Nonlinear Finite Element Code Research Articles

The investigation and estimation of flexural strength in shear-critically designed RC beams considering the steel fiber content

Despite numerous studies investigating the effectiveness of steel fibers in RC members subjected to various loading conditions, the majority ignored the impact of the interaction between the tensile reinforcement ratio, compressive strength of fibrous concrete, and steel fiber dosage. This paper aimed to inspect and quantify the effects of hooked-end steel fiber dosage on the bending behavior of RC beams considering the interaction arising from various longitudinal reinforcement ratios. For this purpose, an extensive and hybrid investigation involving both experimental and numerical techniques was conducted. In the experimental part, an investigation was carried out to evaluate the contribution of a specific amount of fiber ratio and various aspect ratios to the behavior of large-scale RC beams having a shear-deficient design. Three beams with a 0.5% hooked-end steel fiber ratio and one without fibers but with a minimum amount of stirrups were produced, and three-point bending tests were conducted. All beams having fibers utilized full flexural strength as in the beam with stirrups. Once the experimental studies were completed, the numerical models were then developed and validated with those of experimental three-point bending tests using the non-linear finite element code VecTor2 to establish a basis for the comprehensive parametric study. The parametric study consisted of 33 analyses. Rebar and volumetric fiber ratios were selected to be variables, and the ratios adopted were within the typical range used in structural engineering applications. Based on the regression analysis a linear and a quadratic model were proposed for estimating the yield and peak strength depending on the steel fiber content. Finally, the obtained models were verified using work from the literature and found to be effective in forecasting the strength of shear-deficient RC beams with 0.8%, 1.0%, and 1.2% tensile reinforcement ratios and hooked end steel fibers (0.5 to 1.5%).

Numerical Analysis of Out-of-Plane Crushing of Reinforced Honeycomb Core and Effect of Cell Parameters on its Properties

The non-linear finite element code LS-DYNA has been used in this work to conduct the crushing examination of both normal and reinforced honeycomb cores. The honeycomb-like cores are provided with out-of-plane quasi-static conditions of stress via an explicit dynamic approach. We have parametrically investigated the effects of cell properties on crushed behaviour as well as the absorption of energy, including the size of the cell, wall thickness, height, along with cell wall tilted position. Regular honeycomb (R0-HC), reinforced every other ribbon (R1-HC), and reinforced every ribbon (R2-HC) are three different varieties of honeycomb. The findings of the numerical analysis of these three types of honeycomb are compared to understand how reinforcing affects energy absorption and crushing parameters. The sheet material AA3003-H18 was chosen to make the honeycomb core. In comparison to ordinary honeycombs, the reinforced honeycombs demonstrated superior crushing behavior and energy absorption. In comparison to the others, reinforced every ribbon (R2-HC) type honeycombs exhibited the greatest values for crushing characteristics and energy absorption. The crushing characteristics and energy absorption of reinforced every other ribbon (R1-HC) honeycombs were higher than those of ordinary honeycombs (R0-HCThe crushing force, average plateau force, and energy absorption values decrease as the cell size, height, and wall angle are increased, however, all these crushing characteristics increase as the cell wall thickness is increased.

Composite curved hourglass cellular structures: Design optimization for stiffness response and crashworthiness performance

Auxetic lattice structures are known for their superior stiffness-to-density and strength-to-density ratios. Re-entrant hourglass exhibits an acceptable equivalent elastic modulus and remarkable energy absorption capacity among various auxetic configurations due to their flexibility and hinge deflecting during crushing loads. This study introduces a curved hourglass honeycomb which can be produced using 3D printing with pure or reinforced filaments incorporating continuous fibers. New closed-form formulations are analytically derived using an energy method by considering an extracted unit cell to predict the equivalent in-plane mechanical properties for the first time. The plateau stress of the proposed honeycomb is evaluated at the densification state of a unit cell using the energy conservation theory, equating external work with plastic energy dissipation. The accuracy of these extended relations is validated against experimental outcomes, demonstrating good agreement between analytical and experimental results. Additionally, robust linear and nonlinear finite element analyses are conducted to assess the accuracy of the obtained relations, including the equivalent stiffness and plateau stress for structures produced with reinforced filaments. The nonlinear finite element code employs appropriate subroutines to model plasticity/damage events. Based on the established analytical relations for stiffness and plateau stress, multi-objective optimization using Genetic Algorithm is applied to define optimum values for the Pareto front chart's objective functions of stiffness and plateau stress. The optimization process involves exploring the design space and defining the values of geometrical parameters to achieve the desired objectives. In conclusion, this study presents a novel approach to developing curved re-entrant honeycomb structures, with analytical formulations validated against experimental and numerical results. Optimization helps to identify optimal configurations concerning stiffness and plateau stress, offering potential applications in lightweight and high-strength materials design. According to the obtained results, for selection of the best value for curved strut angle which results in the optimum value of stiffness and plateau stress, a range between 10°-34° can be considered depending on the volume fraction of fibers.

A New Approach for Protection against Ejection Trajectory of Scabbed Materials of Ultrahigh-Performance Concrete under Projectile Impact

Scabbing on the rear face of concrete under impact produces fragments that act as additional projectiles causing fatality or severe damage to the occupants or systems. Ultrahigh-performance concrete (UHPC) has outstanding properties and has proven efficacy in the impact-resistant design of structures. However, the potential damage due to the impact of fragments of scabbed pieces still prevails. This study developed a new approach for preventing ejection of scabbed materials of UHPC under single and repeated bullet impact (using a single-stage gas gun facility). The ejection of scabbed materials was controlled using woven carbon–epoxy and glass–epoxy laminated composite sheets attached to the rear face of UHPC samples. The ejection of scabbed pieces was controlled in UHPC targets with composite backing in the case of both single and repeated impact under similar conditions. Furthermore, a numerical simulation based on nonlinear finite-element code was performed for repeated impact on a UHPC target with a carbon–epoxy laminated composite. The results of the numerical simulation had a good agreement with the experimental data. Thus, the synergistic effects of steel fiber–reinforced UHPC with composite backing can be used to enhance the impact performance of UHPC.

Experimental and numerical study of telescopic conical energy absorber under inversion process

In this article, a new model of a conical absorber with an inversion mechanism in form of a telescope is introduced. The purpose of this article is to decrease the initial peak load and improve drawbacks and limitations in the inversion mechanism. When the tube is subjected to axial loading, each component is inverted and moves toward the next component. Therefore, the dissipation of energy is occurred due to the curling of edges and circumferential contraction in the tube wall. The inversion process of tubes under axial compression is simulated using the ABAQUS nonlinear finite element code. To verify the numerical simulation, some experimental tests are carried out. Moreover, a parametric study has been conducted to investigate the geometric effects of tube including end-capped, numbers of conical components, semi-apical angle and edge length of components. The results show that with appropriate selection of geometric dimensions of the new conical absorber has a significant role in reducing the initial peak load without a noticeable change in the specific energy absorption.

Modelling of self-healing in viscoelastic materials

A novel viscoelastic damage-healing model for self-healing materials is proposed coupling continuum damage healing mechanics (CDHM) framework with a viscoelastic constitutive model for self-healing during unloading and rest periods. The viscoelastic damage-healing model is coupled with the novel secondary damage internal variable accounting for the subsequent damage of healed material. The proposed viscoelastic damage-healing model formulation is numerically implemented by return mapping approach employing the elastic strain equivalence hypothesis from CDHM, and model response as stress update is obtained for several strain histories. Detailed parametric studies are conducted by varying the material constants appearing in the damage and healing evolution equations, and their influence on the constitutive model response is analysed. Various tangent moduli expressions are finally derived, and successfully coupled with an in-house developed plane strain nonlinear finite element code while solving different boundary value problems.

Numerical study on influence of target thickness on impact response of GFRP composites

Due to rise in threats like ballistic impacts, blast loading and vehicle collision in armored military vehicles, the demand for materials with high strength and enhanced energy absorption capacity has been increased. Applications of Fiber reinforced composites as armor material in military vehicles is being considered as one of the measures to reduce such threats. The focus of this work is to investigate the energy absorption capacity of a GFRP plates subjected to a rigid projectile with blunt-nosed at the intermediate velocity range by using non-linear finite element code LS-DYNA. It has been found that the numerically computed results of ballistic limit velocity and residual velocity, closely resemble the test results reported in the literature. With altering target thickness, it has also been explored how the energy absorption capacity, projectile's residual velocity, ballistic velocity limit and damage mechanism of composite. The numerical results make it evident that the target thicknesses have a significant impact on the target's ballistic resistance and delamination area.

Modelling the effect of lateral inertia on the dynamic response of aluminium square tube extrusions

Crashworthiness of automotives require the design of crush tubes installed as a frontal structure to absorb energy by deforming plastically during collision. The crushing behaviour of aluminium extrusions modelled as square tubes is investigated under quasi-static and dynamic loading conditions using the non-linear explicit finite element code LS DYNA. Previous works have attributed the dynamic increase of the peak and mean crushing load of aluminium thin-walled structures under axial compression, to inertia effects. Results of our investigation revealed that there is a considerable thickening of the shell side walls before and during progressive folding. This shell thickening is established as the cause of lateral inertia which consequently results in increased crush strength. In addition, a positive correlation was established between the shell thickening and crushing speeds. 

Influence of strands corrosion on the flexural behavior of prestressed concrete beams

In this paper, the research goal was the determination of the flexural response of corroded pre-stressed reinforced concrete beams (PC). A simplified flexural model is bases on the calcualus of the moment and curvature/deflection curves for simply supported beam under uniformly distributed and concentrated loads. Primary research outcomes was the introduction in flexural model of the effects of pitting corrosion though the reduction of area, of the mechanical properties of steel strands and of the loss of bond of steel strands of precast pre-tensioned beams.A comparison with available experimental data of literature and with numerical simulation carried out with nonlinear finite element code (ABAQUS) was made. Results obtaiend showed that the corrosion of strands reduce the bearing capacity of the viaducts with prestressed beams especially and because of the reduction of strain capacity of steel strand, arises a risk of brittle collapse under service conditions due to the strand failure.

Mechanical properties of all-C/C composite hybrid bonded/bolted joints

In this paper, experiments and numerical simulations were used to study the mechanical properties of all-C/C composite hybrid bonded/bolted joints. Experiments were conducted to investigate the failure mechanisms, modes, and strengths of composite single-lap joints, namely, bolted joints with and without bonds. The results demonstrated that the failure mode of all-C/C composite mechanical joints was bolt shear failure, while the failure mode of the bonded joints was cohesive force failure. In hybrid bonded/bolted joints, cohesive force failure of the adhesive layer and bolt shear failure have both been noted. The C/C composite plates of all joints were not discovered to have any evident deterioration. The load-displacement curve of the hybrid joints was a double-peak curve, the first peak load corresponds to bonding failure, and the second peak load corresponds to bolt failure. For the failure process, mode, and strength of hybrid (bonded/bolted) joints, a 3D progressive damage finite element model was proposed. It is based on the nonlinear finite element code ABAQUS and Hashion failure criteria. The VUMAT subroutine compiled Hashion failure criteria to simulate the damage of fiber and matrix in the composite material. Furthermore, the adhesive layer’s failure was simulated using the cohesive element. Comparing failure loads and failure modes to the outcomes of experiments served to validate the model. The gradual damage evolution process and failure mechanism of bonded and hybrid bonded/bolted joints were determined, as well as the mechanism by which the cohesive layer influences the mechanical properties of the hybrid bonded/bolted joints. On the mechanical characteristics of composite joints, the impacts of bolt diameter and adhesive layer modulus were investigated.

Dynamic Response of Structurally Reinforced Wing Leading Edge against Soft Impact

In this current research, a commercial aircraft metallic leading edge structurally reinforced with a Y-shaped and V-shaped plate system is numerically examined to investigate the effectiveness of such reinforcements against soft impacts, more commonly known as bird strikes in the aviation industry. A non-linear finite element code Ansys Explicit is adopted to run the virtual test cases. The computational bird model is presented with the Lagrange algorithm and Mooney–Rivlin hyperelastic material parameters which are validated against the experimental data found in the literature. A second validation of the leading edge deformation pattern is also carried out to ensure the accuracy of the present work. Numerical outcomes suggest that due to the presence of the reinforcement, the leading edge skin is restrained from being drastically deformed and the bird model tears apart into two pieces requiring the leading edge model to absorb much less kinetic energy. Additionally, it is found that both the reinforcements have similar crashworthiness performance against bird impacts. The novelty of the research lies in founding the structural reinforcement as a primary preference to strengthen the vulnerable wing leading edge during bird impacts.

Constitutive modelling of plastically deformable self-healing materials

A novel elasto-plastic constitutive model of self-healing materials is proposed coupling continuum damage–healing mechanics (CDHM) framework with kinematic and isotropic hardening cases. A novel secondary damage internal variable is presented, eliminating an assumption in the existing literature that the healed area does not undergo damage again, thus improving the existing CDHM framework. The necessity of the proposed secondary damage variable is successfully demonstrated by a four spring material model. The improved CDHM framework is coupled with the three-dimensional elasto-plastic formulation containing nonlinear kinematic hardening and isotropic strain hardening effects. The proposed formulation is finally numerically implemented by return mapping approach employing the strain energy equivalence hypothesis from CDHM, and the macro-scale stress update is performed applying several different strain histories. A continuum tangent modulus expression is also derived, and a boundary value problem is successfully solved employing an in-house developed plane strain nonlinear finite element code. It is finally demonstrated, by the numerical results, that the secondary damage variable is crucial while obtaining the physically realistic stress–strain response of self-healing materials leading to the complete failure upon exhaustion of the healing capabilities.

Viscoplastic Material Modeling for the Stretch Blow Molding Simulation

Abstract In this paper, the viscoplastic material model of PET (polyethylene terephthalate), which is intended to be used in the FEM (finite element method) simulation of stretch blow molding process, has been studied. Material tests of PET were performed with the constant strain rates varying from 0.01 to 1 (1/s), at temperatures ranging from 90 to 150 °C, based on the obtained data a two-stage model was proposed. The proposed model could precisely take into account the effects of strain hardening, strain rate sensitivity, variation of the hardening index, and temperature dependency. This model has been implemented into the nonlinear finite element code PBLOW3D, which is developed in the Riken, and its performance in the stretch blow molding simulation has been studied. It has been demonstrated that the proposed material model provides significant improvements, compared with two existing material models, in the simulation of the blow molding process of PET bottles.

Crushing analysis and optimization for bio-inspired hierarchical 3D cellular structure

Three-dimensional (3D) cellular structures have been widely used in many aspects, e.g., protective equipment, aerospace, vehicles and so on, due to its lightweight and excellent energy absorption characteristics. Triply periodic minimal surface (TPMS) has more uniform energy absorption and mechanical properties than foam due to its structural characteristics. Therefore, a novel 3D hierarchical structure based on TPMS inspired by natural hierarchical biological structure is proposed in this study. Then, the numerical simulation is carried out using the nonlinear finite element code through LS-DYNA to study the crushing behavior of the hierarchical 3D cellular structure. And, the accuracy of finite element model is validated by quasi-static compression experiments on hierarchical structures manufactured by 3D printing. According to the numerical simulation results, the bio-inspired hierarchical 3D lattice is found to have excellent energy absorption characteristics than the non-hierarchical 3D lattice. In addition, the energy absorption characteristics of hierarchical structure is found to be affected by the design parameters of density and constant C. In order to obtain the optimal design of the bio-inspired hierarchical 3D lattice, Kriging (KRG) surrogate models and non-dominated sorting genetic algorithm II (NSGA-II) are jointly used to optimize the hierarchical 3D cellular structure. Moreover, the approximate expression of the specific energy absorption (SEA) of the hierarchical 3D cellular structure is obtained by fitting Gibson and Ashby empirical formula for prediction. Based on our study, the novel hierarchical 3D cellular structure has extremely excellent energy absorption characteristics and has very good application prospect in impact engineering.

Numerical modelling and dynamic response analysis of a 10 MW semi-submersible floating offshore wind turbine subjected to ship collision loads

The number of installed offshore wind turbines is continuously growing worldwide in recent years. Offshore wind farms are generally located near the coast close to traffic lanes and are exposed to the risk of collisions from visiting and passing ships. Potential consequences of collisions may vary from local structural damage to the detachment of turbine nacelles and rotors, and even tower collapse and capsizing of the turbine platform, causing significant economic loss and fatalities.This paper investigates ship collision responses of a semi-submersible floating offshore wind turbine (FOWT), i.e. the OO-STAR floater with the DTU 10 MW blades, using the nonlinear finite element code USFOS. The OO-STAR floater is made of post-tensioned concrete designed by Dr. techn. Olav Olsen. The striking ships are selected to be a modern supply vessel of 7500 tons and a shuttle tanker of 150,000 tons, representing respectively service/coastal merchant vessels and large passing vessels. Modelling of the FOWT in USFOS is described in detail including the OO-STAR floater, the DTU 10 MW turbine blade, the turbine tower, and the mooring system. The modelled hydrodynamic loads include buoyancy loads and motion induced radiation loads using the Morrison equation. The effects of external waves and currents are assumed to be small and ignored in all directions. Eigenmode analysis of the turbine model is performed to verify the established model.Global collision response analyses of the FOWT were performed in both parked and operating conditions. The ship resistance is modelled as nonlinear springs in USFOS containing force displacement curves simulated in LS-DYNA. In operating conditions, wind loads are introduced including wind thrust loads and wind induced torque to rotate the turbine blades. The changes of upstream wind speeds and rotor/wake interactions during collisions are neglected. The results are discussed with respect to energy absorption of the ship and the FOWT, and structural responses of the FOWT including global motions, nacelle accelerations, tower clearance, tower vibrations, and responses of the mooring system.

The Effect of Boundary Conditions and Stacking Sequence on the Nonlinear Behavior of Laminated Composite Plates in Bending

This paper presents an effectively numerical approach based on quadrilateral isoperimetric element. Indeed, the Von-Karman’s large deflection theory and the first-order shear deformation theory (FSDT) are also used in the formulation of the element to formulate the geometrically nonlinearity analysis. The nonlinear finite element code has been developed by using Matlab. Therefore, the governing nonlinear equations obtained are solved using Newton–Raphson iterative technique. Finally, the results obtained are compared with those available in the literature and with those obtained by ABAQUS. It has been found that the present approach is accurate and efficient to predict the nonlinear behavior of laminated composite plates under bending loads. Moreover, the effects of the boundary conditions and the stacking sequence on the nonlinear deflection of the plate are treated.

LARGE DEFORMATION BEHAVIOUR OF THIN MILD STEEL RECTANGULAR PLATES SUBJECTED TO UNDERWATER EXPLOSION LOADING UNDER AIR AND WATER BACKED CONDITIONS

Marine vehicles in their operation as military vehicle are susceptible for underwater explosion from mines, torpedo etc. The damage inflicted on such structures made of ductile materials can be large deformation, tearing, rupture etc. It is imperative to design such structures for withstanding explosive loads. The damages inflicted will be mostly localized between the frames and stiffener, which can be considered as plate clamped at the edges. Hence, an attempt has been made in this paper to study the localized deformation of thin mild steel plates subjected to underwater explosion through limited explosion bulge test using small explosives. The experiments exhibited Mode I: large deformation, Mode IIa: Partial tensile tearing, Mode IIc: central rupture and Counter Intuitive Behaviour (CIB). The problem is simulated numerically using LS DYNA nonlinear finite element code considering fluid – structure interaction and the results compared with experiments. Based on the confidence gained for the air backed conditions, the analysis is extended to water backed (fully filled, 75% filled, 50 % filled) conditions and results obtained for the large deformation behaviour for various conditions are presented. The results indicate that the large deformation behaviour considerably reduces the central permanent deformation under water backed conditions compared to air backed conditions due to the fact that part of shock wave gets transmitted to the water medium behind the plate in water backed conditions.

Thermal Delamination Modelling and Evaluation of Aluminium-Glass Fibre-Reinforced Polymer Hybrid.

This paper aims to propose a temperature-dependent cohesive model to predict the delamination of dissimilar metal–composite material hybrid under Mode-I and Mode-II delamination. Commercial nonlinear finite element (FE) code LS-DYNA was used to simulate the material and cohesive model of hybrid aluminium–glass fibre-reinforced polymer (GFRP) laminate. For an accurate representation of the Mode-I and Mode-II delamination between aluminium and GFRP laminates, cohesive zone modelling with bilinear traction separation law was implemented. Cohesive zone properties at different temperatures were obtained by applying trends of experimental results from double cantilever beam and end notched flexural tests. Results from experimental tests were compared with simulation results at 30, 70 and 110 °C to verify the validity of the model. Mode-I and Mode-II FE models compared to experimental tests show a good correlation of 5.73% and 7.26% discrepancy, respectively. Crack front stress distribution at 30 °C is characterised by a smooth gradual decrease in Mode-I stress from the centre to the edge of the specimen. At 70 °C, the entire crack front reaches the maximum Mode-I stress with the exception of much lower stress build-up at the specimen’s edge. On the other hand, the Mode-II stress increases progressively from the centre to the edge at 30 °C. At 70 °C, uniform low stress is built up along the crack front with the exception of significantly higher stress concentrated only at the free edge. At 110 °C, the stress distribution for both modes transforms back to the similar profile, as observed in the 30 °C case.

Comparison of second-order serendipity and Lagrange tetrahedral elements for nonlinear explicit methods

This paper evaluates the performances of second-order finite elements for nodal lumped-mass explicit methods in nonlinear solid dynamics, with a particular emphasis on 10-node “serendipity” and 15-node “Lagrange” tetrahedral elements. Historically, many nonlinear explicit finite element codes have exclusively used first-order elements, until a fairly recent flurry of activity that has resulted in higher-order elements becoming available in explicit codes including the authors' in-house one, ParaAble, and the production software EPIC, IMPETUS, LS-DYNA, and Abaqus. A major attractiveness of tetrahedrons is their ease in meshing and higher-order elements can facilitate the avoidance of severe volumetric locking with unstructured C0 meshes, which are generally used with these codes for the discontinuities of inelasticity, contact, etc. They also can improve modeling of flexure and curved shapes as well as eliminate spurious modes without artificial stabilization. The inclusion of face and body centroid nodes with Lagrange interpolants, including the 15-node tetrahedron, has proven to provide robust overall performance with lumped-mass explicit methods and with contact. Nevertheless, versions of the 10-node tetrahedron have also emerged in lumped-mass explicit software. In contrast to hexahedrons, an important observation about tetrahedrons is that the 10-node serendipity version uses about four times fewer quadrature points and a larger time increment than their 15-node Lagrange counterpart, which could result in tremendous computational differences. Serendipity elements, however, notoriously do not nodal mass lump well and tetrahedron versions have not been rigorously evaluated/documented for their effectiveness, as will be done herein with comparisons of those using 15-node tetrahedrons. Using row-summation lumping for Lagrange elements and the ad hoc HRZ scheme for serendipity ones, performances are assessed in common benchmark problems and practical applications using various elastic and inelastic material models and involving large strains/deformations/rotations and severe distortions. Whereas the 10-node tetrahedrons were found to perform much better than their 20-node serendipity hexahedral counterparts, specifically with substantial computational reductions and reasonable predictions, they are not generally quite as accurate or robust as the 15-node tetrahedral elements. The results thus indicate benefits of including both 10- and 15-node tetrahedrons in an explicit code's element library.

Numerical simulation of a UAV impacting engine fan blades

A 3D digital model of a small Unmanned Aerial Vehicle (UAV) is obtained by using the method of scanning reverse modeling and joint mapping. A numerical simulation of a small UAV strikes on rotary engine blades, presented in this paper, was performed with a Transient Nonlinear Finite Element code PAM-CRASH software. A test of motor strike on plate was developed and the dynamic response of the plate were obtained to validate the numerical simulation method of a UAV strike on blades. Based on this, dynamic damage response caused by UAV on the engine blades were studied. It is indicated that the impact process between the UAV and a single blade can be divided into two typical stages: cutting and impact. Cutting mainly leads to the failure of the leading edge material, and impact mainly leads to the plastic deformation of the blade. At the same time, it is compared with the damage impacted by bird with the same mass. For the same mass of bird and UAV, the damage caused by UAV striking fan blade is more serious, and 1.345 kg UAV striking fan blade of typical civil aviation engine is enough to cause damage to flight safety.