Incremental Finite Element Model Research Articles

Incremental Numerical Approach for Modeling the Macroscopic Viscoelastic Behavior of Fiber-Reinforced Composites Using a Representative Volume Element.

The objective of this study is to describe the stress relaxation behavior of an epoxy-based fiber-reinforced material. An existing incremental formulation of an orthotropic linear viscoelastic material behavior was adapted to Voigt notation and to the special case of an isotropic material. Virtual relaxation tests on a representative volume element were performed, and the behavior of individual components of the relaxation tensor of the transversely isotropic composite material was determined. The study demonstrated that in the case of only one viscoelastic material, each component of the relaxation tensor can be described in terms of a scalar form factor and the behavior of the neat resin. The developed method was implemented in an incremental finite element model (FEM) analysis to calculate the stress relaxation on the macroscopic ply level. A validation of the approach has shown a promising agreement up to a limit below the glass transition temperature of 15 °C in longitudinal and 35 °C in transverse direction. This study therefore demonstrates a novel way to incrementally describe the macroscopic viscoelastic behavior of materials with a single viscoelastic component with good controllability for engineering purposes.

Dynamic Finite Element Analysis of Flexible Double Wishbone Suspension Systems with Different Damping Mechanisms

Suspension systems in running vehicles keep the occupants comfortable and isolated from road noise, disturbances, and vibrations and consequently prevent the vehicle from damage and wearing. To attain comfortable and vibration isolation conditions, both material flexibility and damping should be considered in the considered suspension model. This paper presents an incremental finite element model to study and analyze the dynamic behavior of double wishbone suspension systems considering both material flexibility and damping effects. The flexibility of the suspension links are modeled with plane frame element based on Timoshenko beam hypothesis (TBH). On the other hand, the flexibility of joints connecting the suspension links together and with the vehicle chassis is modeled with the revolute joint element. To incorporate the damping effect, viscoelastic, viscous and proportional damping are considered. An incremental viscoelastic constitutive relations, suitable for finite element implementation, are developed. The developed finite element equations of motion are solved using the Newmark technique. The developed procedure is verified by comparing the obtained results with that obtained by the developed analytical solution and an excellent agreement is found. The applicability and effectiveness of the developed procedure are demonstrated by conducting parametric studies to show the effects of the road irregularities profiles, the vehicle speed, and the material damping on the transverse deflection and the resultant stresses of suspension system. Results obtained are supportive in the mechanical design, manufacturing processes of such type of structural systems.

Modeling and analysis of the transient response of viscoelastic solids

ABSTRACT In this paper, an incremental finite element model (IFEM) for the transient analysis of viscoelastic solids is developed. The viscoelastic constitutive response is modeled based on the hereditary integral. Two new incremental constitutive forms suitable for finite element implementation are derived; creep-based (CB) and relaxation-based (RB) and, as a consequent, the difficulties associated with the interconversion from the relaxation modulus to the creep compliance and vice versa are avoided. Creep compliance and relaxation modulus are, respectively, modeled using generalized Kelvin–Voigt model and generalized Wiechert’s model. To check the validity, the computational procedure, semi-analytical solution is derived for simple viscoelastic cases using Laplace and inverse Laplace transform techniques. The obtained results from the computational procedure are compared with that obtained from the derived semi-analytical solution. To show the validity and applicability of the developed model, two different applications under different excitation patterns are presented. In each application, the time response for displacements and stresses, especially for the dynamic stress concentration factor for both elastic and viscoelastic analyses are investigated. Moreover, the dissipative recoverable nature of the viscoelastic solids under different loading-unloading excitation patterns is illustrated.

A design of active constrained layer damping treatment for vibration control of circular cylindrical shell structure

A new 1-3 viscoelastic composite material (VECM) layer is designed for improved active constrained layer damping (ACLD) treatment of vibration of a functionally graded (FG) circular cylindrical shell. Besides this improved active damping treatment, another objective of this study is to control all the modes of vibration of the shell effectively using the treatment (active constrained layer damping) in layer-form throughout the outer shell-surface. In this design of active constrained layer damping treatment in layer-form, its (active constrained layer damping) necessary conformability with the curved host shell-surface is ensured by the use of a vertically reinforced 1-3 piezoelectric composite (PZC) constraining layer, whereas the effective control of several modes of vibration of the shell is achieved by the use of electrode-patches over the surfaces of the constraining layer. A fruitful strategy in the arrangement of electrode-patches is proposed for effective control of several modes of vibration of the shell using one configuration of the electrode-patches. An electric potential function is assumed for this use of electrode-patches and a geometrically nonlinear coupled electro-visco-elastic incremental finite element model of the overall shell is developed for its analysis in the frequency-domain. The analysis reveals significant improvement of active damping characteristics of the active constrained layer damping layer for the use of the present 1-3 viscoelastic composite material layer instead of the traditional monolithic viscoelastic material (VEM) layer. The analysis also reveals the suitability of the present strategy of arrangement of electrode-patches for achieving aforesaid control-activity of the ACLD layer. The effects of temperature in the host functionally graded shell and different geometric parameters in the design of the 1-3 viscoelastic composite material layer on the damping characteristics of overall shell are also presented.

Performance of a short piezoelectric fiber–reinforced composite actuator in vibration control of functionally graded circular cylindrical shell

For improved flexibility and conformability of piezoelectric fiber–reinforced composite actuator, it is reconstructed in a recent study by the use of short piezoelectric fibers (short piezoelectric fiber–reinforced composite) instead of continuous fibers (continuous piezoelectric fiber–reinforced composite). This modification facilitates its application in short piezoelectric fiber–reinforced composite layer form instead of continuous piezoelectric fiber–reinforced composite patch form particularly in case of host structures with highly curved boundary surfaces. But the corresponding change in actuation capability is a major issue for potential application of short piezoelectric fiber–reinforced composite that is studied in this work through the control of vibration of a functionally graded circular cylindrical shell under thermal environment. First, an arrangement of continuous piezoelectric fiber–reinforced composite actuator patches over the host shell surface is presented with an objective of controlling all modes of vibration. Next, the use of short piezoelectric fiber–reinforced composite actuator layer for similar control activity is demonstrated through an arrangement of electrode patches over its surfaces. Subsequently, an electric potential function is assumed for the consideration of electrode patches and a geometrically nonlinear coupled thermo-electro-mechanical incremental finite element model of the harmonically excited overall functionally graded shell is developed. The numerical results reveal actuation capability of short piezoelectric fiber–reinforced composite actuator layer with reference to that of the existing continuous piezoelectric fiber–reinforced composite/monolithic piezoelectric actuator patches. The effects of temperature, size of electrode patches, properties of piezoelectric fiber–reinforced composite, and functionally graded properties on the control activity of short piezoelectric fiber–reinforced composite/continuous piezoelectric fiber–reinforced composite actuator are also presented.

Plastic deformation behavior of the friction stir welded AA2024 aluminum alloy

In order to study the effect of plastic deformation on the banded texture and flashes in friction stir welding process, a three-dimensional Lagrangian incremental finite element model was developed. The plastic deformation of friction stir welding and the forming and healing of transient keyhole during the welding process were studied visually by numerical simulation and validated by corresponding experiments. The simulation results were acceptably in good agreement with the experimental data. As shown in the numerical and experimental results, the flash of FSW joint which could be divided into two layers was mainly distributed on the retreating side. The forming and healing process of transient state keyhole includes outflow of weld materials from the beginning to 1/3 rotation period and backflow into the keyhole after 2/3 period. The distribution of plastic deformation was inhomogeneous upon the transverse cross-section, while the large deformation region was near the top surface and close to the advancing side.

Harmonically exited nonlinear vibration of heated functionally graded plates integrated with piezoelectric composite actuator

A nonlinear frequency response analysis of a smart functionally graded plate operating under a heated substrate plate surface is presented. The analysis is mainly for investigating the effect of temperature on the harmonically exited nonlinear vibration characteristics of smart functionally graded plates and also on the corresponding control authority of piezoelectric fiber–reinforced composite actuator bonded to the substrate plate surface. A negative velocity feedback control strategy is utilized so as to achieve smart damping. The temperature-dependent material properties of the ceramic metal–based functionally graded plate are graded in the thickness direction. Based on the von Karman nonlinear strain–displacement relations and assuming periodic motion, a nonlinear dynamic incremental finite element model of the overall smart functionally graded plate is developed. An arc-length extrapolation technique with a new strategy for determining the arc length is used for numerical solutions. The analysis reveals significant effects of temperature and metal volume fraction in substrate on the structural dynamic behavior of the overall plate. The analysis also reveals the effects of temperature, metal volume fraction in substrate, fiber volume fraction in piezoelectric fiber–reinforced composite, and fiber orientation in piezoelectric fiber–reinforced composite on the smart damping. For using the piezoelectric fiber–reinforced composite actuator in the form of a patch, its optimal location and size are numerically determined.

History-Based Assessment of the Dome of the Basilica of S. Maria of Carignano in Genoa

This article discusses the assessment of the dome of the Basilica of S. Maria of Carignano in Genoa, designed by Galeazzo Alessi in the 16th century. The access to the private archive of the Sauli Family allowed a detailed history of the Basilica to be reconstructed clarifying several crucial aspects of the structure: the actual depth of the foundation system, the materials of the load bearing structure, mainly of the dome and of the drum, and the actual building sequence. The restoration works (steel hoop) carried out in the past decades, discovered by means of the historical research, are related to the severe crack pattern of the dome, which today necessitates a detailed insight into its mechanical response. It is showed that historical information is the key for understanding several issues that a “technological” engineering approach would leave unsolved. In addition, historical data are used to setup a non-linear incremental finite element model (FEM) procedure, referred to a slice (a ratio of 1/16) of the structure due to symmetry conditions, which is able, in spite of its reduced computational demand, to show that the dome response is strictly related also to the drum features, thus explaining cracking and the role of hooping stresses (and ties) in the global equilibrium. Some issues for the retrofitting of dome-like structures are discussed.

Seismic Assessment of a Medieval Masonry Tower in Northern Italy by Limit, Nonlinear Static, and Full Dynamic Analyses

A comparative numerical study on a 12th-century masonry tower located in northern Italy is described. To assess the safety of the tower under seismic loads, different numerical analyses have been performed: nonlinear static, limit, and nonlinear full dynamic analyses. In the first two cases, a full three-dimensional (3D) detailed finite element model (FEM) is adopted, changing the seismic load direction and assuming different hypotheses for the interconnection between the core and the external walls. When dealing with the FEM incremental analysis, a commercial code is utilized assuming for masonry a smeared crack isotropic model. For limit analysis, a noncommercial full 3D code developed by the authors is utilized. It provides good estimates of limit loads and failure mechanisms to compare with standard FEM results. The dynamical analyses have been performed by a specific two-dimensional (2D) rigid body and spring model (RBSM), accounting for the asymmetries along the thickness and the irregularities of thickness of both the external and internal walls in an approximate but realistic way. Four different accelerograms are utilized—passing from low to high seismicity zones—to evaluate the performance of the tower under dynamic loads. From numerical results, the role played by the actual geometry of the tower is envisaged, as well as a detailed comparison of failure mechanisms provided by the incremental FEM and limit analysis is provided. In all cases, the numerical analysis has given a valuable picture of possible damage mechanisms providing useful hints for the introduction of structural monitoring.

A numerical solution for contact problem with finite deformation in nonlinear Schapery viscoelastic solids

The present paper presents an incremental finite element model for the solution of the two dimensional quasi-static frictionless nonlinear viscoelastic contact problems with large deformations. The nonlinear viscoelasticity is simulated using the Schapery’s single-integral viscoelastic model with stress-dependent properties. The updated Lagrangian formulation is used to model the material and geometrical nonlinearity of the problem. To eliminate the need to store the entire strain histories, the constitutive equations are transformed into an incremental recursive form. The contact constraints are enforced by using the Lagrange multiplier method where the normal contact forces are treated as independent variables. The resulting nonlinear equilibrium equations are solved by the Newton–Raphson method in an incremental-iterative procedure. The capability of the developed numerical incremental-iterative solution procedure is demonstrated by analysing two different contact problems with different nature.

An incremental convex programming model of the elastic frictional contact problems

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

New approaches to catheter navigation for interventional radiology simulation

For over 20 years, interventional methods have improved the outcomes of patients with cardiovascular disease. However, these procedures require an intricate combination of visual and tactile feedback and extensive training. In this paper, we describe a series of novel approaches that have led to the development of a high-fidelity simulation system for interventional neuroradiology. In particular, we focus on a new approach for real-time deformation of devices such as catheters and guidewires during navigation inside complex vascular networks. This approach combines a real-time incremental Finite Element Model (FEM), an optimization strategy based on substructure decomposition, and a new method for handling collision response in situations where the number of contact points is very large. We also briefly describe other aspects of the simulation system, from patient-specific segmentation to the simulation of contrast agent propagation and fast volume-rendering techniques for generating synthetic X-ray images in real time. Although currently targeted at stroke therapy, our results are applicable to the simulation of any interventional radiology procedure.

Dynamic contact of deformable bodies

A new incremental finite element model is developed to simulate the dynamic behavior of elastic bodies in contact. The proposed model exploits the direct simulation method previously reported for the treatment of static problems for the solution of frictionless elasto-dynamic behavior of contact bodies. The analysis is provided with a detailed algorithm. Illustrative examples include a plate resting on elastic foundations and the impact of two identical and two dissimilar elastic bars. Numerical results for a dynamic Hertz problem concerning identical and dissimilar cylinders are also given.

An Analytical Model of Strength Loss in Filament Wound Spherical Vessels

The potential strength degradation of a filament wound sphere was predicted using an incremental finite element model of the composite during fabrication. The sphere was modeled taking into account the winding pattern and the resulting internal layer boundaries. The thickness profile of the sphere’s layers were computed using a pattern simulation program. The total thickness profile and layer thickness profiles were used by the mesh generating program to ensure that the elements generated matched layer boundaries. The elements were isoparametric quadrilaterals which were collapsed to triangular elements for transitions. The main feature of the finite element program was the incremental construction and loading of the model to simulate the winding process. Strength degradation definitely occurs when the average fiber strain in any layer is negative. The negative strain means that all the winding tension has been lost from the layer, and the imposition of compressive strain causes fibers in uncured resin to wrinkle or buckle. Then when the resin cures the buckled region of fibers are degraded in strength. An analysis of a Kevlar/epoxy sphere demonstrated that strength degradation could occur. The innermost layers showed significant tension loss and compressive strain during fabrication which would produce strength degradation. The model sphere was a typical thick wall construction using normal processing conditions.

A numerical, thermo-mechanical model for the welding and subsequent loading of a fabricated structure

In this work a numerical model is developed for the welding and subsequent loading of a fabricated structure. The model treats the weld process as a thermo-mechanical problem. A finite element formulation derived from the uncoupled thermal and mechanical energy balances forms the basis of the model. During the development of the thermal model, two significant problems are discussed. One is the material nonlinearity, which manifests itself in the temperature dependence of the thermal properties, and in the fusion problem, where the material phase change is accompanied by a latent heat effect. This latter is modeled by use of a modified specific heat, since the materials of prime concern are alloys which melt over a finite range of temperature, while the former are introduced through periodic re-evaluation of the properties throughout the analysis. The second problem is that of boundary conditions: The deposition of molten bead on the base is modeled by using the intimate contact boundary condition, which is developed into a set of impulse type equations on the finite element model. Since radiation is a dominant cooldown mechanism, this boundary condition is also included. Thus the first part of work develops a non-linear finite element thermal analyzer capable of modeling all of the above effects. This program is then applied to several problems in order to assess its accuracy. During the second part of the work the mechanical model is described. This is an incremental finite element model in which the basic constitutive descriptions are time independent elastic-plastic behavior with temperature dependent properties, and a creep rate formulation for the time dependent behavior. The development is not based on thermodynamic theories but on direct extension of the classical (isothermal) theories. The model includes finite strain effects during isothermal loading, so that it may be used in the modeling of distortion sensitive structure. The integration of the rate equations is discussed with respect to the introduction of a residual load (total equilibrium) correction; it is shown that suc a correction must be introduced very carefully in a completely incremental formulation such as is developed here. Finally the model is compared with simple bead-on-plate weld experiments, performed with high strength steels. It is found that in one case the experimental approximations are well justified by the finite element results, but there is no agreement with the experimentally measured residual stresses. The suggested explanation for the unique stress patterns observed experimentally is shown to have little effect on the finite element stress predictions, so that it is concluded that the finite element model does not include a significant material behavior in this case. In the second example it is shown that the experimental assumptions were not justified by the results of the present model. In both cases the model predicts the usually expected residual stress patterns. Use of a simple creep formulation is shown to give the same order of residual stress reduction as a result of post weld heat treatment as is measured experimentally.

Deformation of the Diastolic Left Ventricle: I. Nonlinear Elastic Effects

A linear incremental finite element model is used to analyze the mechanical behavior of the left ventricle. The ventricle is treated as a heterogeneous, non-linearly elastic, isotropic, thick-walled solid of revolution. A new triaxial constitutive relation for the myocardium is presented which exhibits the observed exponential length-passive tension behavior of left ventricular papillary muscle in the limit of uniaxial tension. This triaxial relation contains three parameters: (a) a "small strain" Young's modulus, (b) a Poisson's ratio, and (c) a parameter which characterizes the nonlinear aspect of the elastic behavior of heart muscle. The inner third and outer two-thirds of the ventricular wall are assumed to have small strain Young's moduli of 30 and 60 g/cm(2), respectively. The Poisson's ratio is assumed to be equal to 0.49 throughout the ventricular wall. In general, the results of this study indicate that while a linearly elastic model for the ventricle may be adequate in terms of predicting pressure-volume relationships, a linear model may have serious limitations with regard to predicting fiber elongation within the ventricular wall. For example, volumes and midwall equatorial circumferential strains predicted by the linear and nonlinear models considered in this study differ by approximately 20 and 90%, respectively, at a transmural pressure of 12 cm H(2)O.