A computationally effective 3D Boundary Element Method for polycrystalline micromechanics

An effective computational framework for homogenization and microcracking analysis of polycrystalline RVEs is presented. The method is based on a recently developed grain-boundary formulation for polycrystalline materials and several enhancements over the original technique are introduced to reduce the computational effort needed to model three-dimensional polycrystalline aggregates, which is highly desirable, especially in a multiscale perspective. First, a regularization scheme is used to remove pathological entities, usually responsible for unduly large mesh refinements, from Voronoi polycrystalline morphologies. Second, an improved meshing strategy is used, with an aim towards meshing robustness, a requirement often challenged by the inherent high statistical variability of Voronoi tessellations. Additionally, for homogenization purposes, the use of periodic non-prismatic polycrystalline RVEs is proposed as an alternative to the classical prismatic RVEs, generally employed in the literature. The proposed overall scheme promotes a remarkable reduction in the number of DoFs of the problem in hand, and thus outstanding savings in terms of computational time and memory storage. Furthermore, the smoother meshing strategy, combined with a Newton-Raphson method, enhances the convergence of the microcracking algorithm

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 Fick's second law. The model couples the effectiveness of the polycrystalline boundary element micro-mechanics model with the generality of the finite element representation of the inter-granular diffusion process. Few numerical tests are reported, to demonstrate the potential of the proposed technique

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 displace ment 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 nature, it can be naturally employed with nonconventional meshes. In this work, it is combined with the implicitly defined mesh technique, whereby the mesh of the shell modeling domain is constructed by intersecting an easy-to-generate background grid and a level set function implicitly representing the cutouts. Several numerical examples are considered for the buckling loads of plates and shells modeled by different theories and characterized by various materials, geometry, boundary conditions, and cutouts. The obtained results are compared with literature and finite-element solutions, and they demonstrate the accuracy and the robustness of the proposed approac

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- implant interface subjected to Young’s modulus change. The numerical model was validated experimentally by testing bovine bone samples. The EMI response of a PZT, bonded to the abutment screwed to implants inserted to the bone, was measured. To simulate the osseointegration process a pulp canal sealer was used to secure the implant to the bone. It was found that the PZT’s admittance is sensitive to the stiffness variation of the bone-implant interface. The results are promising because they show the potential of EMI method to (i) evaluate the material properties around dental implant, and (ii) promote a novel non-invasive monitoring of dental implant surgical procedure

A grain-scale model for high-cycle fatigue degradation in polycrystalline materials

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, an envelope load representation and a cycle jump strategy. The consistence between the cyclic damage and the action of the external loads, which contribute to the damage due to the redistribution of intergranular tractions between subsequent cycle jumps, is assessed at each solution step, so to capture the onset of macro-failure when the external actions cannot be equilibrated anymore by the critically damaged interfaces. Several numerical tests are reported to illustrate the potential of the developed method, which may find application in multiscale modelling of fatigue material degradation as well as in the design of micro-electro-mechanical devices (MEMS)

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 that the resulting mesh consists of a collection of standard d-dimensional rectangular cells and a relatively smaller number of irregular cut cells in proximity of the boundary of the embedded geometry, with a simple cell merging strategy handling the presence of overly small cut cells. The DG formulation is used to discretize the governing equations in space and to introduce the damping terms. Runge-Kutta algorithms are then employed to integrate the resulting semi-discrete equations in time. Numerical tests are presented to show the high-order accuracy and the shock-capturing capabilities of the proposed approach

Grain-boundary modelling of hydrogen assisted intergranular stress corrosion cracking

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 interface itself. The model couples the advantages of the boundary element representation of the polycrystalline micro-mechanics, namely the reduction of the mechanical degrees of freedom, with the generality of the finite element modelling of the diffusion process, which in principle allows the straightforward coupling of the interfacial effective diffusivity with other local mechanical parameters, e.g. the interfacial damage or displacement opening. Several numerical tests complete the study, showing the potential of the proposed technique