Composite Finite Element Research Articles

Application of a finite element method variant in nonconvex domains to parabolic problems

In this paper we address one of the major difficulties which is the nonconvex behavior of the domains while finding the solution of the problems. The part of the domain where the nonsmoothness appears is where the challenge arises and the way that area is handled using different numerical methods reveals the effectiveness of these techniques. Here in this article, we study the semilinear parabolic problem in nonconvex polygonal domain. For the approximation of the solution we use the Composite Finite Element (CFE) method, which is a classification of the Finite Element Method. CFE discusses the two-scale discretization — the larger mesh also known as the coarse mesh with the size H and the smaller mesh, also known as the fine mesh with the size h. It helps in reducing the dimension of the domain space of consideration. The fine scale grid is used to resolve the nonconvexity of the boundary whereas the coarse scale grid is comprised of larger grids at an appropriate distance from the boundary. The degrees of freedom depends on the coarse grid. This is the precedence of CFE over other methods, i.e., it eases the task of reducing the domain complexity. In this article, we consider two approaches — the semi discrete analysis where only space discretization is carried out, and the fully discrete analysis where both the time and space discretization is done using both backward Euler and Crank–Nicolson method. We study the error analysis in the L∞(L2)-norm and in the L∞(H1)-norm for the semidiscrete case whereas for the fully discrete case, we study the error analysis in the L∞(L2)-norm. Also, we check for the optimal results. For the CFE technique in the L∞(L2)-norm, we derive the convergence having optimal order in time and almost optimal order in space even if the domain is nonconvex. We consider a T-shaped domain and another star shaped domain to carry out the theoretical findings. Thereafter, numerical computations are implemented to validate the theoretical results.

Stress-driven design of incompressible multi-materials under frequency constraints

This paper presents an efficient and comprehensive numerical approach to address topology optimization challenges within the multi-material framework. The focus encompasses several key aspects: solving various stress-related problems from compressible to incompressible materials, broadening the scope to encompass multi-material systems, adopting a flexible methodology suitable for various elements (triangular, quadrilateral, and polygonal), and expanding to incorporate frequency constraints within the stress-driven system. The core idea to accommodate a broad range of materials, from compressible to nearly incompressible, is to implement a specialized polytopal composite finite element (PCE) technique to mitigate volumetric locking issues often prevalent in nearly incompressible materials. Then, to effectively solve the stress-related multi-material system, a well-known P-norm function integrated with the Moved and Regularized Heaviside function (MRHF) is employed, capitalizing on the correlation between topological phases and material allocation to handle multi-material problems effectively. Additionally, to deal with frequency-related multi-material problems, an extended technique addressing localized mode issues based on the relationship between representative solid and void is also employed. Several numerical examples are tested to validate the method’s efficiency and reliability within a multi-material framework, considering a diverse range of materials from compressible to nearly incompressible.

Adaptation of the composite finite element framework for semilinear parabolic problems

In this article, we discuss one type of finite element method (FEM), known as the composite finite element method (CFE). Dimensionality reduction is the primary benefit of CFE as it helps to reduce the complexity of the domain space. The number of degrees of freedom is greater in standard FEM compared to CFE. We consider the semilinear parabolic problem in a 2D convex polygonal domain. The analysis of the semidiscrete method for the problem is carried out initially in the CFE framework. Here, the discretization is carried out only in space. Then, the fully discrete problem is taken into account, where both the spatial and time components get discretized. In the fully discrete case, the backward Euler method and the Crank-Nicolson method in the CFE framework are adapted for the semilinear problem. The properties of convergence are derived and the error estimates are examined. It is verified that the order of convergence is preserved. The results obtained from the numerical computations are also provided.

Frequency-constrained topology optimization in incompressible multi-material systems under design-dependent loads

In the realm of engineering design, structures grappling with fluidic pressure loads within precise frequency constraints necessitate innovative approaches. This study introduces a method to address the intricacies of design-dependent load-based structures, focusing on three key aspects: (i) managing structures constrained by frequency under fluidic pressure loads dependent on the design, (ii) integrating the use of multiple materials, and (iii) dealing with nearly incompressible materials. The proposed approach, detailed in this paper, employs polytopal composite finite elements (PCEs) to overcome the inherent volumetric locking phenomenon in incompressible materials. By incorporating Darcy’s law and a drainage term alongside the representative-solid phase, this approach ensures consistent treatment of fluidic pressure loads, dynamically adjusting their direction and location during the multi-material design process. The porosity of each element, intricately linked to its density variable through a Heaviside function, facilitates a smooth transition between solid and void phases. The application of Darcy’s law establishes a specific pressure field, solved using PCEs, enabling the computation of consistent nodal loads. This method simplifies the assessment of load sensitivities through the adjoint-variable technique. The method’s effectiveness and reliability are validated through numerical examples, demonstrating its capability to optimize compliance within specific volume constraints for frequency-limited structures subjected to design-dependent pressure loading and considering a diverse range of materials from compressible to nearly incompressible.

Exploring the application of composite materials in ceramic design based on fuzzy numerical analysis

Abstract Compared with traditional monolithic carbide ceramics, Cu-based composite ceramics have the advantages of higher hardness, good wear resistance and oxidation resistance and are a new type of structural ceramics with wide application prospects. This paper first proposes a novel bi-directional freezing technique to construct a three-dimensional long-range ordered layer network hierarchical structure based on the pressure infiltration process. Secondly, a composite finite element model based on fuzzy numerical analysis is proposed for the vibroacoustic analysis of the periodic composite coupled system (PCSAS). Finally, thermal analysis experiments and mechanical property tests verify the effectiveness of Cu-based composites applied to ceramic matrices. The experimental results show that the toughness of Cu-based composite ceramics increases with the increase of TiC content, and the toughness increases from 2.15±0.27Mpa.m1/2 to 4.21±0.25Mpa.m1/2 compared with that of conventional monolithic carbide ceramics. The Cu-based composite ceramics designed in this paper give full play to the advantages of the high strength of ceramic particles and high toughness of metal matrix and develop an effective method to prepare structural metal-ceramic composites. This paper has developed an efficient route for preparing structural metal-ceramic composites, which can provide a reference for materials researchers to develop high-toughness composite ceramics.

Static, dynamic and buckling responses of random functionally graded beams reinforced by graphene platelets

This work proposes a multiscale numerical method that can be used to study the static, dynamic and buckling behavior of functionally graded (FG) beams reinforced with graphene platelets (GPLs), whose random gradation is achieved through tailoring the internal porosity and GPLs reinforcement, either along the transverse or the longitudinal direction. The multiscale numerical method consists of microscale homogenization and structural analysis: micromechanics homogenization methods are introduced to predict the elastic moduli of nanocomposite layers with finite thickness along the transverse direction; Explicitly-expressed composite finite elements are then developed through the proposed variational principle and Hamilton principle. In the meantime, the corresponding governing equations are derived for FG beams with Timoshenko theory. On this basis, the static bending deflection, fundamental frequency and critical buckling load of the FG beams are obtained through the proposed FG finite elements. The effectiveness and accuracy of the proposed method are verified against the numerical results in the existing literature and experimental results in 3D printing with good agreement. Based on the credence of the present method, the effects of boundary conditions, gradient distributions of GPLs and pores, microscopic parameters of GPLs and structural geometric dimension on the static and dynamic performance of the FG beams are systematically analyzed, where the bi-directional gradient distribution pattern corresponding to the GPLs along the thickness direction and the pore along the axial direction demonstrates the best improvement of both bending and dynamic performance.

Cardiac hypertrophy simulations using parametric and echocardiography-based left ventricle model with shell finite elements

In our paper, we simulated cardiac hypertrophy with the use of shell elements in parametric and echocardiography-based left ventricle (LV) models. The hypertrophy has an impact on the change in the wall thickness, displacement field and the overall functioning of the heart. We computed both eccentric and concentric hypertrophy effects and tracked changes in the ventricle shape and wall thickness. Thickening of the wall was developed under the influence of concentric hypertrophy, while the eccentric hypertrophy produces wall thinning. To model passive stresses we used the recently developed material modal based on the Holzapfel experiments. Also, our specific shell composite finite element models for heart mechanics are much smaller and simpler to use with respect to conventional 3D models. Furthermore, the presented modeling approach of the echocardiography-based LV can serve as the basis for practical applications since it relies on the true patient-specific geometry and experimental constitutive relationships. Our model gives an insight into hypertrophy development in realistic heart geometries, and it has the potential to test medical hypotheses regarding hypertrophy evolution in a healthy and heart with a disease, under the influence of different conditions and parameters.

Modeling and prediction of short/long term mechanical behavior of FRP-strengthened slabs using innovative composite finite elements

The analysis of plates or slabs strengthened with fiber reinforced polymer (FRP), especially when it comes to geometric irregularity and the time-varying characteristics of adhesive, presents multi-faceted simulation, modeling and computational challenges. In this paper, two new multilayer composite plate elements are proposed to model and analyze FRP-strengthened slabs, aiming at meeting these challenges with efficiency. The novelty relies on that the innovative elements realize the modeling of substrate, adhesive layer and FRP sheet in one “macroscopic” element rather than modeling each component by separate elements. One of them is capable of emulating geometric irregular structures while the other has better accuracy, and the flexible combination of them can be used to achieve accurate simulation and calculation of various strengthening systems. Another novelty is the extension of the study from elastic to viscoelastic by introducing an appropriate rheological interface and correspondence principle. The consistency with literature verifies the correctness of the proposed elements, subsequently, they were used to investigate the influence of the FRP tapering ends and strengthening forms on the reinforcement effectiveness. It is found that the proposed method is convenient to predict the short/long term mechanical behavior of FRP strengthened slabs with accuracy and computational efficiency, thus contributing to the design and optimization of the strengthening system.

Aluminum/steel rolled composite finite element secondary development simulation and experimental study

Given the significant difference in the properties of the two metals, the rolled composite has a severe problem of uncoordinated deformation and low bond strength. The effect of the same diameter and different diameters of the rolls and single roll drive on the composite plate’s coordinated deformation and bond strength is investigated. Simulation modeling employs finite element (FE) secondary development, and the plate warpage mechanism is analyzed by combining synchronous and asynchronous rolling experiments. The aluminum side is subjected to compressive stresses in the rolling direction during the rolling process. The steel side is subjected to tensile stresses in the rolling direction. The roll diameter in contact with the aluminum plate is reduced, the rolling pressure is distributed more evenly along the vertical plate section direction, improving deformation coordination. The side of the roll that touches the aluminum is driven, and the bimetal starts to bond closer to the exit of the roll. The frictional stresses and bending moments between the bimetallic interface are smaller, resulting in better deformation coordination and higher bond strength.

Experimental and numerical full-field displacement and strain characterization of wind turbine blade using a 3D Scanning Laser Doppler Vibrometer

Full-field dynamic measurement is desirable and useful for many purposes including model validation, or experimental characterization of test articles for which a finite element model is not available. Surface full-field strain measurement and test-model correlation have been performed on a small-size isotropic structure with a non-contacting 3D Scanning Laser Doppler Vibrometer (SLDV), which has an advantage over strain gauge tests with measurements at only a few discrete points. However, the application on large-size anisotropic structures has not been explored. This is the first work using the 3D SLDV for measuring the full-field displacement and strain Operational Deflection Shapes (ODSs) of a large composite structure, a 4.2-meter wind turbine blade. The displacement and strain measurement results are also correlated to the corresponding predictions of the blade composite finite element model in both a visual and quantified manner. The correlation is demonstrated for both low-frequency fundamental modes, but also for complex, highly-coupled high-frequency modes, which is challenging for other optical methods. Correlation results show a high degree of agreement between measured and numerically predicted displacements and strains, demonstrating the validity of the 3D SLDV measurement and the developed finite element model of the composite blade. The strain shapes are also compared with the displacement shapes and the blade structural configuration to reveal the effect of the blade structure on the strain distribution. The full-field displacement and strain identified and the proposed measurement and correlation technique would benefit wind turbine blade designers by providing new experimental tools to evaluate blade structural performance and reliability and provides a useful reference for blade structural designers.

Composite finite elements on dynamic and buckling responses of composite beams with independent rotations

To better understand the structural dynamic response and integrity under complex engineering situations, displacement-based variational principles and corresponding composite finite elements (CFEs) are developed for the simulation of vibration and buckling behavior of partial-interaction composite beams. The accuracy of the composite FEs are validated against the analytical and numerical results in the literature where good agreement is always generated. More importantly, the effect of independent-rotation assumption is investigated in the simulation which is tested to have significant impact on the natural frequencies and buckling loads of composite structures with distinct components and generally lead closer results to the plane-stress FE results. The influence of the rotation of sub-structure on the relative slips between sub-structures is discussed. This explains the discrepancies observed in the literature. The construction of CFEs also considers the internal degrees of freedom (DoFs), which are then eliminated through static condensation, to alleviate the shear/curvature locking phenomenon. The convergence of the proposed FEs are tested, along with the capability of the present FEs in avoiding the locking phenomenon. The final explicit expressions of the elements are also offered and can be readily implemented into the commercial packages with high computational efficiency.

Harmonic viscoelastic response of 3D histology-informed white matter model

White matter (WM) consists of bundles of long axons embedded in a glial matrix, which lead to anisotropic mechanical properties of brain tissue, and this complicates direct numerical simulations of WM viscoelastic response. The detailed axonal geometry contains scales that range from axonal diameter (microscale) to many diameters (mesoscale) imposing an additional challenge to numerical simulations. Here we describe the development of a 3D homogenization model for the central nervous system (CNS) that accounts for the anisotropy introduced by the axon/neuroglia composite, the axonal trace curvature, and the tissue dynamic response in the frequency domain. Homogenized models that allow the incorporation of all the above factors are important for accurately simulating the tissue's mechanical behavior, and this in turn is essential in interpreting non-invasive elastography measurements.Geometric and material parameters affect the material properties and thus the response of the brain tissue. More complex, orthotropic, or anisotropic material properties are to be considered as necessitated by the 3D tissue structure. An assembly of micro-scale 3D representative elemental volumes (REVs) is constructed, leading to an integrated mesoscale WM finite element model. Assemblies of microscopic REVs, with orientations based on geometrical reconstructions driven by confocal microscopy data are employed to form the elements of the WM model. Each REV carries local material properties based on a finite element model of biphasic (axon-glial matrix) unidirectional composite. The viscoelastic response of the microscopic REVs is extracted based on geometric information and fiber volume fractions calculated from the relative distance between the local elements and global axonal trace. The response of the WM tissue model is homogenized by averaging the shear moduli over the total volume (thus deriving effective properties) under realistic external loading conditions. Under harmonic shear loading, it is proven that that the effective transverse shear moduli are higher than the axial moduli when the axon moduli are higher than the glial. Methodologically, the process of using micro-scale 3D REVs to describe more complex axon geometries avoids the partition process in traditional composite finite element methods (based on partition of finite element grids) and constitutes a robust algorithm to automatically build a WM model based on available axonal trace information. Analytically, the model provides unmatched simulation flexibility and computational power as the position, orientation, and the magnitude of each tissue building block is calculated using real tissue data, as are the training and testing processes at each level of the multiscale WM tissue.

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

AbstractThe goal of this work is to develop a complete theoretical framework for the numerical modeling of three‐dimensional prestressed reinforced concrete structural members, soil mixture, and their interactions. This numerical formulation is based on the construction of a new composite finite element, in order to tackle the multi‐scale problem. For this purpose, the mechanical behavior of each microstructure component material will be modeled as follows: (a) for the plain concrete (PC) and the soil mixture, an anisotropic‐damage‐elastoplastic model equipped with the strong discontinuity approach will be taken into account; (b) a polycrystal plasticity model, for the steel rebars and prestrssed tendons will be captured through a new strategy solution of discontinuous bifurcation problem, with the main objective to represent the multi‐cracking phenomenon; (c) regarding the mechanical behavior of the aggregates and rocks (skeleton—hydro mechanic problem) in the PC and soil mixture, respectively, an anisotropic‐damage‐double‐poro‐polycrystal plasticity model equipped with softening material will be considered. An advanced failure algorithm based on the marching tetrahedron and the pseudo‐termic problem will be developed. Finally, the zone that characterizes the interaction between the structural member and the soil mixture will be encrusted inside the composite finite element.

Versatile cutting fracture evolution modeling for deformable object cutting simulation

Background and ObjectivesSoft body cutting simulation is the core module of virtual surgical training systems. By making full use of the powerful computing resources of modern computers, the existing methods have already met the needs of real-time interaction. However, there is still a lack of high realism. The main reason is that most current methods follows the “Intersection-IS-Fracture” mode, namely cutting fracture occurs as long as the cutting blade intersects with the object. To model real-life cutting phenomenon considering deformable objects’ fracture resistance, this paper presents a highly realistic virtual cutting simulation algorithm by introducing an energy-based cutting fracture evolution model. MethodsWe design the framework based on the co-rotational linear FEM model to support large deformations of soft objects and also adopt the composite finite element method (CFEM) to balance between simulation accuracy and efficiency. Then, a cutting plane constrained Griffth’s energy minimization scheme is proposed to determine when and how to generate a new cut. Moreover, to provide the contact effect before the fracture occurs, we design a material-aware adaptation scheme that can guarantee indentation consistent with the cutting tool blade and visually plausible indentation-induced deformation to avoiding large computational effort. Results and conclusionThe experimental results demonstrate that the proposed algorithm is feasible for generating highly realistic cutting simulation results of different objects with various materials and geometrical characteristics while introducing a negligible computational cost. Besides, for different blade shapes, the proposed algorithm can produce highly consistent indentation and fracture. Qualitative evaluation and performance analysis indicate the versatility of the proposed algorithm.

Polygonal composite elements for stress-constrained topology optimization of nearly incompressible materials

We in this paper propose an efficient and vigorous approach based on flexible polygonal meshes for solving stress-constrained topology optimization problems involving both compressible and nearly incompressible materials. The core idea is to employ a polygonal composite finite element technique to deal with volumetric locking phenomena in nearly incompressible material limit. Then, to effectively solve topology optimization problems with local stress constraints, an augmented Lagrangian technique that allows treating problems with a large number of constraints is exploited. By employing the augmented Lagrangian method, the solution of the original optimization problem with a lot of constraints could be obtained by solving a series of unconstrained optimization ones and updating the design variables based on the method of moving asymptotes. The significant contribution of this work is to promote a unified formulation for stress-constrained topology optimization possessing the following salient features: (a) being valid for both compressible and nearly incompressible materials; (b) being valid for triangular, quadrilateral and polygonal elements; (c) sole displacement field involved; and (d) no constraint aggregation technique required. Through several numerical examples, for the first time, distinguishing and intriguing features of the optimized topology for nearly incompressible materials with stress constraints are exhibited in the present work.

Linear and nonlinear mechanical responses of FG-GPLRC plates using a novel strain-based formulation of modified FSDT theory

In the present paper, a composite finite element is proposed using the assumed natural strain (ANS) method, which is based on the unified strain interpolations and the minimized potential energy. In the proposed formulation, the linearized weak form of compatibility and equilibrium equations is obtained for the geometrically nonlinear analysis. Additionally, the parabolic strain interpolation functions without any shear correction coefficient are imposed into the first-order shear deformation theory (FSDT) to verify the zero shear stresses condition at the top and bottom surfaces. The iterative arc-length method is applied to handle the post-buckling and free vibration responses. For the micromechanical part, the effective elasticity modulus based on the modified Halpin–Tsai micromechanical model is attained to analyze functionally graded graphene platelet-reinforced composite (FG-GPLRC) plates with and without hole. Furthermore, the effective mass density and the Poisson’s ratio are assessed via the rule of mixture. Therefore, the major novelty of this paper is in detecting the nonlinear thermomechanical behavior of GPLRC plates using robust strain-based interpolations. Hence, nonlinear equilibrium paths are plotted to illustrate the effects of different boundary conditions, weight fractions and distribution schemes on GPLRC plates.

Thermal conduction modeling of composites by embedding technique

Composite materials are extremely important in several industrial areas and have been thoroughly used to solve many engineering problems. In more recent years, new numerical models and manufacturing processes made interest grow on those materials. This work contributes to the state of the art of composite materials modeling by proposing an embedding technique for thermal problems using the finite element method. The technique relies on rewriting the reinforcement finite element variables according to the composite matrix finite element form functions. By doing so, it is possible to embed the reinforcement element without increasing the total number of degrees of freedom. The embedding method is capable of modeling the phase’s orientation as well as it’s placement. It’s also possible to make use of nonlinear conductive parameters to model nonlinear thermal problems. Numerical examples are described to show the technique’s capability. The numerical results show good agreement with references, as well as reducing the total number of degrees of freedom and being able to model nonlinear material behavior. Such characteristics make the model suitable to perform more complex analysis such as reliability, optimization, multi-physics, among others.

Toward Elucidating the Physiological Impacts of Residual Stresses in the Colorectum.

Irritable bowel syndrome afflicts 10-20% of the global population, causing visceral pain with increased sensitivity to colorectal distension and normal bowel movements. Understanding and predicting these biomechanics will further advance our understanding of visceral pain and complement the existing literature on visceral neurophysiology. We recently performed a series of experiments at three longitudinal segments (colonic, intermediate, and rectal) of the distal 30 mm of colorectums of mice. We also established and fitted constitutive models addressing mechanical heterogeneity in both the through-thickness and longitudinal directions of the colorectum. Afferent nerve endings, strategically located within the submucosa, are likely nociceptors that detect concentrations of mechanical stresses to evoke the perception of pain from the viscera. In this study, we aim to: (1) establish and validate a method for incorporating residual stresses into models of colorectums, (2) predict the effects of residual stresses on the intratissue mechanics within the colorectum, and (3) establish intratissue distributions of stretches and stresses within the colorectum in vivo. To these ends we developed two-layered, composite finite element models of the colorectum based on our experimental evidence and validated our approaches against independent experimental data. We included layer- and segment-specific residual stretches/stresses in our simulations via the prestrain algorithm built into the finite element software febio. Our models and modeling approaches allow researchers to predict both organ and intratissue biomechanics of the colorectum and may facilitate better understanding of the underlying mechanical mechanisms of visceral pain.

Higher Order Composite DG approximations of Gross–Pitaevskii ground state: Benchmark results and experiments

Discontinuous Galerkin composite finite element methods (DGCFEM) are designed to tackle approximation problems on complicated domains. Partial differential equations posed on complicated domain are common when there are mesoscopic or local phenomena which need to be modelled at the same time as macroscopic phenomena. In this paper, an optical lattice will be used to illustrate the performance of the approximation algorithm for the ground state computation of a Gross–Pitaevskii equation, which is an eigenvalue problem with eigenvector nonlinearity. We will adapt the convergence results of Marcati and Maday 2018 to this particular class of discontinuous approximation spaces and benchmark the performance of the classic symmetric interior penalty hp-adaptive algorithm against the performance of the hp-DGCFEM.

Robust multiscale design of incompressible multi-materials under loading uncertainties

Most of the multiscale topology optimization (TO) approaches, which have been proposed for multi-material designs, are based on the assumption of deterministic loads and the exclusion of uncertain quantities like positions, directions, and magnitudes of loads. This contribution deals with: (1) multiscale design; (2) multi-materials; (3) loading uncertainties; and (4) incompressible materials such as rubbers and biological soft tissues. The proposed approach, in this paper is to exploit polytopal composite finite elements (PCEs) to overcome the inherent volumetric locking phenomenon in incompressible materials and employ adaptive geometric components (AGCs) to model porous multi-materials on an analysis grid of PCEs, which allows simultaneously optimizing incompressible multi-materials at both macro- and micro-scales. Besides the mixed displacement–pressure formulation and traditional concurrent TO, the proposed approach is purely developed from the displacement formulation and the AGCs-based direct-multiscale TO whose only constraint is global volume. The effectiveness of the current technique was demonstrated by solving several examples of incompressible porous multi-material designs under single and multiple random loads.