this contribution, we propose a cohesive grain-boundary model for hydrogen-assisted inter-granular stress corrosion cracking at the grain-scale in 3D polycrystalline aggregates. The inter-granular strength is degraded by the presence of hydrogen and this is accounted for by employing traction-separation laws directly depending on hydrogen concentration, whose diffusion is represented at this stage through simplified phenomenological relationships. The main feature of the model is that all the relevant mechanical fields are represented in terms of grain-boundary variables only, which couples particularly well with the employment of traction-separation laws.
A Microstructural Model for Micro-Cracking in Piezoceramics
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 electromechanical 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…
An extended Ritz formulation for buckling and post-buckling analysis of cracked multilayered plates
Abstract An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Karman’s theory to account for geometric non-linearities ; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results fr…
Onthe repeatability of electromechanical impedance for monitoring of bonded joints
The repeatability and sensitivity of the electromechanical impedance (EMI) method when employed for the structural health monitoring of bonded joints were investigated. A simple joint was assembled by bonding an aluminum strip to a square aluminum plate. Two rounds of experiments were performed. The first set aimed at verifying the repeatability of the method. The joint was monitored by using one piezoelectric sensor. The PZT was glued to the plate and never removed, whereas a poorly bonded joint was assembled and disassembled three times. For each case, the electromechanical signature was measured during the curing of the adhesive. After the three tests, the same joint was built with a dif…
A novel boundary element formulation for anisotropic fracture mechanics
Abstract A novel boundary element formulation for two-dimensional fracture mechanics is presented in this work. The formulation is based on the derivation of a supplementary boundary integral equation to be used in combination with the classic displacement boundary integral equation to solve anisotropic fracture mechanics problems via a single-region approach. The formulation is built starting from the observation that the displacement field for an anisotropic domain can be represented as the superposition of a vector field, whose components satisfy a suitably defined anisotropic Laplace equation, and the gradient of the Airy stress function. The supplementary boundary integral equation is …
Microcracking in piezoelectric materials by the Boundary Element Method
A 3D boundary element model for piezoelectric polycrystalline micro-cracking is discussed in this contribution. The model is based on the boundary integral representation of the electro-mechanical behavior of individual grains and on the use of a generalized cohesive formulation for inter-granular micro-cracking. The boundary integral formulation allows to address the electro-mechanical boundary value problem in terms of generalized grain boundary and inter-granular displacements and tractions only, which implies the natural inclusion of the cohesive laws in the formulation, the simplification of the analysis pre-processing stage, and the reduction of the number of degrees of freedom of the…
A Microstructural Model for Micro-Cracking in Piezoceramics
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 th…
Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method
A novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent-single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displacement field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its discontinuous natur…
An implicit mesh discontinuous Galerkin formulation for higher-order plate theories
In this work, a discontinuous Galerkin formulation for higher-order plate theories is presented. The starting point of the formulation is the strong form of the governing equations, which are derived in the context of the Generalized Unified Formulation and the Equivalent Single Layer approach from the Principle of Virtual Displacements. To express the problem within the discontinuous Galerkin framework, an auxiliary flux variable is introduced and the governing equations are rewritten as a system of first-order partial differential equations, which are weakly stated over each mesh element. The link among neighboring mesh elements is then retrieved by introducing suitably defined numerical …
A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries
Author(s): Gulizzi, Vincenzo; Almgren, Ann S; Bell, John B | Abstract: We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an $hp$ adaptive mesh refinement ($hp$-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The $hp$-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a…
Modelling intergranular and transgranular micro-cracking in polycrystalline materials
Abstract In this work, a grain boundary formulation for intergranular and transgranular micro-cracking in three-dimensional polycrystalline aggregates is presented. The formulation is based on the displacement and stress boundary integral equations of solid mechanics and it has the advantage of expressing the polycrystalline problem in terms of grain boundary variables only. The individual grains within the polycrystalline morphology are modelled as generally anisotropic linear elastic domains with random spatial orientation. Transgranular micro-cracking is assumed to occur along specific cleavage planes, whose orientation in space within the grains depend upon the crystallographic lattice.…
An integrated structural health monitoring system based on electromechanical impedance and guided ultrasonic waves
We propose a structural health monitoring (SHM) paradigm based on the simultaneous use of ultrasounds and electromechanical impedance (EMI) to monitor waveguides. Methods based on the propagation of guided ultrasonic waves (GUWs) are increasingly used in all those SHM applications that benefit from built-in transduction, moderately large inspection ranges, and high sensitivity to small flaws. Meantime, impedance-based SHM promises to adequately assess locally the structural integrity of simple waveguides and complex structures such as bolted connections. As both methods utilize piezoelectric transducers bonded or embedded to the structure of interest, this paper describes a unified SHM para…
A Novel Numerical Formulation for Crystal Plasticity
Crystal plasticity plays a crucial role in the mechanics of polycrystalline materials and it is commonly modeled within the framework of the crystal plasticity finite element method (CPFEM). In this work, an alternative formulation for small strains crystal plasticity is presented. The method is based on a boundary integral formulation for polycrystalline problems and plasticity is addressed using an initial strains approach. Voronoi-type micro-morphologies are considered in the polycrystalline case. A general grain-boundary incremental/iterative algorithm, embedding the flow and hardening rules for crystal plasticity, is developed. The key feature of the method is the expression of the mic…
Buckling and post-buckling analysis of cracked composite plates via a single-domain Ritz approach
Thin and moderately thick composite multi-layered plates are widely employed in many engineering applications, especially in naval and aerospace structures. These structural components can experience in service the presence of cracks, generated for example by corrosion, fatigue or accidental external causes. Cracks can affect the load carrying capability, buckling and post-buckling behaviour of plates; therefore, their effects need to be investigated and taken into account for fail safe or damage tolerant design. Additionally, attention should be devoted to the interaction of cracks with buckling and post-buckling behaviour, as the energy release rate in post-buckling regimes can be adverse…
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation…
Grain-boundary modelling of hydrogen assisted intergranular stress corrosion cracking
Abstract A novel hybrid strategy for modelling intergranular hydrogen embrittlement in polycrystalline microstructures is proposed. The technique is based on a grain-boundary integral representation of the polycrystalline micro-mechanics, numerically solved by the boundary element method, coupled with an explicit finite element model of the intergranular hydrogen diffusion. The intergranular interaction between contiguous grains in the aggregate is modelled through extrinsic cohesive-frictional traction-separation laws, whose parameters depend on the concentration of intergranular hydrogen, which diffuses over the interface according to the Fick’s second law, inducing the weakening of the i…
X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks
The analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz approach based on the first-order shear deformation theory and von Karman’s geometric nonlinearity assumptions. The trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are assessed to validate the approach and show its efficiency and potential. Original results are then…
Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates
In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design o…
Boundary Element Crystal Plasticity Method
A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and har…
Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators
In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansions…