Shell Formulation Research Articles

Assessing the effect of poly (ethylene oxide-b-lactide) block copolymer on the characteristics of perfluoropentane phase-shift nanoemulsions

Acoustic droplet vaporization is the ultrasound-mediated phase shift of liquid perfluorocarbon emulsions into echogenic microbubbles. To reduce the emulsion's interfacial surface tension and minimize coalescence, the perfluorocarbon is coated with a surfactant. Copolymer shelled phase-shift nanoemulsions have emerged as potential diagnostic and therapeutic agents. The goal of this study is to understand how adding Poly (ethylene oxide-b-lactide) (PEO-PLLA) to a Pluronic F-68 shell formulation impacts the perfluoropentane (PFP) nanoemulsion size and polydispersity index (PDI). PFP nanoemulsions coated with Pluronic F-68 or a Pluronic F-68: PEO-PLLA (1:0.05 (v/v)) blend was prepared using high shear pressure homogenization (LV1, Microfluidics International, Corp.). Nanoemulsion size distributions and concentrations were measured (n=5) using a Beckman Coulter Multisizer 4. At 10,000 psi pressure and 1 passage through the homogenizer, the copolymer blend and Pluronic F-68 nanoemulsions had modal diameters of 0.73 ± 0.09 μm and 1.25 ± 0.09 μm, respectively. Additionally, the concentration was larger (6.6 ± 0.1×10−2 vs 5.56 ± 0.2×10−2 ml/ml) and the PDI smaller (0.070 ± 0.004 vs 0.129 ± 0.004) for the copolymer blend. All differences were statistically significantly different (p < .05). The inclusion of PEO-PLLA with Pluronic F-68 reduced the PFP nanoemulsion size and polydispersity, which may reduce experimental variability in acoustic droplet vaporization experiments.

A general theory for anisotropic Kirchhoff–Love shells with in-plane bending of embedded fibers

This work presents a generalized Kirchhoff–Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for heterogeneous and fibrous materials such as textiles, biomaterials, composites and pantographic structures. The presented theory is a direct extension of classical Kirchhoff–Love shell theory to incorporate the in-plane bending resistance of fibers. It also extends existing second-gradient Kirchhoff–Love shell theory for initially straight fibers to initially curved fibers. To describe the additional kinematics of multiple fiber families, a so-called in-plane curvature tensor—which is symmetric and of second order—is proposed. The effective stress tensor and the in-plane and out-of-plane moment tensors are then identified from the mechanical power balance. These tensors are all second order and symmetric in general. Constitutive equations for hyperelastic materials are derived from different expressions of the mechanical power balance. The weak form is also presented as it is required for computational shell formulations based on rotation-free finite element discretizations. The proposed theory is illustrated by several analytical examples.

Phase field modeling of brittle fracture in large-deformation solid shells with the efficient quasi-Newton solution and global–local approach

To efficiently predict the crack propagation in thin-walled structures, a global–local approach for phase field modeling using large-deformation solid shell finite elements considering the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods for the alleviation of locking effects is developed in this work. Aiming at tackling the poor convergence performance of standard Newton schemes, a quasi-Newton (QN) scheme is proposed for the solution of coupled governing equations stemming from the enhanced assumed strain shell formulation in a monolithic manner. The excellent convergence performance of this QN monolithic scheme for the multi-field shell formulation is demonstrated through several paradigmatic boundary value problems, including single edge notched tension and shear, fracture of cylindrical structure under mixed loading and fatigue induced crack growth. Compared with the popular alternating minimization (AM) or staggered solution scheme, it is also found that the QN monolithic solution scheme for the phase field modeling using enhanced strain shell formulation is very efficient without the loss of robustness, and significant computational gains are observed in all the numerical examples. In addition, to further reduce the computational cost in fracture modeling of large-scale thin-walled structures, a specific global–local phase field approach for solid shell elements in the 3D setting is proposed, in which the full displacement-phase field problem is considered at the local level, while addressing only the elastic problem at the global level. Its capability is demonstrated by the modeling of a cylindrical structure subjected to both static and fatigue cyclic loading conditions, which can be appealing to industrial applications.

Oyster shell reuse: A particle engineering perspective for the use as emulsion stabilizers

Oyster shells are an important bioresource that causes serious environmental problems and is currently only partially repurposed. Its versatile nature is reflected in the manifold studies already proposed for the material. In this study, we add to this effort by first grinding the material with a hammer mill, beater disc mill, pin mill and wet media mill, treating part of it in a muffle furnace, noting the shift in its properties such as particle size, morphology, surface free energy, specific surface area and choosing a fraction to incorporate in a particle stabilized emulsion. The particle stabilized emulsions were prepared with oyster shells grinded by the agitated wet media mill at 2000 rpm for 30 min, with a media at x 50 = 0.79 μm, a SSA at 17.16 m 2 /g, a SFE at 32.53 mN/m and with particles resembling a spherical shape. The emulsion was studied in terms of particle concentration, ranging from 2 to 10 wt% with the 8 wt% showing the best stability. The 8 wt% oyster shell formulation was tested and compared with a formulation using 2 wt% Aerosil particles and a surfactant store-bought product. The oyster shell particle formulation exhibited minor viscosity changes in the studied period of 8 weeks, a constant LVE range and promising behaviour in the proposed application. • Description of applications suggested for waste oyster shells in different sectors. • Grinding experiments for oyster shells performed with four different types of mills. • Characterization of the physicochemical properties of the grinded fractions including size, shape and surface interactions. • Proposition of an innovative application for oyster shells as emulsion stabilizers. • Rheological analysis to support suitability of the particles as stabilizers.

Vibration analysis of piezoelectric Kirchhoff–Love shells based on Catmull–Clark subdivision surfaces

AbstractAn isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialized to infinitesimal deformations and follow the Kirchhoff–Love hypothesis. Both the geometry and physical fields are discretized using Catmull–Clark subdivision bases. This provides the required ‐continuous discretization for the Kirchhoff–Love theory. The crystalline structure of piezoelectric materials is described using an anisotropic constitutive relation. Hamilton's variational principle is applied to the dynamic analysis to derive the weak form of the governing equations. The coupled eigenvalue problem is formulated by considering the problem of harmonic vibration in the absence of external load. The formulation for the purely elastic case is verified using a spherical thin shell benchmark. Thereafter, the piezoelectric shell formulation is verified using a one dimensional piezoelectric beam. The piezoelectric effect and vibration modes of a transverse isotropic curved plate are analyzed and evaluated for the Scordelis–Lo roof problem. Finally, the eigenvalue analysis of a CAD model of a piezoelectric speaker shell structure showcases the ability of the proposed method to handle complex geometries.

Thermo-elastic solid shell formulation with phase field fracture for thin-walled FGMs

Thermo-elastic fracture is a matter of important concern for thin-walled structures made of functionally graded materials (FGMs). Based on this practical relevance, a thermodynamically consistent framework is herein proposed to solve the coupled thermo-mechanical phase-field fracture problem in thin-walled structures made of FGMs. The formulation of the current model is constructed via the evaluation of the phase-field in the Clausius–Duhem inequality leading in to first-order stability conditions in order to ensure thermodynamic consistency. The three-dimensional Kirchhoff–Saint–Venant constitutive model is modified to accommodate the functional grading in the material properties. The computational model is combined with Enhanced Assumed Strain (EAS) and Assumed Natural Strains (ANS) to alleviate locking pathologies concerning the solid shell formulation, leading to a coupled non-linear variational formulation. Several benchmark examples (straight and curved shells) are examined to assess the model capabilities. Moreover, crack deflection, and temperature distributions in the FGM structures are compared with their homogeneous surrogates, to show the importance of the technological solutions with two or even three FGM phases.

A large deformation isogeometric continuum shell formulation incorporating finite strain elastoplasticity

A large deformation isogeometric continuum shell formulation incorporating finite strain elastoplasticity

A nonlocal nonlinear stiffened shell theory with stiffeners modeled as geometrically-exact beams

In the present work, we have developed a nonlocal and nonlinear structure mechanics theory and computational formulations for the nonlinear stiffened shell with its stiffeners modeled by the three-dimensional geometrically exact beam model while the shell part is modeled by three-dimensional geometrically exact shell model. This hybrid beam-shell geometrically exact stiffened shell model is used for solving dynamic problems of stiffened shell structures, including dynamic fracture of the shell.We first formulate the nonlocal equations for geometrically nonlinear beams using the kinematics of geometrically exact beam theory. Then, we develop a stiffened shell model by coupling the nonlocal geometrically exact beam and shell formulations. Several numerical examples are presented to validate and verify both the nonlocal and nonlinear beam formulation and the nonlocal/nonlinear stiffened shell formulation. We have demonstrated that the proposed nonlocal stiffened shell theory can model the crack growth in stiffened shell structures.

On vibrational-based numerical simulation of a jet engine cowl shell-like structure

The present research proposes an applicable and impressive analytical model of Aircraft Engine Cowl (AEC) due to auspicate its frequency parameter. For the first time, the authors configured the structure of AEC by joining two well-known shapes of shell, including elliptical and conical. This procedure is implemented by obtaining the governing motion organization of differential equations affiliated with the Joined Elliptical-Conical Shells (JECS) in line with first-order shear deformation theory (FSDT) and General Shell Formulation (GSF). Moreover, Functionally Graded Materials (FGMs) with various spreading forms along the structure’s thickness are used to enhance the dynamic performance of AEC. It is worth mentioning that the recognized Rule of Mixture (RM) is engaged for achieving the equivalent mechanical characteristics of FGM. Finally, a well-known semi-analytical Generalized Differential Quadrature (GDQ) procedure is hired to extract the resulting system of motion equations to access the free vibration responses of AEC with diverse Boundary Conditions (BCs). It is worth mentioning that an applicable and interesting numerical model is done to inspect the remnants of geometric and material features on the oscillation demeanor of AEC structures. It will be verified that the projected procedure can be helpful for AEC’s vibration analysis and extendable for other types of studies to predict the AEC structure's static and dynamic treatment.

High-precision computation in mechanics of composite structures by a strong SaS formulation: Implementation for laminated cylindrical shells and panels with clamped and free edges

The paper focuses on the three-dimensional (3D) stress analysis of laminated composite cylindrical shells and panels with general boundary and loading conditions using the strong sampling surfaces (SaS) formulation and the extended differential quadrature (EDQ) method, recently developed by the first author. In the strong SaS formulation, the SaS parallel to the middle surface and located at Chebyshev polynomial nodes in layers are utilized to introduce displacements of these surfaces as shell unknowns. This choice of unknowns with the use of Lagrange polynomials in the approximation of displacements, strains and stresses through the thickness leads to an efficient shell formulation. The outer surfaces are not included into a set of SaS that makes it possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of the equilibrium equations of elasticity in the thickness direction in conjunction with the EDQ method can be effectively applied to high-precision calculations for laminated composite cylindrical shells and panels with arbitrary boundary conditions. This is due to the fact that in the SaS/EDQ formulation the displacements, strains and stresses of SaS are interpolated in a rectangular domain, which is mapped into the middle surface by using the Chebyshev-Gauss-Lobatto grid and the Lagrange polynomials are also utilized as basis functions.

Three-dimensional thermoelectroelastic analysis of structures with distributed piezoelectric sensors and actuators with temperature-dependent material properties

In this paper, a geometrically exact hybrid-mixed four-node laminated solid-shell element with piezoelectric patches with temperature-dependent material properties through the sampling surfaces (SaS) formulation is developed. The SaS formulation is based on the choice of SaS, parallel to the middle surface and located at Chebyshev polynomial nodes within the layers, to introduce the temperatures, displacements and electric potentials of these surfaces as basic shell unknowns. The outer surfaces and interfaces are also included into a set of SaS. Such a choice of unknowns with the use of Lagrange polynomials in the through-thickness approximations of temperatures, temperature gradient, displacements, strains, electric potential and electric field leads to a very compact higher-order thermopiezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed for all components of the temperature gradient, strain tensor and electric field vector. The developed hybrid-mixed four-node laminated solid-shell element with piezoelectric sensors and actuators is based on the extended Hu-Washizu variational principle and shows superior performance in the case of coarse meshes. This can be useful for the three-dimensional temperature-dependent response of laminated composite shells with piezoelectric patches, since the SaS formulation allows one to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of thermopiezoelectricity as a number of SaS tends to infinity.

Higher order theories for the buckling and post-buckling studies of shallow spherical shells made of functionally graded materials

For composite shallow spherical shells (including functionally graded materials) the buckling and post-buckling behaviour is strongly affected by the material characteristics of a shell wall constructions. Using a power series expansion for a parameter (z/h) different variants of 2-D shell formulations are discussed herein starting from the Love-Kirchhoff theory and finishing on the 9th order theory (stretching effects). The solutions are searched for with the use of the Bubnov-Galerkin method and the finite element analysis (the h- and p-approximations). Due to geometrical limits of shallowness shell theory the investigations can be carried out for structures having the moderate thickness – the h/R ratio should be less than 0.15.

Non-linear thermoelastic analysis of thin-walled structures with cohesive-like interfaces relying on the solid shell concept

In this work, a thermodynamically consistent framework for coupled thermo-mechanical simulations for thin-walled structures with the presence of cohesive interfaces is proposed. Regarding the shell formulation, a solid shell parametrization scheme is adopted, which is equipped with the mixed Enhanced Assumed Strain (EAS) method to alleviate Poisson and volumetric locking pathologies. It is further combined with the Assumed Natural Strain (ANS) method leading to a locking-free thermo-mechanical solid shell element using a fully-integrated interpolation scheme. In order to model thermo-mechanical decohesion events in thin-walled structures with imperfect internal boundaries, an interface finite element for geometrical nonlinearities is herein extended to account for the thermal field and thermo-elastic coupling. The computational implementation of the current finite element formulation has been performed as a user element in ABAQUS via user-defined capabilities. The predictability of the model is demonstrated using several representative examples.

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.

Dynamically Evaluating the Performance of Naturally Occurring Additives to Control Lost Circulation: On the Effect of Lost Circulation Material Type, Particle-Size Distribution, and Fracture Width

Summary Lost circulation is one of the most challenging problems during drilling of oil and gas wells. This issue leads to significant loss of drilling fluid, increase of nonproductive time as well as dictating additional costs to drilling companies. Lost circulation may also lead to other consequences, including stuck pipe, poor hole cleaning, and well control issues. How to efficiently control lost circulation have been traditionally depending on the type of the used lost circulation material (LCM). Injection of commonly available materials (without any further process on their chemical properties) into the thief zone is a common method of lost circulation control. These nonmodified materials are named as conventional LCMs against the unconventional LCMs which are designed/produced just for fluid lost control. The objective of this paper is to comparatively investigate the performance of cane, oak shell, wheat, and mica as LCM of water-based drilling fluid exposed to fractured formations. These materials were chosen because of their low cost, easy access, and compatibility with the environment. The sealing efficiency of these materials was assessed at different particle-size distributions (PSDs) for proper treatment of loss circulation. To do so, an experimental setup containing a cell with adjustable fracture size was designed. Among the LCM formulations made of each of the materials, oak shell formulations are better than the others, followed by mica and cane blends, respectively. The results reveal that combining the materials together is a better treatment than the separate use of them. As it will be seen in detail later, high diversity in particle size (broad PSD) causes more efficient control of fluid loss. Also, to reduce the dependency of sealing ability of LCM formulation on fracture size, mixing of the materials with different particle sizes and shapes is recommended.

Simulation of the column bending test using an anisotropic viscoelastic shell model

Finite element simulation of the column bending test (CBT) is carried out using shell elements with anisotropic viscoelastic section properties. The CBT is an experimental method for evaluating the bending behavior of thin-ply high strain composites (TP-HSC), to support development of deployable composite booms for space structures. A linear viscoelastic shell formulation is derived and implemented using two solution techniques: quasi-elastic (QE) and direct integration (DI). The model inputs, namely Prony series of the ABD matrix, are obtained using Mechanics of Structure Genome. The model is implemented in Abaqus as a UGENS user-subroutine. Recent CBT experiments are briefly reviewed, and a shell element model is developed including the geometrically nonlinear features of the test. Comparisons of the test and analysis results show that the model is capable of predicting most of the measured trends. Nonuniform deformation is captured and emphasized in data reduction considerations. Although relaxation can be captured with QE implementation of the viscoelastic model, to capture the residual curvature DI implementation is necessary. Residual curvature measured in the tests, but not predicted by the present model, suggests that viscoplasticity should be considered. A demonstrative study also shows the potential of material model calibration using the virtual CBT developed in this work.

Investigation of functional characteristics of composites used for brake pads

The friction material used for the brake pads should have a low wear rate, outstanding thermal stability to hold the braking properties of the vehicle and coefficient of friction should constant under different operating conditions which include loads which applied, temperature, dry or wet braking environment and speed. Due to this reason, every newly developed friction material’s fabrication should undergo a series of experimental tests to evaluate the friction as well as wear properties. In this article a study of frictional and wear behavior of friction material for ecological brake pads of road vehicles discussed. In the formulation of the friction material shells as a filler, a small amount of metal, silicon carbide, graphite, resin and hexametiltetramine were used. The main objective of the paper refers to the investigation of the impact of the working regime on friction material’s tribological characteristics. In this sense, were studied the evolution of the coefficient of friction and the thermal field at the contact surface between the friction couplings, the influence of load on the friction coefficient at different speeds and the influence of load on wear rate at a constant speed. The knowledge of the functional properties of the newly developed friction material produced in the laboratory provides the possibility of pertinent assessments regarding the durability of the brake pads during operations, as well as on the quantity of wear products released into the atmosphere. The results concluded that as a filler material this species of shells may be used in the fabrication of brake pads for road vehicles.

Nonlinear material identification of heterogeneous isogeometric Kirchhoff–Love shells

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for describing incompressible material behavior as well as initially curved shells. The material distribution is discretized by bilinear elements such that the nodal values are the design variables to be identified. Independent FE analysis and material discretization, as well as flexible incorporation of experimental data, offer high robustness and control. Three elementary test cases and one application example, which exhibit large deformations and different challenges, are considered: uniaxial tension, pure bending, sheet inflation, and abdominal wall pressurization. Experiment-like results are generated from high-resolution simulations with the subsequent addition of up to 4% noise. Local optimization based on the trust-region approach is used. The results show that with a sufficient number of experimental measurements, design variables and analysis elements, the algorithm is capable to reconstruct material distributions with high precision even in the presence of large noise. The proposed formulation is very general, facilitating its extension to other material models, optimization algorithms and meshing approaches. Adapted material discretizations allow for an efficient and accurate reconstruction of material discontinuities by avoiding overfitting due to superfluous design variables. For increased computational efficiency, the analytical sensitivities and Jacobians are provided.

SHELL-3D MULTISCALE MODELING OF MASONRY VAULTS BASED ON THE TFA PROCEDURE

This paper investigates the response of masonry curved structural elements with periodic texture by adopting the modeling strategy recently developed by the authors in [1]. Relying on a multiscale approach, the Mindlin-Reissner shell formulation is assumed at the macroscale and the classical 3D Cauchy continuum is adopted at the microscopic level to model the representative masonry unit cell (UC). The procedure for linking the two scales involves a Transformation Field Analysis (TFA) homogenization technique based on piece-wise uniform distributions of the damaging and frictional mechanisms over the mortar joints. Advantages and limitations of this assumption are explored considering a masonry vault with stack bond texture, that is assuming a UC made of one linear elastic brick surrounded by one head and one bed joint modeled as nonlinear interfaces. The more appropriate interface discretizations required by the TFA model are identified in relation to the activated deformation modes and the resulting computational effort is evaluated. Hence, an enriched TFA procedure is proposed to limit the computational cost and the time of analysis associated to the denser joint partitions, while still preserving the model accuracy. Finally, the efficiency of the model is investigated at the structural level by analyzing the response of the vault to differential settlements. The comparison between results obtained with the proposed multiscale formulation and those recovered by detailed micromechanical analysis confirms that the TFA approach is a very reliable and effective method for resorting to a fast reduced order model also for curved geometries.

Finite Element Modelling Approach for Progressive Crushing of Composite Tubular Absorbers in LS-DYNA: Review and Findings

Robust finite element models are utilised for their ability to predict simple to complex mechanical behaviour under certain conditions at a very low cost compared to experimental studies, as this reduces the need for physical prototypes while allowing for the optimisation of components. In this paper, various parameters in finite element techniques were reviewed to simulate the crushing behaviour of glass/epoxy tubes with different material models, mesh sizes, failure trigger mechanisms, element formulation, contact definitions, single and various numbers of shells and delamination modelling. Six different modelling approaches, namely, a single-layer approach and a multi-layer approach, were employed with 2, 3, 4, 6, and 12 shells. In experimental studies, 12 plies were used to fabricate a 3 mm wall thickness GFRP specimen, and the numerical results were compared with experimental data. This was achieved by carefully calibrating the values of certain parameters used in defining the above parameters to predict the behaviour and energy absorption response of the finite element model against initial failure peak load (stiffness) and the mean crushing force. In each case, the results were compared with each other, including experimental and computational costs. The decision was made from an engineering point of view, which means compromising accuracy for computational efficiency. The aim is to develop an FEM that can predict energy absorption capability with a higher level of accuracy, around 5% error, than the experimental studies.