Nonlinear Finite Element Simulations Research Articles

The in-plane mechanical properties of highly compressible and stretchable 2D lattices

Highly compressible and stretchable lattice materials are perfectly suitable to be exploited in a range of cutting edge engineering applications such as low band-gap acoustic metamaterials, vibration absorbers, soft robotics, stretchable electronics and stent devices. Physics-based understanding and efficient computational methods are of paramount importance for the analysis and design of such cellular metamaterials. This paper develops the analytical framework to understand the nonlinear mechanics of hexagonal lattices subject to in-plane compressive and tensile stresses. Nonlinear equivalent elastic moduli and Poisson’s ratios of the stressed lattice are expressed through the coefficients of the stiffness matrices of the constitutive beam elements. The stiffness coefficients, in turn, are derived from the transcendental displacement function which is the exact solution of the corresponding governing ordinary differential equation with appropriate boundary conditions. The closed-form analytical expressions of the equivalent elastic properties of the lattice are expressed in terms of trigonometric functions for the case of compressive stress and hyperbolic functions for the case of tensile stress. The general expressions are then used to investigate three special cases of wide interest, namely, auxetic hexagonal lattices, rhombus-shaped lattices and rectangular lattices. Analytical expressions are validated using independent nonlinear finite element simulation results. Numerical results are displayed for applied compressions and tensions in both directions separately and together. The equivalent elastic moduli show a softening effect under compression and a stiffening effect under tension. The Poisson’s ratios are not significantly affected by the applied stresses. The proposed analytical approach and the new closed-form expressions provide a computationally efficient and physically intuitive framework for the analysis and parametric design of lattice materials under external stresses.

Methodology for the simulation of a ship's damage stability and ultimate strength conditions following a collision

This paper presents a methodology called SHARC developed for the simulation and analysis of a ship's damage stability and ULS conditions following a collision. SHARC combines three types of methods: advanced nonlinear finite element simulations that simulate the collision scenario, a dynamic damage stability simulation tool called SIMCAP, and a modified Smith method for the ULS analysis of a collision-damaged ship structure. The novelty of the presented methodology is that it can be used for real-time simulations to study the ingress of water through the damage opening of a struck vessel and how it affects the ship's stability, structural integrity (ULS) and survival capability against, e.g., capsizing. The results for an intact and a damaged oil tanker under noncorroded and corroded structural conditions and various sea states are presented to demonstrate the features of SHARC.

Deployment of a foldable tensegrity‐membrane system via configuration transitions using linear parameter‐varying control

Controlled deployment of a foldable tensegrity-membrane system is investigated in this article. A membrane folding technique referred to as the spiral folding pattern is applied to the attached membrane to achieve compact folded shapes for the system. The foldable tensegrity-membrane system experiences transitions between two system configurations (i.e., the tensegrity configuration and the tensegrity-membrane configuration) due to the variation of membrane loading states during system deployment. A closed-loop control strategy consisting of two linear parameter-varying (LPV) controllers is designed based on control-oriented models to regulate system dynamics. A nonlinear finite element model is used to examine the control performance. Senor noise is considered in another nonlinear finite element simulation to examine the robustness of the designed controllers.

Subspace tracking method for non-smooth yield surface

The corners of non-smooth yield surfaces, e.g., Mohr–Coulomb or Hoek–Brown criteria, often cause problems in numerical applications due to the gradient discontinuities, which boil down to the abrupt order interchange of two principal stresses. Nevertheless, when the stress components cross the corners, the principal stresses, which are smoothly dependent on the components of stress tensor, can be smoothly tracked through subspace tracking method. Thus, all the six auxiliary yield functions based on Koiter’s rule will be smooth functions of components of stress. Finally, the corner problems are eliminated. As an application, three boundary–value​ problems (a 3D one-element, a 2D slope with a soft band, and a 3D soil slope) are analyzed to investigate the performance of the proposed method in a non-linear finite element simulation.

Experimental, analytical, and finite element assessment of the shear strength of concrete‐rock interfaces at different scales

AbstractThis paper presents an original analytical approach to assess the shear strength of concrete‐rock interfaces while accounting for the effects of scale, roughness and matching conditions. The technique proposed is based on experimental data obtained from small core samples extracted from existing dam sites, with diameters varying from 83 to 145 mm, and larger rectangular samples with side lengths comprised between 320 and 492 mm. The predictions of the analytical formulation are validated against results of direct shear tests, as well as 3D nonlinear finite element simulations. Sensitivity analyses are conducted to evaluate the influence of roughness and matching conditions on the shear behavior of concrete‐rock contacts at different scales. The main results show that: (i) roughness inhomogeneity is one of the main causes of scale effects on the shear strength of concrete‐rock interfaces; (ii) contact geometries proportional in both length and height are expected to present quite similar shear strengths; and (iii) geometry matching conditions must be accounted for as they might be the source of scale effects affecting the evaluation of the shear strength at concrete‐rock interfaces. New equations are also proposed to suggest values of apparent cohesion and friction angle for concrete‐rock contacts.

Numerical modeling and analysis of the ballistic impact response of ceramic/composite targets and the influence of cohesive material parameters

Hybrid ceramic/composite targets are acknowledged to provide effective impact protection against armor piercing projectiles, which is why the research on this topic is continuously developing further. In this work, a nonlinear dynamic finite element (FE) simulation method is developed to systematically explore the ballistic perforation behaviors of hybrid ceramic/woven-fabric reinforced polymer (WFRP) composite when impacted by a non-deformable projectile. The hybrid system is composed by an alumina ceramic plate forming the front surface and glass or carbon WFRP composite back-up plate. The simulations are carried out using ABAQUS/Explicit FE code, wherein three different constitutive material models are formulated and implemented. The Johnson–Holmquist and composite damage models are used for alumina and composite material behaviors, respectively. The brittle fracture and fragmentation of the ceramic plate and the failure criteria based on fracture of fibers or matrices of composite materials during perforation are considered. Besides, interlaminar delamination between composite plies as well as ceramic/composite interfacial decohesion are modeled using a cohesive surface method, and the behaviors of interlayer degradation and failure are described using a traction-separation law. The accuracy of the developed model is validated with available experimental and analytical results. What’s more, the perforation process against the projectile and the ballistic mechanism of each layer in the composite backplate and in the ceramic as well are profoundly explored. Meanwhile, the numerical simulations are used to evaluate the changes of energy of the projectile and ceramic/composite panels. The influence of key parameters, such as interface cohesive properties and friction, on the ballistic performance in terms of energy absorption capability is additionally addressed. For the preliminary and early design phase, the present dynamic model could provide an efficient approach for numerical predictions of ballistic impact responses of the hybrid ceramic/FRP composites.

An innovative model for predicting the displacement and rotation of column-tree moment connection under fire

In this study, we carried out nonlinear finite element simulations to predict the performance of a column-tree moment connection (CTMC) under fire and static loads. We also conducted a detailed parameter study based on five input variables, including the applied temperature, number of flange bolts, number of web bolts, length of the beam, and applied static loads. The first variable is changed among seven levels, whereas the other variables are changed among three levels. Employing the Taguchi method for variables 2–5 and their levels, 9 samples were designed for the parameter study, where each sample was exposed to 7 different temperatures yielding 63 outputs. The related variables for each output are imported for the training and testing of different surrogate models. These surrogate models include a multiple linear regression (MLR), multiple Ln equation regression (MLnER), an adaptive network-based fuzzy inference system (ANFIS), and gene expression programming (GEP). 44 samples were used for training randomly while the remaining samples were employed for testing. We show that GEP outperforms MLR, MLnER, and ANFIS. The results indicate that the rotation and deflection of the CTMC depend on the temperature. In addition, the fire resistance increases with a decrease in the beam length; thus, a shorter beam can increase the fire resistance of the building. The numbers of flanges and web bolts slightly affect the rotation and displacement of the CTMCs at temperatures of above 400°C.

Analysis of the Aerodynamics in the Heating Section of an Anode Baking Furnace Using Non-Linear Finite Element Simulations

The emissions from the industrial furnaces impact the environment. Among the various factories, those having anode baking furnaces are working on reducing the pollutant emissions. The aerodynamics in the furnace influences the emissions due to the high dependence of combustion and radiation phenomena on the mixing characteristics. Therefore, this paper aims to establish the numerical simulation results for the three-dimensional turbulent flow in a single section of an anode baking furnace with a high rate of fuel injection. The stabilized non-linear finite element approach on the Reynolds-averaged Navier-Stokes (RANS) equation is used with COMSOLMultiphysics. The turbulent viscosity ratio is highly sensitive to the mesh for the standard k-ϵ model. The requirements of the Cartesian and refined mesh near the jet development region is explained. The comparison of meshes generated by two meshing tools namely cfMesh and COMSOL Multiphysics default Mesher is carried out. The high numerical diffusion in the flow models due to the coarser mesh leads to convergence but deficit the precision in the results. This paper shows that the mesh generated by cfMesh with flow aligned refinement combined with the non-linear finite element solver in COMSOL Multiphysics proves to provide accurate results of turbulent quantities.

Finite Element Analysis on Lining Structure of Diversion Tunnel in a Hydropower Station

Aiming at the high internal and external water pressure tunnels built in unfavorable geological bodies, this study proposes a novel type of composite support structure in which steel plates are poured inside concrete linings. Compared with traditional structures, it has the advantages of higher tensile strength, better crack resistance, and impermeability. Taking the diversion tunnel of a hydropower station as an example, based on linear and non-linear finite element simulations, mechanical properties of the steelconcrete composite lining structure for a hydraulic tunnel in soft surrounding rocks are analyzed. On this basis, the concrete crack control under this supporting condition is verified. Research results can provide a reference for the selection of reasonable steel plate thicknesses and reinforcement types in design.

2D linear finite element simulation of laser metal heating for digital twins

In the context of laser-based additive manufacturing, the thermal behavior of the substrate is relevant to define process parameters vis-à-vis piece quality. The existing literature focuses on two process variables: (a) lumped laser power and (b) process speed. However, this literature does not consider other variables, such as those related to the laser power distribution. To fill this vacuum, this manuscript includes the laser power spatial distributions (Gaussian, uniform circular and uniform rectangular) in addition to (a) and (b) above in 2D linear substrate heating simulations. The laser energy is modeled as a time dependent heat flux boundary condition on top of the domain. The total laser delivered power was identical for all spatial distributions. The results show that the laser intensity spatial distribution strongly affects the maximum temperature, and the depth and width of the heat affected zone. These 2D finite element simulations prove to be good options for digital twin based design environments, due to their simplicity and reasonable temperature error, compared to non-linear analysis (considered as ground truth for this case). Future publications address non-linear finite element simulations of the laser heating process (including convection and radiation and temperature dependent substrate properties).

Analysis and prediction of shock formation in acoustic energy transfer systems

Losses associated with nonlinear wave propagation and exhibited by acoustic wave distortion and shock formation compromise the efficiency of contactless acoustic energy transfer systems. As such, predicting the shock formation distance and its dependence on the amplitude of the excitation is essential for their efficiency, design, and operation. We present an analytical approach capable of predicting the shock formation distance of acoustic waves generated by a baffled disk with arbitrary deformation in a weakly viscous fluid medium. The lossless Westervelt equation, used to model the nonlinear wave propagation, is asymptotically expanded based on the amplitude of the excitation. Because the solutions of the first- and second-order equations decay at different rates, we implement the method of renormalization and introduce a coordinate transformation to identify and eliminate the secular terms. The approach yields two partial differential equations that can be solved to predict the formation distance either analytically or numerically much faster than time-domain numerical simulations. The analysis and results are validated with solutions obtained from a nonlinear finite element simulation and previous experimental measurements.

Experimental and numerical research on the bond‐slip behavior of square‐rebar reinforced concrete during the republic of China (1912–1949)

AbstractSquare‐rebar reinforced concrete structures during the republic of China (ROC) (1912–1949) have special material properties and structural characteristics. To perform nonlinear finite element simulations of this special type of structure more accurately, a specialized bond‐slip constitutive model is built. Eighteen central pullout specimens were designed based on the ROC concrete mix proportions and the square‐rebar. Then, the test data were fitted with the universal global optimization method and the minimum Euclidean distance point method was chosen to calculate the inflection point matrix of the bond‐slip constitutive model. Finally, the main factors influencing the bond‐slip behavior of the ROC square‐rebar reinforced concrete were analyzed. The research results show that the corrosion of the square‐rebar produces a negative effect on the whole structure and a modified bond‐slip regression curve considering the size effect is obtained. The research results can provide a scientific basis for the nonlinear calculation of ROC square‐rebar reinforced concrete structures considering the bond‐slip behaviors.

Modelling and stress analysis for double-row curvic couplings

This paper proposes a parameterized modelling method that considers the details of the machining process for double-row curvic couplings and presents a modified stress analytical method that can take the deep beam bending effect into account. The modified method provides a more accurate equivalent stress estimation than the classic Gleason method, which is demonstrated by the nonlinear finite element simulation. The contact stress and the contact status of the curvic couplings in high-speed rotation situations are analysed with the nonlinear FEA method under different loads. The results show that the strength of the weak regions of the double-row curvic couplings occur at the tooth root and the tooth to near the bolts. The bolt preload has the greatest influence on the contact stress and the contact status. The rotating speed reduces the bolt preload, causing the stress to decrease. The torque results in contact stress and contact status of different sides of the tooth being obviously different. Finally, the modified analytic method is recommended during the preliminary design, and the FEA method considering the contact effects is recommended for the detailing design.

Experimental & numerical investigation of mechanical properties in steel fiber-reinforced UHPC

This paper presents experimental and numerical investigations on mechanical properties of ultra-high-performance fiber-reinforced concrete (UHPFRC) with four types of steel fibers; micro steel (MS), crimped (C), round crimped (RC) and hooked-end (H), in two fiber contents of 1% and 2% (by volume) and two lengths of 13 and 30 mm. Compression, direct tension, and four-point bending tests were carried out on four types of specimens (prism, cube, dog-bone and cylinder), to study tensile and flexural strength, fracture energy and modulus of elasticity. Results were compared with UHPC specimens without fibers, as well as with available equations for the modulus of elasticity. Specimens with MS fibers had the best performance for all mechanical properties. Among macro fibers, RC had better overall performance than H and C fibers. Increased fibers improved all mechanical properties of UHPFRC, except for modulus of elasticity, which saw a negligible effect (mostly less than 10%). Moreover, nonlinear finite element simulations successfully captured flexural response of UHPFRC prisms. Finally, nonlinear regression models provided reasonably well predictions of flexural load-deflection behavior of tested specimens (coefficient of correlation, R2 over 0.90).

Perturbation theory for Kerr nonlinear leaky cavities.

In emerging open photonic resonators that support quasinormal eigenmodes, fundamental physical quantities and methods have to be carefully redefined. Here, we develop a perturbation theory framework for nonlinear material perturbations in leaky optical cavities. The ambiguity in specifying the stored energy due to the exponential growth of the quasinormal mode field profile is lifted by implicitly specifying it via the accompanying resistive loss. The capabilities of the framework are demonstrated by considering a third-order nonlinear ring resonator and verified by comparing against full-wave nonlinear finite element simulations. The developed theory allows for efficiently modeling nonlinear phenomena in contemporary photonic resonators with radiation and resistive loss.

Systematic two-scale image analysis of extreme deformations in soft architectured sheets

The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations. The present work demonstrates that state-of-the art image processing methods combined with numerical and analytical models provide a comprehensive quantitative description of these solids and their global behaviour, including the influence of the boundary conditions, of the manufacturing process, and of geometric and constitutive non-linearities. To this end, an adapted multi-scale digital image correlation analysis is used to track both elongations and rotations of particular features of the unit cell at the local and global (homogenized) scale of the material. This permits to observe with unprecedented clarity the strain fields for various unit cells in the structure and to detect global deformation patterns and heterogeneities of the homogenized strain distribution. This method is here demonstrated on elastic sheets undergoing extreme longitudinal and shear deformations. These experimental results are compared to non-linear finite element simulations, which are also used to evaluate the effects of manufacturing imperfections on the response. A skeletal representation of the architectured solid is then extracted from the experiments and used to create a purely-kinematic truss-hinge model that can accurately capture its behaviour. The analysis proposed in this work can be extended to guide the design of two-dimensional architectured solids featuring other regular, quasi-regular or graded patterns, and subjected to other types of loads.

A Hybrid Approach for Fusing Physics and Data for Failure Prediction

This work describes the architecture for developing physics of failure models, derived as a function of machine sensor data, and integrating with data pertaining to other relevant factors like geography, manufacturing, environment, customer and inspection information, that are not easily modeled using physics principles. The mechanics of the system is characterized using surrogate models for stress and metal temperature based on results from multiple non-linear finite element simulations. A cumulative damage index measure has been formulated that quantifies the health of the component. To address deficiencies in the simulation results, a model tuning framework is designed to improve the accuracy of the model. Despite the model tuning, un-modelled sources of variation can lead to insufficient model accuracy. It is required to incorporate these un-modelled effects so as to improve the model performance. A novel machine learning based model fusion approach has been presented that can combine physics model predictions with other data sources that are difficult to incorporate in a physics framework. This approach has been applied to a gas turbine hot section turbine blade failure prediction example.

Full-scale fire test on a high-rise RC wall

This paper describes a full-scale test carried out on a high-rise reinforced concrete wall subjected to fire loading conditions in the special Vulcain furnace (very large and modular gas furnace) at CSTB, France. The test sample was designed to represent a slender wall with a very large height/thickness ratio. The experimental results showed a large deflection of the high wall in fire conditions (almost equal to the wall height/24) even for a fire exposure time of 90 min. Such a deflection was significantly higher than the maximum value recommended by design codes (about the wall height/30 for 120 min of fire exposure). Furthermore, other test results (full-field displacements in the 3 directions, residual deformed shape after the heating and cooling phases) may also provide additional useful experimental data for validating available or future models (which are usually based on some specific assumptions). In addition, the measurements of thermal-induced deformed shape of the wall are compared to those predicted by an analytical solution derived from a simplified one-dimensional (1D) beam model, as well as to those obtained from non-linear finite-element simulations (with 2D plate elements), in order to assess the practical applicability of these simulations. These comparisons show a reasonably good agreement between the experimental results and the predictions of these models, thereby providing a first validation of the latter.

Numerical modeling of axially compressed circular concrete columns

Concrete compressive strength and ductility are strongly affected by the level of confinement and significantly improve with its magnitude. In concrete columns such enhancement can be achieved by properly designed transverse reinforcement. The behavior under axial loading can be accurately described by numerous models from the literature or more conservatively using the design codes; however, their applicability is rather limited to the most common reinforcement layouts and very often to monotonous axial compression.This deficiency can be eliminated by incorporating nonlinear finite element simulations, which allow for arbitrary loading configuration and topology, into the design process. In this paper an advanced constitutive model Concrete Damage-Plastic Model (CDPM 2) by Grassl and coworkers is thoroughly compared against the experimental data from the literature on confined concrete. Subsequently, based on numerical simulations of axially compressed circular columns with various alternatives of reinforcement it is shown that the results are inconsistent with the generally accepted assumptions incorporated into the design codes in the case of spiral reinforcement but perfectly match when the circular hoops are used.

Thermal analysis of the RFX-mod2 operating conditions for the design of the temperature measurement system

High heat fluxes are exchanged in fusion machines (up to 50 MW m−2), thus producing elevated temperature and requiring thermal monitoring and control. The design of a temperature measurement system for the RFX experiment is developed through three-dimensional nonlinear transient finite element simulations of the torus assembly under upgrade from “mod” to “mod2” with enhanced magnetic front-end, vacuum confinement barrier, and first wall. Analyses show how heat fluxes applied at the plasma-facing materials are transmitted, attenuated and delayed, through the machine parts. Results identify the passive stabilising shell as the instrumentable component closest to the plasma boundary able to follow the thermal behaviour by the detection of temperature variations at least of 10 °C during plasma pulses with a response time of about 200 s. Allowable temperature limits of materials are verified simulating a full experimental day with 24 plasma pulses, in particular at the shell supporting rings made of polyamide-imide and at the vessel spacers made of polyether-ether ketone-coated stainless steel. Simulations of the pulse discharge cleaning demonstrated the capability of the system to provide the required power for first wall conditioning (25 kW) and the need to realise a duty cycle (1-h on/3-h off) limiting the average heat flux and the maximum temperature (55 °C) at the vacuum vessel sealing elements in order to minimise differential thermal deformations. Proposed layouts of temperature sensors are able to detect the maximum temperatures expected during operation.