Incremental Finite Element Method Research Articles

An optimization method of wall thickness distributions in T-shaped tube compound-forming method with unconventional tube blank

The thin-walled T-shaped tube is widely applied in aviation pipeline systems with the development of lightweight manufacturing technology. However, the severe wall thickness thickening is a bottleneck problem restricting the application of T-shaped tubes. In order to avoid excessive thickening and improve the overall performance of the formed parts, an optimization method of wall thickness distributions in T-shaped tube compound forming by using optimized unconventional tube blank is proposed. The strain spline method is adopted to investigate the stress-strain state and deformation mechanism of T-shaped compound forming. The optimization model of tube blank is established and includes two parts: the initial optimization based on the geometric analytic method and the iterative optimization based on the incremental finite element method. The optimal tube blank is achieved through two-step optimizations. The numerical simulations and experiments of T-shaped tube compound forming using conventional and optimized tube blanks are carried out to investigate the forming height and the wall thickness distributions. The simulation and experimental results agree with a no more than 20 % relative error. The optimal tube blank could effectively improve the wall thickness distributions compared with the T-shaped tube compound using the conventional tube blank. The final experimental results show that the maximum thickening rate decreases from 48.67 % to 28.67 %, the maximum thinning rate decreases from 25.33 % to 18 %, and the maximum difference in the wall thickness decreases from 1.11 mm to 0.7 mm. The comparison results are further verified to be the correctness of the optimization method and the effectiveness of the T-shaped tube compound forming method with unconventional tube blank in the actual experiments.

Complete constitutive model of CFRP including continuous damage in low strain rate compression and temperature generation in high strain rate impact

AbstractThis paper reports a method to construct the complete constitutive model of carbon fiber‐reinforced plastic (CFRP) by distinguishing the strain rate state and modifying the material stiffness. In quasistatic (low strain rate) compression, the initial nonlinear effect caused by the material defects was described by introducing an nonlinear increasing factor. In dynamic (high strain rate) impact, the nonlinear strengthening effect was described by introducing the dynamic amplification factors of stress and strain based on the reference state. Considering the instantaneous temperature rise obtained from the impact work–temperature generation equation and the influence of temperature on modulus and strength, the coupled thermomechanical constitutive models combining the strain rate effect and the temperature effect were established. The user‐defined material subroutines (VUMAT) were developed, and then these constitutive models were verified by finite element analysis (FEA). Finally, the developed material subroutine was applied to predict the impact penetration of CFRP laminates, and the results show that the opening holes, damage and energy dissipation are in good agreement with the reference experiment. This work comprehensively analyzed the construction method of CFRP constitutive models, which would provide a guidance for the coupled thermomechanical behavior under dynamic impact.Highlights An anisotropic continuum mechanical constitutive behavior considering strain rate effect and damage evolution behavior was established. A macroscopic anisotropic constitutive model including the coupled impact temperature generation‐mechanical behavior was established. Combined with the incremental finite element method, the three‐dimensional user‐defined material subroutines (VUMAT) were developed and verified. The thermomechanical impact penetration behaviors of CFRP laminates was predicted, and the stress field, temperature field and failure characteristics were visualized.

Influence of Single External Store on Geometrical Nonlinear Flutter of High-aspect-ratio Wings

High-altitude and long-endurance UAVs, distributed electric propulsion aircraft and large passenger aircraft often use high-aspect-ratio wings, which have obvious geometric nonlinear large deformation effect, and are usually arranged with a certain number of external stores, which have an impact on their geometric nonlinear aeroelastic characteristics. Based on the “quasi-linear” hypothesis, the updated Lagrange incremental finite element method and doublet-lattice method are used to perform the geometrically nonlinear static aeroelastic analysis, and the mass, stiffness and aerodynamic matrices of large deformation are updated, and the geometrically nonlinear flutter characteristics of high-aspect-ratio wings are calculated. The influence of the position and mass of the external store on geometrical nonlinear flutter characteristics of high-aspect-ratio wing structure is investigated. Results show that the change of the position and mass of the external store causes the relative position between the elastic axis and the center of gravity of the wing, and the wing’s large deformation equilibrium state to change, resulting in differences in the stiffness characteristics of the wing and the natural vibration frequency of the equilibrium state, thus affecting the wing flutter characteristics. When a single external store is installed near the wing root, changing the mass and direction of the store has no significant effect on the geometric nonlinear flutter characteristics of the wing. The improvement of wing flutter speed is most obvious when the hanging point is moved to the leading edge of the wing near 0.65 times the wingspan.

き裂先端場における微細構造の変形シミュレーションによる延性-ぜい性遷移解析

The nacre-like biomaterials, which are being studied more and more by scientists, exhibit a perfect combination of toughness and strength thanks to their hierarchical microstructure made up of alternately soft proteins and hard mineral tablets. Recent investigations have revealed a correlation between fracture toughness and fracture patterns such like crack bifurcation and crack deflection. However, the relationship between the fracture patterns and toughness of the nacre-like biomaterials hence requires more investigation. In this study, we investigated the Mode I crack extension and microstructure deformation near the crack tip, in small scale yielding condition, using incremental finite element method. We identified the microstructure-dependent brittle-ductile transition and the 3 associated fracture patterns. We discovered the mechanism of how microstructure affects fracture patterns and brittle-ductile transition, and hence fracture toughness. These findings will help to explain the toughening mechanism associated with crack extension, which will provide a clue to the design of nacre-like artificial materials for high applicability.

A Simple Elasto-Plastic Iterative Method by Fem for the Analysis of Plane Articulated Truss: Case of a 3-Bar Truss

This paper presents a simplified numerical simulation tool for the elasto-plastic calculation of plane articulated truss by the finite element method (FEM) in MATLAB. The simplified approach consists of linearizing isotropic strain-hardening (to obtain a bilinear material law). The numerical implementation is built on the basis of the incremental and iterative FEM algorithms. The numerical resolution technique used is based on the projection methods of the modified Newton-Raphson solution. The MATLAB program is developed for the application of a 3-bar truss under monotonous quasi-static loading. Different values of the approximation error of the convergence criterion are used to study its impact on the quality of the algorithm. Numerical simulations have shown the reliability and quality of our simplified approach regardless of the approximation error.

Data for ultimate bearing capacity of concrete-filled steel tubular members and arches by the elastic modulus reduction method.

Homogeneous generalized yield function is adopted in this article to calculate the ultimate bearing capacity of 93 concrete-filled steel tubular components with detailed test data, and the ratios of the ultimate bearing capacity calculated to the tested are presented. Moreover, the incremental nonlinear finite element method and elastic modulus reduction method are adopted to evaluate the ultimate bearing capacity of 11 concrete-filled steel tubular arches, 7 among which with detailed test data. The component data cover those under different loading conditions, material strength and geometric parameters, and the arch data include those under different loading conditions and rise to span ratios. The data provided are useful to investigate the strength of CFST members and arches and to demonstrate the validation of other numerical methods. The current data are considered as a complementary for the main work “Linear elastic iteration technique for ultimate bearing capacity of circular CFST arches” [1].

Stress analysis near crack tip of nacre-like biomaterial

In this paper, to elucidate the toughening mechanism of nacre-like biomaterial due to crack propagation, stress analysis near the crack tip was performed based on the cohesive zone model. First, a one-dimensional model was constructed, and the stability analysis was performed. The strain energy distribution within the solution space under various load conditions is obtained. The crack propagation is classified into four stages, and the transition of the stable solution and the quasi-stable solution is analyzed, and the equilibrium condition is searched. Also, a two-dimensional model was created based on the incremental finite element method, and a method for analyzing crack propagation in nacre-like biomaterials was explored. The stress state near the crack tip was analyzed using the quasi-static implicit method. The spatial distribution and temporal evolution of DCZ separation were studied.

Coupled thermo-structural analysis of a bimetallic strip using the absolute nodal coordinate formulation

A bimetallic strip consists of two different metal pieces that are bonded together. Due to the different coefficients of thermal expansion, exposing the strip to temperature induces thermal stresses that cause the structure to bend. Most often, incremental finite-element methods that introduce element nodal coordinates have been successfully applied to analyze the thermally induced vibrations in such systems. The exposure of these bimetallic strips to high temperatures results in large deflections and deformations, where the effects of the rigid-body motion and large rotations must be taken into account. For classic, non-isoparametric elements such as beams and plates the incremental methods do not result in zero strains under arbitrary, rigid-body motion. Therefore, in this paper a new model of a bimetallic strip is proposed based on a coupled thermo-structural analysis using the absolute nodal coordinate formulation. The applied, non-incremental, absolute nodal coordinate formulation uses a set of global displacements and slopes so that the beam and the plate elements can be treated as isoparametric elements. In order to simulate the bimetallic strip’s dynamic response, the formulation of the shear-deformable beam element had to be extended with thermally induced stresses. This made it possible to model the coupled thermo-structural problem and to represent the connectivity constraints at the interface between the two strips of metal. The proposed formulation was verified by comparing the responses using a general-purpose finite-element software.

Anisotropic Swelling in Fiber-reinforced Hydrogels: An Incremental Finite Element Method and Its Applications in Design of Bilayer Structures

In this paper, we present a theoretical and finite element framework for the inhomogeneous swelling of fiber-reinforced anisotropic hydrogels and investigate the effects of their orientations and moduli on the swelling behaviors of hydrogel bilayers. The effects of fibers on swelling are incorporated into the constitutive equations by introducing the corresponding energy contribution, expressed as the invariants related to the deformation of fibers, into the Flory–Rehner model. Unified constitutive equations and corresponding tangent moduli for anisotropic hydrogels reinforced with two families of fibers are deduced. A nonlinear finite element procedure is developed to simulate the inhomogeneous steady anisotropic swelling, where the chemical potential is prescribed in an incremental way. The accuracy and effectiveness of the numerical procedure are demonstrated by the anisotropic swelling of hydrogel blocks with one or two families of fibers. Based on the numerical procedure, many kinds of swelling configurations for hydrogel bilayers with different fiber orientations and modulus coefficients can be obtained, ranging from pure bending, twisting or saddle-like to combinations of them, which provide systematic guidance for the design of anisotropic-hydrogel based bilayers.

Creep of Steam-Turbine Diaphragm Under Variable Loading Conditions

The authors put forward a procedure of creep analysis for variable loading conditions, which involves the use of the incremental creep theory and finite element method. Variable loading with load increase and relief at a constant temperature is considered as a stepwise process. The authors study a growth of deflections and stress relaxation in a intermediate-cylinder diaphragm of a steam turbine in various loading modes as well as special features of residual stress distribution in fixed blades.

Anisotropic Swelling in Fiber-Reinforced Hydrogels: An Incremental Finite Element Method and Its Applications in Design of Bilayer Structures

In this paper, we present a theoretical and finite element framework for the inhomogeneous swelling of fiber-reinforced anisotropic hydrogels and investigate the effects of their orientations and moduli on the swelling behaviors of hydrogel bilayers. The effects of fibers on swelling are incorporated into the constitutive equations by introducing the corresponding energy contribution, expressed as the invariants related to the deformation of fibers, into the Flory–Rehner model. Unified constitutive equations and corresponding tangent moduli for anisotropic hydrogels reinforced with two families of fibers are deduced. A nonlinear finite element procedure is developed to simulate the inhomogeneous steady anisotropic swelling, where the chemical potential is prescribed in an incremental way. The accuracy and effectiveness of the numerical procedure are demonstrated by the anisotropic swelling of hydrogel blocks with one or two families of fibers. Based on the numerical procedure, many kinds of swelling configurations for hydrogel bilayers with different fiber orientations and modulus coefficients can be obtained, ranging from pure bending, twisting or saddle-like to combinations of them, which provide systematic guidance for the design of anisotropic-hydrogel based bilayers.

Incremental elastoplastic FEM for simulating the deformation process of suction caissons subjected to cyclic loads in soft clays

This paper presents an incremental elastoplastic finite element method (FEM) to simulate the undrained deformation process of suction caisson foundations subjected to cyclic loads in soft clays. The method is developed by encoding the total-stress-based bounding surface model proposed by the authors in the ABAQUS software package. According to the model characteristics, elastoplastic stress states associated with the incremental strains of each iteration are determined using the sub-incremental explicit Euler algorithm, and the state parameters describing the cyclic accumulative rates of strains are updated by setting state variables during the calculations. The radial fallback method is also proposed to modify the stress states outside the bounding surface to the surface during determination of the elastoplastic stress states. The stress reversals of soil elements are judged by the angle between the incremental deviatoric stress and the exterior normal vector at the image stress point on the bounding surface to update the mapping centre and state variables during cyclic loading. To assess the general validity of the method, the reduced scale model tests and centrifuge tests of suction caissons subjected to cyclic loads are simulated using the method. Predictions are in relative good agreement with test results. Compared with the limit equilibrium and quasi-static methods, the method can not only determine the cyclic bearing capacity, but can also analyse the deformation process and the failure mechanisms of suction caisson under cyclic loads in soft clays.

Effects of Process Parameters on the Formability of Miniature Layered Cups

Based on materials, different punch radii (0.3, 0.35, 0.4, 0.45, and 0.5 mm), two sets of diameter-diameter ratio 1.(.167, 1.25, 1.33, 1.4167, and 1.5) and 2.(1.6, 1.45, 1.33, 1.231, and 1.143), and two sets of depth ratio 1.(1.3, 1.4, 1.5, 1.6, and 1.7) and 2.(2.14, 1.875, 1.67, 1.5, and 1.36) are used for the stamping processes to analyze the simulation and experimental difference in copper sheet-metal (C1100) miniature layered cups. Prandtl-Reuss flow rule is integrated with finite deformation theory and Updated Lagrangian Formulation (ULF) to establish the incremental elastic-plastic deformation Finite Element Method in Coulomb’s Friction Law for simulating the miniature layered cup process. Generalized rmin algorithm is utilized in the forming process for dealing with elastic-plastic behaviors and die contact. From the simulation data, the relationship among deformation history, punch load, and punch stroke, the stress-strain distribution, and the distribution of the thinnest thickness by different punch radii are acquired.

Modeling and simulation of material degradation in biodegradable wound closure devices

Biodegradable materials have been used as wound closure materials. It is important for these materials to enhance wound healing when the wound is vulnerable, and maintain wound closure until the wound is heal. This article studies the degradation process of bioresorbable magnesium micro-clips for wound closure in voice/laryngeal microsurgery. A novel computational approach is proposed to model degradation of the biodegradable micro-clips. The degradation process that considers both material and geometry of the device as well as its deployment is modeled as an energy minimization problem that is iteratively solved using active contour and incremental finite element methods. Strain energy of the micro-clip during degradation is calculated with the stretching and bending functions in the active contour formulation. The degradation rate is computed from strain energy using a transformation formulation. By relating strain energy to material degradation, the degradation rates and geometries of the micro-clip during degradation can be represented using a simulated degradation map. Computer simulation of the degradation of the micro-clip presented in the study is validated by in vivo and in vitro experiments.

Post-Buckling Analysis of Functionally Graded Three-Dimensional Beams Under the Influence of Temperature

In this study, post-buckling behavior of functionally graded beams under the influence of temperature loading is investigated by using total Lagrangian finite element model of three-dimensional continuum approximations. Material properties of the beam are both temperature-dependent and position-dependent. In this study, there is no restriction on the magnitudes of deflections and rotations in the beam. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in connection with Newton-Raphson iteration method. With the effects of material gradient property and thermal load, thermal post-buckling configurations are illustrated in detail in post-buckling cases.

Application of a modified semismooth Newton method to some elasto-plastic problems

Some elasto-plasticity models with hardening are discussed and some incremental finite element methods with different time discretisation schemes are considered. The corresponding one-time-step problems lead to variational equations with various non-linear operators. Common properties of the non-linear operators are derived and consequently a general problem is formulated. The problem can be solved by Newton-like methods. First, the semismooth Newton method is analysed. The local superlinear convergence is proved in dependence on the finite element discretisation parameter. Then it is introduced a modified semismooth Newton method which contain suitable “damping” in each Newton iteration in addition. The determination of the damping coefficients uses the fact that the investigated problem can be formulated as a minimisation one. The method is globally convergent, independently on the discretisation parameter. Moreover the local superlinear convergence also holds. The influence of inexact inner solvers is also discussed. The method is illustrated on a numerical example.

Simulation of material flow in friction stir processing of a cast Al–Si alloy

The objective of the current paper is using DEFORM-3D software to develop a 3-D Lagrangian incremental finite element method (FEM) simulation of friction stir processing (FSP). The developed simulation allows prediction of the defect types, temperature distribution, effective plastic strain, and especially material flow in the weld zone. Three-dimensional results of the material flow patterns in the center, advancing and retreating sides were extracted using the point tracking. The results reveal that the main part of the material flow occurs near the top surface and at the advancing side (AS). Material near the top surface was stretched to the advancing side resulting in a non-symmetrical shape of the stir zone (SZ). Furthermore, macrostructure and temperature rise were experimentally acquired to evaluate the accuracy of the developed simulation. The comparison shows that the stir zone shape, defect types, powder agglomeration, and temperature rise, which were predicted by simulation, are in good agreement with the corresponding experimental results.

Pre-offset-based Approach to Optimizing and Compensating Weld-line of Tailor-welded Blanks

In forming process of tailor welded blanks(TWBs),weld-line movement leads to the inconsistency between the design weld-line and the actual weld-line.Therefore,aimed at the deep drawing process of TWBs,a weld-line compensating approach based on pre-offset is proposed,which employs the incremental finite element method(FEM) solver.A mesh model for FEM analysis is created.By comparing the difference between the designed and the formed weld-line,an estimation method is deducted.An optimization model is established,in which the nodal pre-offsets of the weld-line are selected as design variables and the minimum deviation between the designed and formed weld-lines is selected as the objective function.The weld-line movement during the forming process is compensated through FEM iterative solving,thus reaching a positional agreement between the formed weld-line and the designed one.An example shows the feasibility of the proposed approach.

Analysis of Optimal Vertical in Angular U-Bending Process

This study aims to analyze the effects of angular U-bending process on the springback of metal sheets. Based on Updated Lagrangian Formulation (ULF), the 3D incremental elastic-plastic Finite Element Method was inferred to simulate the U-bending process of metal sheets. The die/blank holder profile with angles of α=-4°, α=-2°, α=0°, α=2°, α=4° and die/punch profile with radiuses of Rp=Rd=6.0mm were analyzed to determine the influence of tool angles on the springback. With different tool angles to proceed the U-bending process of metal sheets, it is found that the larger or smaller die angles, the more springback magnitude. When perpendicular U-sheets are required, θ1 of the U-sheet presents 90 degree on the tool angle α=-1.2° and θ2 shows 90 degrees on the tool angle α=-0.4°. The aim of this study is to investigate the effects of angle variables on the springback in the U-bending process and to obtain useful data from the industrial field.

Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.