Continuum Shell Elements Research Articles

Comparative Analysis of Finite Element Formulations for Simulating Hot Forming of Ti-6Al-4V Aerospace Components

This study presents a comprehensive finite element analysis to compare the performance of different element formulations (classic shell elements, solid elements, and continuum shell elements) in simulating the hot-forming process at 725 °C of a complex Ti-6Al-4V aerospace component with an initial blank thickness of 1.6 mm (0.063 inches). The Ti-6Al-4V blank is modeled as a deformable body exhibiting anisotropic plastic behavior, whereas the forming tools (matrix and punch) are assumed to be rigid bodies. The simulation accounts for temperature and strain rate effects on the material properties, incorporating phenomena such as friction and anisotropy. Three different element types are studied and compared: S4R and S4 (classic shells), C3D8R and C3D8 (solids), and SC8R (continuum shell with reduced integration). Finally, the model is validated by comparing the predicted final part geometry, especially the thickness distribution, against the experimental measurements. The model can also predict the springback effect on the final geometry. The SC8R continuum shell element provides the smoothest representation of thickness variations along critical regions of the final part. The study highlights the importance of selecting the appropriate element type for the accurate simulation of hot-forming processes involving large deformations and complex contact conditions. The ability of continuum shell elements to accurately capture the thickness variations makes them an ideal candidate for such applications.

Promoting bridging in adhesively bonded composites with polymer inserts: A computational perspective

Preventing catastrophic failure due to delamination in adhesively bonded carbon fiber reinforced polymer (CFRP) is crucial to enhancing the reliability of structures. Experimental evidence from another study demonstrated that introducing inserts into the adhesive bond line creates bridging, effectively arresting the delamination process. In this paper, a numerical model was proposed to mimic the experiment and then utilized for conducting parametric studies. An embedded cell approach was adopted, representing a double cantilever beam (DCB) with linear-elastic continuum shell elements, beam elements for the bridging bundles, and connector elements for the adhesive. The crack propagation was initiated with adhesive failure and subsequently followed by bridging bundle failure. The numerical simulation results closely replicated the experiment’s global response in the force–displacement curve, thereby effectively validating the existence of the bridging effect. Furthermore, our study revealed that enhancing the adhesive strength and insert ductility can further improve crack resistance.

Design of Type-IV Composite Pressure Vessel Based on Comparative Analysis of Numerical Methods for Modeling Type-III Vessels

Compressed gas storage of hydrogen has emerged as the preferred choice for fuel cell vehicle manufacturers, as well as for various applications, like road transport and aviation. However, designers face increasing challenges in designing safe and efficient composite overwrapped pressure vessels (COPVs) for hydrogen storage. One challenge lies in the development of precise software programs that consider a multitude of factors associated with the filament winding process. These factors include layer thickness, stacking sequence, and the development of particularly robust models for the dome region. Another challenge is the formulation of predictive behavior and failure models to ensure that COPVs have optimal structural integrity. The present study offers an exploration of numerical methods used in modeling COPVs, aiming to enhance our understanding of their performance characteristics. The methods examined include finite element analysis in Abaqus, involving conventional shell element, continuum shell element, three-dimensional solid element, and homogenization techniques for multilayered composite pressure vessels. Through rigorous comparisons with type-III pressure vessels from the literature, the research highlights the most suitable choice for simulating COPVs and their practicality. Finally, we propose a new design for type-IV hydrogen composite pressure vessels using one explored method, paving the way for future developments in this critical field.

Effect of Cohesive Properties on Low-Velocity Impact Simulations of Woven Composite Shells

The effect of the interface stiffness and interface strength on the low-velocity impact response of woven-fabric semicylindrical composite shells is studied using finite element (FE) models generated with continuum shell elements and cohesive surfaces. The intralaminar damage is accounted for using the constitutive model provided within the ABAQUS software, while the interlaminar is addressed utilising cohesive surfaces. The results show that the interface stiffness has a negligible effect on the force and energy histories for values between 101 N/mm3 and 2.43 × 106 N/mm3. However, it has a significant impact on the delamination predictions. It is observed that only the normal interface strength affects the maximum impact force and the delamination predictions. Increasing its value from 15 MPa to 30 MPa resulted in an 8% growth in the maximum force, and a substantial reduction in the delaminated area. The obtained results serve as guidelines for the accurate and efficient computation of delamination. The successful validation of the FE models establishes a solid foundation for further numerical investigations and offers the potential to significantly reduce the time and expenses associated with experimental testing.

Structural analysis of REBCO coated conductors and quasi-isotropic strands under bending using continuum shell element

The electro-mechanical properties of Rare-Earth Barium Copper Oxide (REBCO) coated conductors (CCs) are crucial for practical structures such as power cables, magnet coils and so on. Many tests including tension and bending tests were conducted to estimate the critical current of REBCO CCs under different loadings. However, standard test method for the electro-mechanical properties of REBCO CCs has not been established, especially for bending tests. Therefore, finite element simulations of bending tests of REBCO CCs are still needed to further analyze the electro-mechanical behavior under loading. Structural responses of REBCO CCs and quasi-isotropic (Q-IS) strands under bending are analyzed using continuum shell element in this study. The numerical results indicate that bending strains obtained from finite element simulations match well with the analytical calculations in pure bending state. Furthermore, the influences of former shapes are also discussed to evaluate the bending tolerance of REBCO CCs in different cases. In addition, the mechanical properties and critical current degradation of Q-IS strands under bending are analyzed.

Impact based characterization of composites using a computational framework

This article has employed a computational method to evaluate the dynamic response of Carbon fiber reinforced polymers composite material. Three Dimensional, Computational Shell and Two Dimensional modelling of a protective system has been conducted by the authors using Finite Element Method. In order to simulate the influence of space debris impacts on carbon epoxy composites, velocity variation in high and hyper speed range has been conducted. Rigid elements were utilized to model the projectile, while three dimensional stress elements, Continuum Shell elements and Plane stress elements were used for three dimensional, Continuum Shell and two dimensional modelling of the plate. The computational results indicated a good convergence with the available experimental results with variation less than 10%. It was observed that the generated stresses, energy absorbed, damaged area as well as the computation time of the models increased with the subsequent increase in impacting velocity. An increase of 75% in the energy absorbed, 86% increase in the generated stress and 93% increase in the deformation was observed against an increase in the impact velocity from 150 m/s to 1674 m/s. A maximum increase of 12% in the overall damage area, 41% increase in delamination of plies and 95% enhanced computation time was also observed against the above mentioned velocity variation.

Experimental and Numerical Research of Delamination Process in CFRP Laminates with Bending-Twisting Elastic Couplings.

This paper aims at experimental and numerical research of delamination process in carbon/epoxy composite laminates with different fiber orientation angles in stacking sequence exhibiting the bending-twisting elastic couplings. Experimental specimens were subjected to the double cantilever beam (DCB) tests according to the ASTM D5528 regulations. Values of the mode I strain energy release rates were calculated by using three different data reduction schemes: the modified beam theory, the compliance calibration method and the modified compliance calibration. Determination of delamination initiation point was conducted in twofold way: by visual observation of crack tip using high resolution camera and by utilization of the acoustic emission technique. Numerical analyss were prepared in Abaqus/CAE Software environment by using the virtual crack closure technique (VCCT). The numerical beam model consisted of SC8R continuum shell elements. Obtained outcomes revealed that extensive fiber bridging phenomenon occurring during delamination process pronouncedly affected propagation values of strain energy release rate (GIprop) and numerically obtained load-displacement curves. Nevertheless, in initial stage of delamination, results obtained by using the VCCT were in agreement with experimental data. The greatest value of the mode I fracture toughness equal 0.56 N/mm was obtained for the BT45 laminate.

Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations

This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.

A failure model for the analysis of cross-ply Non-Crimp Fabric (NCF) composites under in-plane loading: Experimental & numerical study

In the present work, a set of physically-based failure criteria are applied to a cross-ply Non-Crimp Fabric (NCF) composite. The proposed criteria account for the stitch reinforcement and the induced in- and out-of-plane fibre misalignment. A distinction between matrix and fibre failures in tension and compression is introduced, while the in-plane shear non-linear response is directly incorporated to the model as well. The constitutive model is associated with an energy-based damage mechanics method, which consists of five in-plane damage variables per layer level. Within this study, a novel approach to obtain the effective longitudinal stiffness of the composite, as a function of the in- and out-of-plane misalignment, is described. An experimental study characterises the internal structure and the mechanical response of the composite in tension, compression, in-plane shear and Mode I & II interlaminar fractures. In this paper, validation examples for the failure criteria, implemented in Abaqus/Explicit as a VUMAT subroutine, are presented. Tensile, in-plane shear and compressive responses are modelled at a coupon level with continuum shell elements and correlate well with the experimental data. Fibre misalignment, mainly out-of-plane, had a strong influence on the compressive modulus and strength of the composite.

A geometrically nonlinear variable-kinematics continuum shell element for the analyses of laminated composites

To facilitate further gains in structural efficiency, the use of composite materials in engineering structures is on the rise. Simultaneously, a drive for thinner components is leading to structural behaviour that is governed by elastic nonlinearities such as large deflections and instabilities. For efficient and reliable design, numerical models must predict the nonlinear displacements, as well as the corresponding stress and strain responses, both accurately and at minimal computational cost. In this work, we present a novel tensor-based variable kinematics continuum shell (VKCS) formulation that is geometrically nonlinear in a total Lagrangian sense. The key contribution is the development and validation of a nonlinear continuum shell model that is completely general in terms of its geometric and kinematic descriptions. The governing equations are derived and presented in tensorial form, which enables a straightforward spatial mapping for models with complex curvatures. The ‘variable-kinematics’ capability means that the element field variables can be refined in a hierarchical and orthotropic manner, i.e. the in-plane and through-thickness displacements can be independently discretised using any polynomial functions with arbitrary orders of expansion. With this feature, the model configurations can be tailored for specific nonlinear problems, whilst also achieving fast solution convergence rate through the use of higher-order basis functions. For validation, the VKCS model has been benchmarked against existing nonlinear problems in the literature that feature large displacements with complex equilibrium paths. In addition, we have proposed two new benchmarks to investigate the 3D Cauchy stress in a snapped shallow roof, and the postbuckling behaviour of a wind turbine blade section. The VKCS formulation is shown to be a versatile tool that allows the user to easily switch between a multitude of model configurations, and can thus accommodate the varying fidelity of analyses required across different design stages. Furthermore, our benchmarks have demonstrated that the variable-kinematics model requires fewer degrees of freedom and run time to track complex 3D stresses when compared to conventional low-order continuum elements. • A novel hierarchical finite element formulation for analysis of laminated structures. • Easily switch between model configurations required across different design stages. • Shell element with completely general geometric and kinematic discretisation. • 3D stress tracking in snapped roof and post-buckling analysis of wind turbine blades.

Experiments and Finite Element Simulations of Composite Laminates Following Low Velocity On-Edge Impact Damage.

Composites are widely used in aircraft structures that have free edges and are vulnerable to impact events during manufacturing and maintenance. On-edge impact may have a great contribution in terms of the compression strength loss of composites, but the influence remains unclear. This paper presents experiments and simulations of carbon-fiber-reinforced plastic (CFRP) materials with on-edge impact and compression after edge impact (CAEI). On-edge impact damage was introduced to the composite laminates through the drop weight method with 4, 6, 8 and 10 J impact energies, respectively. A special guide-rail-type fixture was used in the compression tests in which strain–force and load–displacement relationships were obtained. A continuous-step finite element model was proposed to simulate impact and compression. Continuum shell elements and Hashin failure criteria were used to simulate in-ply damage, and interlaminar damage was modelled by cohesive elements. The model was validated by correlating the experimental and numerical results. The investigation results revealed the relationships of the damage size and residual strength with the different impact energies. The crack length and delaminated area grow with the increase in impact energy. The residual compressive strength follows a downward trend with increasing impact energy.

Experimental and Numerical Analysis of Carbon/Epoxy Composite Plate Subject to Low-Velocity Impact

The present work compared experimental and finite element analysis on the low-velocity impact response of a carbon/epoxy composite plate. Finite element analysis was based on the utilization of cohesive zone elements with the Benzeggagh-Kenane fracture criterion to predict the initiation and propagation of delamination. A Kirchhoff based formulation of a continuum shell element was used to model the stiffness of each lamina and the Hashim-Rotem damage mechanism to predict damages in every lamina. Five specimens of a 16-layer uni-directional carbon/epoxy composite plate with fiber orientation [+45°/90°/-45°/0°/+45°/90°/-45°/0°] s were subjected to low-velocity impact with a single energy value of 2.75 Joule/mm. The experimental results were then compared to the finite element results. Good agreement was achieved for the size and shape of the total projected delamination and visual damage to the top and bottom surface in the form of matrix and fiber failure. Slight differences were found for the dynamic response in the impact force history. Furthermore, a significant difference was found for the quantity of absorbed energy.

Finite Element Modelling for Bending and Vibration Analysis of Composite and Sandwich Spherical Shells

Finite element modelling is used to illustrate the bending and vibration response of composite and sandwich spherical shells. ABAQUS is used to model the shell as a three-dimensional deformable solid part. Composites are modelled using mixed modelling technique. The quadrilateral continuum shell element, which has eight nodes, is used for finite element meshing. For a three-layered composite spherical shell with simply supported boundary conditions, the accuracy of the employed element is first evaluated. After that, three potential end conditions are evaluated for further analysis: cantilever (CFFF), two opposing sides clamped (CFCF), and all sides clamped (CCCC). Bending response is produced by applying two types of pressure loads to the exterior surfaces of composite and sandwich spherical shells: uniformly distributed load (UDL) and sinusoidal load (SINO). For various span to thickness ratios, free vibration response and forced vibration response (Time History) are provided under step pressure (UDL and SINO) loading. The element type being used is found to be quite precise and sturdy.

A computationally efficient methodology to simulate hybrid bolted joints including thermal effects

Carbon-aluminum bolted assemblies are difficult to simulate because of the complex phenomenology involved (contact, friction, preload and thermal expansion). Therefore, accurate but computationally feasible methodologies are necessary. We propose two simplified methodologies, one based on continuum shell elements and the other on conventional shells, and compare them with a full 3D solids model. The two cases explored are a single-lap shear coupon with one bolt, and a hybrid wingbox subcomponent with 46 bolts. The effect of temperature jumps on the bolt preloads are explored. Results show that the continuum shell model presents the best tradeoff between accuracy and computational cost.

An adaptive isogeometric shell element for the prediction of initiation and growth of multiple delaminations in curved composite structures

In order to model prominent failure modes experienced by multi-layered composites, a fine through-thickness discretisation is needed. If the structure also has large in-plane dimensions, the computational cost of the model becomes large. In light of this, we propose an adaptive isogeometric continuum shell element for the analysis of multi-layered structures. The key is a flexible and efficient method for controlling the continuity of the out-of-plane approximation, such that fine detail is only applied in areas of the structure where it is required. We demonstrate how so-called knot insertion can be utilised to automatise an adaptive refinement of the shell model at arbitrary interfaces, thereby making it possible to model multiple initiation and growth of delaminations. Furthermore, we also demonstrate that the higher-order continuity of the spline-based approximations allows for an accurate recovery of transverse stresses on the element level, even for doubly-curved laminates under general load. With this stress recovery method, critical areas of the simulated structures can be identified, and new refinements (cracks) can be introduced accordingly. In a concluding numerical example of a cantilever beam with two initial cracks, we demonstrate that the results obtained with the adaptive isogeometric shell element show good correlation with experimental data.

An Explicit Finite-Element Modeling Method for Masonry Walls Using Continuum Shell Element

This paper presents an explicit finite-element (FE) model formulated using the continuum shell element to examine the behavior of unreinforced and externally strengthened masonry walls. Masonry is modeled as a homogenized material capable of producing elastic and inelastic behavior with distinct directional properties. The macroscopic properties of masonry are defined using a Hill-type and a Rankine-type yield surface to model its behavior under compression and tension, respectively, which are embedded in a VUMAT user material subroutine developed using the ABAQUS Explicit algorithm. Alongside the mechanical properties of masonry, the thickness direction properties of the continuum shell element are defined through the input file to ensure compatibility between the algorithm used in the VUMAT and the continuum shell formulation. The parameters of the FE model have been validated with the test data sets of a total of six out-of-plane and in-plane loaded masonry walls taken from three separate experimental programs reported in the literature. A close match between the experimental and FE model failure mode and load–displacement relation was observed. The model is extended to predict the behavior of externally strengthened walls, which experienced the debonding of the carbon fiber-reinforced polymer (CFRP) layers from the masonry substrate. A significant increase in the in-plane capacity of the strengthened walls was observed.

Dynamic evaluation of aluminum alloys using a virtual framework

This research paper has utilized a computational based approach to assess the impact response of Aluminum alloys. The authors have conducted Two Dimensional, Continuum Shell and Three Dimensional modelling of a shielding system using Finite Element Method. Effect of thickness and velocity variation has been emphasized with a view to simulate the effect of space debris on the metallic shielding system. Plane stress elements, Continuum Shell elements and Three Dimensional stress elements were used for Two Dimensional, Continuum Shell and Three Dimensional modelling of the plate, while rigid elements were used to model the projectile. The computational results showed a good agreement with the experimental results available. A maximum of 14 % increase in the relative damaged area of the specimen was observed, while the maximum stress generated under the impact was 395 MPa, leading to an immediate failure of the plate at a velocity of 1674 m/s. The numerical damage topologies also showed confidence with the published experimental results.

FEA of Circular Embedded Delamination with Variations in Temperature in a Composite Laminate using VCCT

The FRP laminates are widely implemented in aviation industry due to its advantages and applications other materials in terms of strength to weight ratio, design features and many more. The strength of the interface compared to longitudinal and lateral directions of the plies are comparatively less and give rise too poor transverse direction strength. Hence a failure mechanism called delamination will occur in case when tools are dropped or due to poor manufacturing which would give rise to interface delamination. In this paper, VCCT is employed at the interface between base and sub laminate to investigate for a circular shape delamination geometry of 60mm buckling driven delamination growth with variations in temperature for -20C, room temperature, 523C, 773C and 1273C. The computational prediction of delamination growth initiation is obtained by solving a CFRP specimen for geometric non linearity using SC8R continuum shell elements of Abaqus CAE and by plotting the required energy release rate versus inplane strains and inplane loads versus compressive strains.

Computational Investigation of Square Embedded Delamination of a Composite Laminate using Surface based Cohesive Contact Behavior

The fiber reinforced polymer laminates have found extensive applications because of its advantages over other materials in terms of thrust to weight ratio, strength to weight ratio, manufacturing benefits such as tailoring, resistance to erosion and corrosion and so on. In the transverse direction, strength, stiffness and stability are comparatively less so that a failure mechanism called interface delamination comes into picture due to poor manufacturing or when tools are dropped that would create an impact load. In this paper, Surface based Cohesive contact behavior is implemented at the interface between base and sub laminate to investigate for 60mm square embedded buckling driven delamination growth. The computational prediction of delamination growth initiation is obtained by solving a HTA/6376C composite laminate specimen for geometric non linearity using SC8R continuum shell elements of Abaqus CAE and by plotting the inplane loads versus out of plane displacements.

Computational Investigation of through the Width Delamination of a Composite Laminate using Surface based Cohesive Contact Behaviour

The fiber reinforced polymer laminates have found extensive applications because of its advantages over other materials in terms of strength to weight ratio, manufacturing flexibility and so on. But in the transverse direction, strength is comparatively less so that a failure mechanism called delamination will occur in case of poor manufacturing or when tools are dropped. In this paper, Surface based Cohesive contact behavior is implemented at the interface between base and sub laminate to investigate for 60mm through the width buckling driven delamination growth. The computational prediction of delamination growth initiation is obtained by solving a HTA/6376C composite laminate specimen for geometric non linearity using SC8R continuum shell elements of Abaqus CAE and by plotting the inplane loads versus out of plane displacements.