Finite Element Description Research Articles

Effects of singular and non‐singular stress fields on very high cycle fatigue life of adhesive joints

AbstractSingular stress fields represent a concern during the design of mechanical connections as they could trigger cracks within the joint, under low‐amplitude loads, generating failures and reducing its service life. Appropriate design plans should therefore be implemented to produce more reliable apparatus. This paper explores the effects induced by both the presence and the absence of stress singularities on the very high cycle fatigue (VHCF) performance of adhesively bonded butt joints through analytical, numerical, and experimental methods. Analytical models defined the conditions to design a stress singularity‐free joint, global–local finite element descriptions studied the stress distributions in detail, and then VHCF experiments extracted S–N outcomes. The suitability of this approach is confirmed numerically while a substantial increase of the joint life is experimentally observed if the singularity is removed. Nonetheless, a non‐singular configuration leads to higher scatter data compared to the original specimen configuration.

Theoretical description of the electrical double layer for a mixture of n ionic species with arbitrary size and charge asymmetries. I. Spherical geometry.

In this work, we propose a theoretical finite element description of the ionic profiles of a general mixture of n species of spherical charged particles dissolved in an implicit solvent, with arbitrary size and charge asymmetries, neutralizing a spherical macroion. This approach aims to close the gap between the nano- and the micro-scales in macroion solutions, taking into account the ion correlations and ionic excluded volume effects consistently. When these last two features are neglected, the classical non-linear Poisson-Boltzmann theory for n ionic species-with different ionic closest approach distances to the colloidal surface-is recovered as a limit case. As a proof of concept, we study the electrical double layer of an electroneutral mixture of oppositely charged colloids and small microions, with an asymmetry 1:333 in size and 1:10 in valence, in salt-free and added salt environments. Our theoretical approach displays a good agreement regarding the ionic profiles, the integrated charge, and the mean electrostatic potential obtained from molecular dynamics simulations with explicit-sized microions. Although the non-linear Poisson-Boltzmann colloid-colloid and colloid-microion profiles differ notably from those obtained via molecular dynamics simulations with explicit small-sized ions, the associated mean electrostatic potential agrees well with the corresponding explicit microion simulations.

Numerical Simulation of Electrochemical Systems by Coupling Analytical Calculation of the Diffuse Double Layer and Finite Element Description of Solution Bulk

AbstractNumerical modelling of electrochemical systems covers length scales from the nanometers up to the macroscopic scale. With finite element methods, the mesh must be extremely fine to describe the diffuse double layer, thus increasing the needed computational resources. We propose a method to describe the diffuse double layer by analytical equations, expressed as boundary conditions for the partial differential equations describing the solution bulk. We apply the method to a one‐dimensional system, i. e. to a cell with plane parallel electrodes, in the presence of a redox couple and a supporting electrolyte. We provide evidence of the precision of the method.

Retrieval Study of Brown Dwarfs across the L-T Sequence

A large suite of 228 atmospheric retrievals is performed on a curated sample of 19 brown dwarfs spanning the L0–T8 spectral types using the open-source Helios-r2 retrieval code, which implements the method of short characteristics for radiative transfer and a finite-element description of the temperature–pressure profile. Surprisingly, we find that cloud-free and cloudy (both gray and nongray) models are equally consistent with the archival SpeX data from the perspective of Bayesian model comparison. Only upper limits for cloud properties are inferred if log-uniform priors are assumed, but the cloud optical depth becomes constrained if a uniform prior is used. Water is detected in all 19 objects, and methane is detected in all of the T dwarfs, but no obvious trend exists across effective temperature. As carbon monoxide is only detected in a handful of objects, the inferred carbon-to-oxygen ratios are unreliable. The retrieved radius generally decreases with effective temperature, but the values inferred for some T dwarfs are implausibly low and may indicate missing physics or chemistry in the models. For the early L dwarfs, the retrieved surface gravity depends on whether the gray-cloud or non-gray-cloud model is preferred. Future data are necessary for constraining cloud properties and the vertical variation of chemical abundances, the latter of which is needed for distinguishing between the chemical instability and traditional cloud interpretation of the L-T transition.

Equivalent 3D properties of thin-walled composite structures using mechanics of structure genome

Equivalent 3D properties are obtained for composite thin-walled 3D structures using the concept of mechanics of structure genome. The adopted homogenization technique interprets the unit cell associated with the thin-walled 3D structures as an assembly of plates, and the overall strain energy density of the unit cell as a summation of the plate strain energies of these individual plates. The concept of mechanics of structure genome is then applied to drop all higher-order terms and the remaining energy is minimized with respect to the unknown fluctuating functions. This has been done by discretizing the two-dimensional unit cell into one-dimensional frame elements in a finite element description. This allows the handling of structures with different levels of complexities and internal geometry within a general framework. Comparisons have been made with existing work to show the advantage the proposed model offers over existing ones.

Evaluation Method for Cohesive Crack Propagation in Fragile Locations of RCC Dam Using XFEM

Roller compacted concrete (RCC) dams own a large number of horizontal construction layers, which can easily lead to weak joints among layers and generate interlayer joints with different scales to reduce the dam bearing capacity. In this study, extended finite element method (XFEM) is used to simulate crack propagation, the finite element description is first taken on the strong discontinuity. Subsequently, the displacement function of the crack-tip in the quadrilateral element and the geometric determination method of the crack-tip strengthening region are established. Afterwards, the discrete form of the governing equation is derived and the XFEM increment discretization method of the cohesive crack with the crack-tip reinforcement is proposed using the virtual node method to represent the discontinuity of the fracture element. These methods are validated through simulating mixed-mode cracking of one-sided notched asymmetric four-point bending beam. Eventually, the proposed methods are applied to RCC gravity dam to study the development rule and propagation path of the interlayer joints, so as to evaluate the effect of different lengths of the interlayer joints on the dam structural performance. The estimated critical values of dam deformation are helpful to prevent the dam failure during long term operation.

Equivalent plate properties of composite corrugated structures using mechanics of structure genome

Equivalent plate properties are obtained for composite corrugated structures using mechanics of structure genome. The method developed in this paper interprets the unit cell associated with the corrugated structure as an assembly of plates, and the overall strain energy density of the unit cell as a summation of the plate strain energies of these individual plates. Mechanics of structure genome is then applied to drop all higher-order terms and the remaining energy is minimized with respect to the unknown fluctuating functions. This has been done by discretizing the two-dimensional unit cell into one-dimensional frame elements in a finite element description. This allows the handling of structures with different levels of complexities and internal geometry within a general framework. Comparisons have been made with existing work to show the advantage the proposed model offers over existing ones.

SISO Piezo Based Circuit Development for Active Structural Vibration Control

This paper deals with the issue of developing a smart vibration control platform following an innovative model-based approach. As a matter of fact, obtaining accurate information on system response in pre-design and design phases may reduce both computational and experimental efforts. From this perspective, a multi-degree-of-freedom (MDOF) electro-mechanical coupled system has been numerically schematized implementing a finite element formulation: a robust simulation tool integrating finite element model (FEM) features with Simulink® capabilities has been developed. Piezo strain actuation has been modelled with a 2D finite element description: the effects exerted on the structure (converse effect) have been applied as lumped loads at the piezo nodes interface. The sensing (direct effect) has instead been modelled with a 2D piezoelectric constitutive equation and experimentally validated as well. The theoretical study led to the practical development of an integrated circuit which allowed for assessing the vibration control performance. The analysis of critical parameters, description of integrated numerical models, and a discussion of experimental results are addressed step by step to get a global overview of the engineering process. The single mode control has been experimentally validated for a simple benchmark like an aluminum cantilevered beam. The piezo sensor-actuator collocated couple has been placed according to an optimization process based on the maximum stored electrical energy. Finally, a good level of correlation has been observed between the forecasting model and the experimental application: the frequency analysis allowed for characterizing the piezo couple behavior even far from the resonance peak.

Feasibility of a weakly intrusive Generalized Finite Element Method implementation in a commercial code: Application to Ceramic Matrix Composite micro-structures

As the development of new grades of Ceramic Matrix Composites (CMC) for civil aviation grows, different manufacturing processes have been perfected and several of them can be used successively in order to obtain different types of micro-structures and a variable material quality. Consequently a versatile model should be developed in order to compare these materials and create a tool to help engineers to predict the mechanical behavior at the fiber scale. Here the Generalized Finite Element Method (GFEM) is proposed. It consists in enriching the classical Finite Element (FE) approached displacement by numerical functions to deliver an accurate description of the fiber-scale structure while limiting the number of degrees of freedom compared to a classical finite element description. A pattern-based description of the microscale is depicted using an industrial code for an engineering purpose. Four main difficulties are highlighted (i) the choice of the enrichment functions regarding the literature (ii) their stiffness matrix computation in a commercial code (iii) the construction of the pattern-based structure and (iv) the post-processing. Two GFEM strategies are presented and demonstrate the feasibility of an enriched kinematics within a classical finite element modeler. The selection of such modeler is conditioned by the possibility of weakly intrusive automation of the various stages of construction of the enriched patterns with the help of an external scripting language.

Mesoscale analysis of multi-span masonry arch bridges

Masonry arch bridges often include multiple spans, where adjacent arches and piers interact with each other giving rise to a complex response under traffic loading. Thus, the assumption commonly used in practical assessment that multi-span masonry viaducts behave as a series of independent single-span structures, may not be realistic for many configurations. While several experimental and numerical studies have been conducted to investigate single-span masonry arches and bridges, only limited research has been devoted to the analysis of the response of multi-span masonry bridges. This study investigates numerically masonry arch bridges with multiple spans subjected to vertical loading. For this purpose, an advanced finite element description, which is based upon a mesoscale representation for masonry and accounts for both material and geometric nonlinearities, is employed to shed some light on the actual behaviour of these structural systems. A validation study is first carried out to confirm that the adopted modelling strategy is capable to accurately simulate previous experimental results. Then, the influence of some critical geometrical and mechanical parameters that affect the bridge response is evaluated through a parametric study. The effects of pier settlements and brickwork defects are also investigated, as well as the interaction between adjacent spans through comparisons against the response of single-span counterparts.

Topologically robust CAD model generation for structural optimisation

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this can at best be performed semi-manually. We propose a fully automated and topologically accurate approach to synthesise a structurally-sound parametric CAD model from topology optimised finite element models. Our solution is to first convert the topology optimised structure into a spatial frame structure and then to regenerate it in a CAD system using standard constructive solid geometry (CSG) operations. The obtained parametric CAD models are compact, that is, have as few as possible geometric parameters, which makes them ideal for editing and further processing within a CAD system. The critical task of converting the topology optimised structure into an optimal spatial frame structure is accomplished in several steps. We first generate from the topology optimised voxel model a one-voxel-wide voxel chain model using a topology-preserving skeletonisation algorithm from digital topology. The weighted undirected graph defined by the voxel chain model yields a spatial frame structure after processing it with standard graph algorithms. Subsequently, we optimise the cross-sections and layout of the frame members to recover its optimality, which may have been compromised during the conversion process. At last, we generate the obtained frame structure in a CAD system by repeatedly combining primitive solids, like cylinders and spheres, using boolean operations. The resulting solid model is a boundary representation (B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and surfaces.

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The fibres are treated as 1D structural elements that may intersect the mesh of the embedding structure in an arbitrary manner. No meshing of the unidimensional elements is required. Instead, fibre solution fields are described using the trace of the background mesh. A regularised “cut” finite element formulation is carefully designed to ensure that analyses using such non-conforming finite element descriptions are stable. We also design a dedicated primal/dual operator splitting scheme to resolve the coupling between structure and fibrous reinforcements efficiently. The novel computational strategy is applied to the solution of stiff computational models whereby fibrous reinforcements may lose their bond to the embedding material above a certain level of stress. It is shown that the primal-dual 1D/3D CutFEM scheme is convergent and well-behaved in variety of scenarios involving such highly nonlinear structural computations.

Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

During angiogenesis, new blood vessels sprout and grow from existing ones. This process plays a crucial role in organ development and repair, in wound healing and in numerous pathological processes such as cancer progression or diabetes. Here, we present a mathematical model of early stage angiogenesis that permits exploration of the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of Vessel Endothelial Growth Factor, adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite element description of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1 ligands determines tip cell selection and vessel branching. Through their production rates, competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may be favored or impeded depending on the mechanical configuration of strain vectors in the ECM near tip cells. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Capillary interactions between soft capsules protruding through thin fluid films.

When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size, inducing local interface deformations that lead to strong capillary interactions among the particles. Although capillary interactions between rigid particles are well studied, much is still to be understood about the behaviour of soft particles and the role of their softness during the final stages of film drying. Here, we use our recently-introduced numerical method that couples a fluid described using the lattice Boltzmann approach to a finite element description of deformable objects to investigate the drying process of a film with suspended soft particles. Our measured menisci deformations and lateral capillary forces, which agree well with previous theoretical and experimental works in case of rigid particles, show that the deformations become smaller with increasing particle softness, resulting in weaker lateral interaction forces. At large interparticle distances, the force approaches that of rigid particles. Finally, we investigate the time dependent formation of particle clusters at the late stages of the film drying.

Dynamic Characteristics Numerical Simulation of Sea Entrance Soil under Dynamic Load

Li, H.; Wang, S., and Cheng, L., 2018. Dynamic characteristics numerical simulation of sea entrance soil under dynamic load. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 1–5. Coconut Creek (Florida), ISSN 0749-0208.The traditional numerical simulation method of sea entrance soil dynamic characteristics has some problems, such as the low simulation value and the poor accuracy of the numerical simulation. In order to improve the above situation, a new numerical simulation method based on dynamic load is built. Through three steps of soil grid partition, finite element model establishment and load setting scheme selection, the finite element description of sea entrance soil dynamic characteristics is completed based on dynamic load theory. Through the three steps of dynamic characteristic numerical determination, simulation boundary condition determination and damping setting, the construction of a new numerical simulation method for the sea entrance soil dynamic characteristics is completed. The simulation application environment and design contrast experiment results show that compared with the traditional methods, the new method can completely improve the problem of low total numerical simulation and poor accuracy of numerical simulation.

Heterogeneous directions of orthotropy in three-dimensional structures: finite element description based on diffusion equations

Heterogeneous materials such as bone or woven composites show mesostructures whose constitutive elements are all oriented locally in the same direction and channel the stress flow throughout the mechanical structure. The interfaces between such constitutive elements and the matrix are regions of potential degradations. Then, when building a numerical model, one has to take into account the local systems of orthotropic coordinates in order to properly describe the damage behavior of such materials. This can be a difficult task if the orthotropic directions constantly change across the complex three-dimensional geometry as is the case for bone structures or woven composites. In the present paper, we propose a finite element technique to estimate the continuum field of orthotropic directions based on the main hypothesis that they are mainly triggered by the external surface of the structure itself and the boundary conditions. We employ two diffusion equations, with specific boundary conditions, to build the radial and the initial longitudinal unit vectors. Then, to ensure the orthonormality of the basis, we compute the longitudinal, the circumferential, and the radial vectors via a series of vector products. To validate the numerical results, a comparison with the average directions of the experimentally observed Haversian canals is used. Our method is applied here to a human femur.

A wave and finite element approach for computing the optimal damping layer characteristics for composite structures

The optimal mechanical and geometric characteristics for layered composite structures having damping layer inclusions and subject to vibroacoustic excitations are derived. A finite element description coupled to periodic structure theory is employed for the considered layered damped panel. Structures of arbitrary anisotropy as well as geometric complexity can be modeled by the exhibited approach. A numerical continuum-discrete approach for computing the sensitivity of the acoustic wave characteristics propagating within the modeled periodic composite structure is exhibited. The sensitivity of the acoustic transmission coefficient expressed within a statistical energy analysis context is subsequently derived as a function of the computed acoustic wave characteristics. The optimal mechanical and geometric characteristics satisfying the considered mass, stiffness and vibroacoustic performance criteria are sought by employing Newton's optimization method.

Fatigue-Damage Evolution of Notched Composite Multilayered Structures under Tensile Loads

The problems discussed in the present paper are well-known both from the theoretical (numerical) and experimental point of view. The novelty of our approach depends on the application of hybrid experimental methods and a comparison of their effectiveness in the description of complicated fatigue problems arising in the analysis of the behavior of laminated panels with open holes and subjected to tensile loading. Three experimental methods were used: infrared thermography (passive), structural health monitoring (active), and digital image correlation. The experimental investigations were supplemented by the finite element description of the problem dealing mainly with the static behavior, monitoring the development and final fracture of composites. The considerations concern laminated panels oriented at ±45° with different types of holes, i.e., vertical elliptical, horizontal elliptical, and circular.

Identification of mesoscale model parameters for brick-masonry

Realistic assessment of existing masonry structures requires the use of detailed nonlinear numerical descriptions with accurate model material parameters. In this work, a novel numerical-experimental strategy for the identification of the main material parameters of a detailed nonlinear brick-masonry mesoscale model is presented. According to the proposed strategy, elastic material parameters are obtained from the results of diagonal compression tests, while a flat-jack test, purposely designed for in-situ investigations, is used to determine the material parameters governing the nonlinear behaviour. The identification procedure involves: a) the definition of a detailed finite element (FE) description for the tests; b) the development and validation of an efficient metamodel; c) the global sensitivity analysis for parameter reduction; and d) the minimisation of a functional representing the discrepancy between experimental and numerical data. The results obtained by applying the proposed strategy in laboratory tests are discussed in the paper. These results confirm the accuracy of the developed approach for material parameter identification, which can be used also in combination with in-situ tests for assessing existing structures. Practical and theoretical aspects related to the proposed flat-jack test, the experimental data to be considered in the process and the post-processing methodology are critically discussed.

Fatigue damage growth monitoring for composite structures with holes

The problem discussed in the present paper deals with theoretical (numerical) and experimental analysis of static and fatigue problems for composite open holes laminated panels. The novelty of our approach depends on the application of the hybrid experimental methods and the comparison of their effectiveness in the description of complicated fatigue problems arising in the analysis of the behavior of laminated panels with open holes and subjected to tensile loading. Three experimental methods are used herein: the infrared thermography (passive), the structural health monitoring (active) and the digital image correlation. The experimental investigations are supplemented by the finite element description of the problem dealing mainly with the static behavior, monitoring the development and final fracture of composites. The considerations concern the laminated panels oriented at ±45° with different types of holes, i.e. vertical elliptical, horizontal elliptical and circular.