FEM Code Research Articles

Biot’s Variational Method to determine the thermal strain in layered glazings

A critical issue in the structural design of glazed surfaces is the evaluation of the strain consequent to temperature variations due to environmental actions such as solar radiation, which represents one of the main causes of breakage. In the practice, approximate solutions are used, where the temperature profile across the glass thickness is constant or linear, but the consequent thermal stress cannot be adequately estimated from these. On the other hand, sophisticated thermal software is available only for important tasks.Here, we propose a semi-analytical approach, easily implementable in a simple FEM code, to evaluate the time-dependent temperature profile through the thickness of layered glazing, which is based on the variational method proposed by Biot in the Fifties. A prompt evaluation not only of the temperature field, but also of the heat flux, can be obtained. Compared to other numerical approaches, this method rigorously accounts for energy conservation and, since it does not involve temperature gradients in the formulation, it is particularly efficient for problems with steep temperature variations. Temperature profiles that are not necessarily linear can be approximated by Hermite–splines, for a precise evaluation of the thermally-induced stress. Comparisons with a direct numerical solution of the heat-conduction differential equations confirm the accuracy and the effectiveness of the proposed approach.

On the stability of POD basis interpolation on Grassmann manifolds for parametric model order reduction

Proper Orthogonal Decomposition (POD) basis interpolation on Grassmann manifolds has been successfully applied to problems of parametric model order reduction (pMOR). In this work we address the necessary stability conditions for the interpolation, all defined from strong mathematical background. A first condition concerns the domain of definition of the logarithm map. Second, we show how the stability of interpolation can be lost if certain geometrical requirements are not satisfied by making a concrete elucidation of the local character of linearization. To this effect, we draw special attention to the Grassmannian exponential map and the optimal injectivity condition of this map, related to the cut–locus of Grassmann manifolds. From this, an explicit stability condition is established and can be directly used to determine the loss of injectivity in practical pMOR applications. A third stability condition is formulated when increasing the number p of POD modes, deduced from the principal angles of subspaces of different dimensions p. Definition of this condition leads to an understanding of the non-monotonic oscillatory behavior of the Reduced Order Model (ROM) error-norm with respect to the number of POD modes, and on the contrary, the well-behaved monotonic decrease of the error-norm in the two numerical examples presented herein. We have chosen to perform pMOR in hyperelastic structures using a non-intrusive approach for inserting the interpolated spatial POD ROM basis in a commercial FEM code. The accuracy is assessed by a posteriori error norms defined using the ROM FEM solution and its high-fidelity counterpart simulation. Numerical studies successfully ascertained and highlighted the implication of stability conditions which are general and can be applied to a variety of other linear or nonlinear problems involving parametrized ROMs generation based on POD basis interpolation on Grassmann manifolds.

Predictive Capability of a Finite Element Micro-Mechanical Model for Masonry Elements Reinforced Using CFRP

Different commercial Finite Element Codes proved to be able to describe the mechanical behavior of masonry materials externally reinforced by means of Carbon Fiber Reinforced Polymers (CFRP); the behavior of fracturing materials, characterized by low tensile strength, with adhered strips can be reproduced relying on parameters based on fracture mechanics and the theories of adhesion.In this report the comparison is made of previous experimental test results with numerical analysis, carried out on masonry panels reinforced with CFRP strips and subjected to out of plane actions. The comparison is especially addressed to the evaluation of the post peak branch; in addition to the slopes of the diagram in the pre-critic phase, available kinematic ductility and energy shares both prior and after the peak load were considered in order to interpret the capability of the micro-mechanical model implemented in the FEM Code to account for the local phenomena influencing the interaction between masonry and FRP strengthening systems.

Effect of temperature and strain rate on the formation of shear bands in polymers under quasi-static and dynamic compressive loadings: Proposed constitutive model and numerical validation

The mechanical behaviour of polymers is strongly influenced by temperature and strain rate conditions. Their effects are clearly observed in the Young modulus and Yield strength assessment. In some cases, a change in material failure mode can be noted, which can be both ductile and brittle. For polymers exhibiting shear bands during compression loading, test conditions may enhance or diminish this effect. In this study, isotactic Polypropylene has been considered due to its strong sensitivity to test conditions; with some combinations of strain rate and temperature, the material is able to undergo large compression with nearly uniform strain distribution, whereas significant shear bands can be observed with other strain rate and temperature combinations. This paper proposes a constitutive law for the mechanical characterization of polymers that show shear banding in compression loading. The proposed law extends a visco-plastic model present in literature, allowing to predict the onset or not of micro-shear banding compression instability. The dependence of constitutive parameters with test conditions is determined by applying the Ree-Eyring equation. The model parameters have been calibrated analytically according to experimental data obtained from compression tests performed in a wide range of strain rates (10−3 to 103 1/s) and temperatures (253–313 K). In addition, the constitutive model has been implemented in a commercial FEM code by means of a user-defined subroutine. Results show a good correspondence between experimental observations and numerical calculations, regarding both stress-strain relationship and shear band formation.

A generalized non-linear flow law based on Modified Zerilli–Armstrong model and its implementation into Abaqus/Explicit FEM code

A generalized non-linear flow law based on Modified Zerilli–Armstrong model and its implementation into Abaqus/Explicit FEM code

A Generalized Non-Linear Flow Law Based on Modified Zerilli-Armstrong Model and Its Implementation into Abaqus/Explicit FEM Code

Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerical simulation uses finite element codes where the models already integrated are not based on shapes adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also shown through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows highlighting the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.

Identification of Material Constants of Single-Layer CFRP Thin Plate Using Vibration Analysis with General Purpose FEM Code and Differential Evolution Method

This study discusses identification of material constants of Single-Layer CFRP thin plate using vibration analysis with general purpose FEM code and differential evolution method. This identification method is a method to select material parameters to match the vibration characteristics of the experiment and the vibration characteristics of the analysis. In the method, a general-purpose FEM code calculates vibration modes and natural frequencies of thin CFRP plate using material parameters which are selected by differential evolution method (DE). To reduce number of generations, ILSDE (DE based on Improved Learning Strategy) is used instead of DE. The number of generations is lowest when the number of random select individual is three. Comparison of the reference data and the two FEM models show no significant difference in the identification results. The results show that the identification method has sufficient capability to reproduce well the experimental natural frequencies.

Efficient implementation of non-linear flow law using neural network into the Abaqus Explicit FEM code

Machine learning techniques are increasingly used to predict material behavior in scientific applications and offer a significant advantage over conventional numerical methods. In this work, an Artificial Neural Network (ANN) model is used in a finite element formulation to define the flow law of a metallic material as a function of plastic strain ɛp, plastic strain rate ɛ.p and temperature T. First, we present the general structure of the neural network, its operation and focus on the ability of the network to deduce, without prior learning, the derivatives of the flow law with respect to the model inputs. In order to validate the robustness and accuracy of the proposed model, we compare and analyze the performance of several network architectures with respect to the analytical formulation of a Johnson–Cook behavior law for a 42CrMo4 steel. In a second part, after having selected an Artificial Neural Network architecture with 2 hidden layers, we present the implementation of this model in the Abaqus Explicit computational code in the form of a VUHARD subroutine. The predictive capability of the proposed model is then demonstrated during the numerical simulation of two test cases: the necking of a circular bar and a Taylor impact test. The results obtained show a very high capability of the ANN to replace the analytical formulation of a Johnson–Cook behavior law in a finite element code, while remaining competitive in terms of numerical simulation time compared to a classical approach.

Dynamic FEM Analysis of Crashworthiness of Sidewalk-Driveway Boundary Columns

Recently, there have been frequent automobile collisions with pedestrians on sidewalks, and there is a movement to review the role of the sidewalk-driveway boundary column (car stop) from the viewpoint of crashworthiness. In this study, material models were obtained for SS400, SPCC and FCD450 with using Tanimura-Mimura model 2009, which can represent the response of viscoplastic materials subjected to impact loading, and the finite element model of the column were built to carry out numerical simulations of car collision with column. The collision velocity was varied from 20 km/h, 40 km/h, and 60 km/h. The deformation and fracture behavior of that FE model were investigated using the dynamic FEM code LS-DYNA. From the viewpoint of crashworthiness, the effects of material properties on histories of velocity, deceleration, and kinetic energy were focused on. The effects of the geometry and placement of the column were also examined in a parametric study. With one sidewalk-driveway boundary column, the SS400 and SPCC ones were able to stop a numerical model car at 20 km/h. When the column failed, the bending failure occurred at the root anchored to the ground. The FCD450 one was broken at all collision velocities. The SS400 one reduced the velocity and kinetic energy the fastest, but also had the greatest deceleration, albeit to a lesser extent.

異種混合プロセッサにおける並列FEMコードの性能評価

The main computations in finite element analysis are basic linear algebra operations on matrices and vectors, and even load distribution is suitable for these parallel computations. Therefore, parallel FEM codes implemented with OpenMP and simple scheduling often achieve good efficiency in conventional multi-core processors. However, in recent years, desktop CPUs such as Intel's Alder Lake and Apple's M1 have adopted heterogeneous architectures with high-efficiency and high-performance cores. Therefore, it is unclear whether the conventional parallel FEM code can extract the processor's performance on those parallel computers. This research evaluates the performance of a heterogeneous processor using a parallel FEM code that uses the conjugate gradient method as a linear solver and discusses the results.

Development and publication of hyperelastic, damage, and viscoelastic constitutive laws incorporated into commercial FEM codes through NPO activities

It is important to select appropriate material model for non-linear CAE. However, the models provided in commercial software are limited. In addition, it is not efficient to implement the specific material models to many commercial FEM codes individually. In the activity of sub committees in the Nonlinear CAE Association (JANCAE), we have developed hyperelastic, damage, and viscoelastic constitutive laws using user subroutines to be incorporated into commercial FEM codes. The developed subroutines, called Unified Material Model Driver for rubber (UMMDr), have recently been released to the public. This paper presents an overview of the subroutines and examples of their use.

Effect of hole interaction in the initiation of damage in laminates

In open-hole laminates, when a second hole is made, the stresses and the damage evolution are modified. The main failure mechanisms in laminates subjected to compressive loads are fibre microbuckling and matrix breakage. In this work, the influence of the presence of a second hole in these mechanisms is analysed for two distances between holes. The Serial/Parallel Mixing Theory was used to model the elastic behaviour of the material and a Continuum Damage Model to represent the fibre microbuckling and matrix failure. The equations were implemented in a FEM code developed by the authors. The proposed model has been validated with results from the literature for a laminate with two holes positioned transversally to the applied load. In this problem, it was shown that the growth of the fibre damage is different from that of the matrix.  The laminate is damaged mainly in the zone between the holes. When the distance between holes is reduced, both types of damage around the holes increase.

Header Shape Effect on the Inlet Velocity Distribution in Cross-Flow Double-Layered Microchannel Heat Sinks

Counter-flow double-layered microchannel heat sinks are very effective for thermal control of electronic components; however, they require rather complicated headers and flow maldistribution can also play a negative role. The cross-flow configuration allows a much simpler header design and the thermal performance becomes similar to that provided by the counter-flow arrangement if the velocity distribution in the microchannels is not uniform. The aim of this work is to show the possibility of achieving a favorable flow distribution in the microchannels of a cross-flow double-layered heat sink with an adequate header design and the aid of additional elements such as full or partial height baffles made of solid or porous materials. Turbulent RANS numerical simulations of the flow field in headers are carried out with the commercial code ANSYS Fluent. The flow in the microchannel layers is modeled as that in a porous material, whose properties are derived from pressure drop data obtained using an in-house FEM code. It is demonstrated that, with an appropriate baffle selection, inlet headers of cross-flow microchannel heat sinks yield velocity distributions very close to those that would allow optimal hotspot management in electronic devices.

Combined numerical and experimental studies on the dynamic and quasi-static failure modes of brittle rock

Loading rate affects not only the mechanical properties of rock but also the cracking behaviour or the failure mode. Firstly, experimental studies on the mechanical properties and the related cracking behaviour are studied based on the Carrara marble specimens containing a preexisting flaw under different loading rates. The result shows that both the compressive and tensile strengths are rate-dependent but with different sensitivities to strain rate. Meanwhile, the cracking processes of the single-flawed specimens are also found to be rate-dependent with the aid of an ultra-high-speed video system. Secondly, to investigate the mechanism behind the experimental phenomena, a material model based on the experimental strength data is proposed and applied to the numerical model. The influence of the rate-dependent strength on the cracking behaviour is studied comprehensively by using the 2D and 3D explicit dynamic FEM code. The numerical results reveal how the rate-dependent strength affect fracturing behaviour, as well as the failure stress of the single-flawed specimen. The plastic zones do not equal the damaged zone or the cracks. The dynamic loadings lead to the “X” shaped failure mode of the single-flawed specimen regardless of the flaw inclination angle. In contrast, the quasi-static loadings lead to the diagonal failure mode. It indicates that shear displacement dominates the whole cracking process under dynamic loadings, while it only dominates the failure period under quasi-static loadings.

Measurement and analysis of welding deformation and residual stress in CMT welded lap joints of 1180 MPa steel sheets

Ultra-high strength steel (UHSS) sheet has been used in automobile structures for light weight and energy efficiency. The objective of this study is to investigate the characteristics of the heat softening phenomenon and its effect on the formation of welding residual stresses and deformation in UHSS lap joints. Firstly, the lap joints of 1180 MPa steel sheets were fabricated using the cold metal transfer (CMT) welding process, and obvious heat softening was observed in the tempered area by hardness measurement. Miniature tensile test shows that the heat softening zone has about 33% reduction in strength comparing with the base metal. To identify the softening temperature, the simulated thermal cycle experiment was performed by applying various thermal cycles to the 1180 MPa sheet. It was found that the softening zone corresponds to the range of peak temperature from 500 °C to 720 °C. Based on the in-house FEM code JWRIAN, heat softening was modeled and included in the numerical models of CMT welded lap joints. By the verification with measured data, more accurate simulation results were obtained by the numerical model considering heat softening behavior. It was found that there exist the compressive or small tensile residual stress in the weld zone due to low temperature solid-state phase transformation and large tensile residual stress in the heat softening zone. A combined out-of-plane deformation was observed in the 1180 MPa steel lap joint. The upper plate has a downward angular distortion and concave longitudinal deflection, while the lower plate is deformed in the opposite manner. The effects of plate thickness on the welding distortion and residual stresses in 1180 MPa steel lap joints were parametrically analyzed using the developed model.

Design and manufacturing of monolithic mechanical metastructures governing ultrawide low frequency three-dimensional bandgaps

The design and manufacturing of innovative monolithic mechanical metastructures capable of inducing ultrawide low-frequency subwavelength bandgaps, incorporating simple structure morphology and reliable performance, have received enormous attention amongst the scientific community due to the marvellous dynamic characteristics and their potential industrial application in vibration and noise control technology. Specifically, more emphasis is devoted to the mechanical and dynamical properties and innovative design of phononic structures, which leads to periodic systems with unprecedented mechanical and effective medium properties, including ultrawide bandgaps. The present study proposes two types of easily manufacturable 3-D monolithic mechanical metastructure designs, which possess the ability to induce ultrawide low frequency three-dimensional (3-D) complete bandgaps. Employing the principle of mode separation and numerical modal analysis through two different FEM codes, the generation mechanism of ultrawide bandgaps is examined and discussed. The finite supercell structure for both designs is created and numerical frequency response study is performed to validate the claimed properties. The 3-D prototypes are prepared by additive manufacturing technology and vibration tests are performed to confirm the wave attenuation over a broadband frequency range. Both numerical and experimental results are compared and possible discrepancies are discussed. The proposed monolithic metastructures can undoubtedly be manufactured by the conventional additive manufacturing technology, with potential applications in metadevices, where low frequency ultrawide multi-directional vibrations and noise control is desirable. Furthermore, the proposed designs can be employed for underwater acoustic wave manipulation and design of metasurfaces to be embedded at the water surface for ultrahigh transmission of acoustic waves at the water-air interface. • Additively manufactured metastructure designs, governing low-frequency ultrawide 3-D bandgaps, are studied. • Based on the principle of mode separation, the bandgap generation mechanism is examined and discussed. • Two finite element analysis codes are utilised for the numerical study to investigate the performance of ultrawide bandgaps. • Vibration test is performed on 3-D printed prototypes, which validates the efficacy of vibration attenuation. • Proposed metastructures can be deployed for elastic and acoustic waves manipulation over an ultrawide frequency range.

Investigation of effective geometrical parameters on wear of hot forging die

The hot forging process has better formability than cold forging, however, the hot forging die sustains higher temperature and coupled pressure and temperature effect. The die wear is faster than those of cold forging. The objective of this research is to combine the previous experimental techniques in wear coefficients, numerical method, and wear model to predict the wear behavior of hot forging die in 3D, obtain the most critical wear points and geometry types on the die surface and investigate the effect of these geometrical parameters on the most critical wear points of the die surface. These investigations are done based on the combined effects of the pressure, temperature, and velocity as functions of step time and contact geometry. DEFORM FEM code is used to analyze the hot forging die in 3D and Archard wear model is applied to obtain the wear surface of the die. To deeply investigate the geometrical effects of the surface slope angle of the contact surface and fillet radius, a 2D FE model is implemented in ABAQUS commercial code and a velocity field distribution on the die surface is defined and contact temperature effect in wear coefficient and contact pressure for each node at each step time is considered to obtain the final wear depth. Although increasing the surface slope angle from 0° to 45° usually moderates the highest amount of wear and the corresponding position on the die, the surface slope angle of 30° shows a reverse trend. A statistical analysis based on the Taguchi method is carried out and an empirical model to predict the wear on hot forging dies is presented.

Micromechanical thermo-hydro-mechanical coupled model for fractured rocks considering multi-scale structures and its engineering application

Most existing studies on the coupled thermal-hydro-mechanical models for fractured rock mass are formulated using the macroscopic phenomenology method. As a result, the micromechanical behaviors of discontinuities, which essentially control the macroscopic response of the material, are not well considered in modeling the thermal-hydro-mechanical coupling processes for disturbed rock mass. In this study, the fractured rock mass is characterized by an anisotropic medium containing arbitrarily distributed penny-shaped microcracks in rock blocks separated by multiple sets of critically orientated fractures of large scales. This is an anisotropic coupled thermal-hydro-mechanical model for deformed saturated rock masses, which is capable of considering the alteration of macro-meso discontinuities. A multiscale damage constitutive model for fractured rock mass with the thermal-hydro-mechanical coupling is presented based on the Mori-Tanaka homogenization method and the thermodynamics theory. The influences of anisotropic damage growth, sliding dilatancy and normal compression of small-scale microcracks, and shear sliding and mobilized degradation of large-scale fractures are commendably accounted for. To reflect the anisotropic strength, the interaction between large-scale fractures and small-scale microcracks is also considered by practically relating the microcracks damage resistance to the orientation of fractures. By capturing the deformation of fractures and the opening and connectivity variations of microcracks with the constitutive model, the multi-scale structural change-induced permeability variation is modeled by the volumetric averaging method. The constitutive model and permeability tensor formulation have been implemented in a FEM code, which is then coupled with the well-established non-isothermal fluid flow simulator TOUGHREACT by an interlaced algorithm to establish a coupled thermal-hydro-mechanical numerical simulation platform. A numerical example is finally performed to investigate the effects of multi-scale structures and thermal-hydro-mechanical couplings on the water injection-induced temperature, pressure, and deformation responses of a deeply buried geothermal reservoir. The research may provide a useful reference for deepening the study of the thermal-hydro-mechanical couplings in deep rocks.

Nonlinear solutions for the steady state oscillations of a clamped–free rotating beam

The rotating beam problem has been extensively used as a benchmark for testing nonlinear finite element implementations. The remarkable characteristic of this benchmark is the coupling between axial a transverse deformations due to the centrifugal forces. The rotating beam dynamics exhibits a centrifugal stiffening effect that can only be captured either by including a kinematic coupling between axial and transverse deformation or by using a nonlinear description of the elastic forces. This paper presents simplified models of the rotating beam that capture the centrifugal stiffening effect due to the inclusion of an axial to transverse kinematic coupling of the beam centreline. The simplified models allow a discussion on their accuracy and a meaningful analysis of the nonlinear oscillations present in the steady state rotation. The results of the simplified models are compared to finite element solutions obtained by using the absolute nodal coordinate formulation and a commercial FEM code.

A Box element to model semi-rigid connections in shell-based thin-walled structures analysis

In this study, we develop and propose a finite element (Box Element) designed specially to improve the shell-based simulation of elastic thin-walled structures. The Box Element (BE) allows a simple and automatic connection between beams and columns, as well as, between slabs and beams. The BE stiffness is assembled by bracing panels immersed in its numerical structure simulating the flexibility of connections. Its formulation is developed using an in house positional FEM code, whose 3D rotation degrees of freedom are replaced by generalized vectors, facilitating bending couplings and large rotation modeling. Instability and geometrical nonlinear path-following analysis are studied in examples, comparing results with literature benchmarks and proposing a practical application.