• To Download — Second Edition of the Book "Finite Element Procedures" (6th printing)
You are welcome to download the second edition of the book, 6th printing, however, please note that the book is copyrighted and should only be used in the same manner as a purchased hard-copy of the book.
Improved versions will be made available here, from time to time, as the 7th printing, and so on.
"Finite Element Procedures", 2nd Edition (.pdf)
Solutions to exercises in the book "Finite Element Procedures", 2nd Edition, 2014 are given in this manual (.pdf)
Following are more than 700 publications — that we know of — with reference to the use of ADINA. Since there are numerous papers published in renowned journals, we can only give here a selection. The pages give the Abstracts of some papers published since 1986 referring to ADINA. The most recent papers are listed first. All these papers may be searched using the box:
Numerical simulation of outer die angle of equal channel angular extrusion process
Abioye, O.P.1, Abioye, A.A.1, Atanda, P.O.2, Osinkolu, G.A.3, Folayan, A.J.4
1 Mechanical Engineering Department, Covenant University, Canaan Land, Ota, Ogun State, Nigeria
2 Materials Science and Engineering Department, Obafemi Awolowo University, Ile-Ife, Nigeria
3 Centre for Energy Research and Development, Obafemi Awolowo University, Ile Ife, Nigeria
4 Petroleum Engineering Department, Covenant University, Canaan Land, Ota, Ogun State, Nigeria
International Journal of Mechanical Engineering and Technology, Volume 8, Issue 12, December 2017, Pages 264-273
Abstract: The study of the simulation of effect of outer die angle in Equal Channel Angular Extrusion (ECAE) process was investigated. The simulation was carried out on 6063 aluminium alloy with a view to achieve ultra-fine grain structures. ADINA Version 8.6 (900 modes) was used for the simulation. The unextruded parameters of the 6063 aluminium alloy were used as input codes and some basic assumptions were made in designing the model on 2-Dimensional scale. The billet was meshed by dividing the vertical and horizontal geometry into 30 and 4 elements respectively. The die angle was varied from 0° to 90° and the simulation results were displayed. The results showed that the force of 27.5X106 N, 27.5X106 N, 27.6X106 N and 31.2 X106 N was required to deform when the outer die angle was 0°, 22.5°, 45° and 90° respectively. Also, the strains achieved were 0.61, 0.62, 0.66 and 0.69 respectively. Thus, highest force is required at 90° and the strain achieved at 0o is the lowest. Based on the results, it was recommended that it is more economical to extrude at an outer angle between 22.5° and 45° as a relatively higher effective strain will be induced.
Keywords: ADINA software - Deformation - Mechanical properties - Nanostructured materials - Simulation - StrainStress - Ultra-fine grains
Three-dimensional fluid-structure interaction case study on cubical fluid cavity with flexible bottom
Ghelardi, S., Rizzo, C., Villa, D.
DITEN - Polo Navale, Università degli Studi di Genova, via Montallegro, Genova 1, I-16145, Italy
Journal of Marine Science and Application: Volume 16, Issue 4, 1 December 2017, Pages 382-394
Abstract: In this paper, we report our study on a numerical fluid-structure interaction problem originally presented by Mok et al. (2001) in two dimensions and later studied in three dimensions by Valdés Vazquez (2007), Lombardi (2012), and Trimarchi (2012). We focus on a 3D test case in which we evaluated the sensitivity of several input parameters on the fluid and structural results. In particular, this analysis provides a starting point from which we can look deeper into specific aspects of these simulations and analyze more realistic cases, e.g., in sails design. In this study, using the commercial software ADINA™, we addressed a well-known unsteadiness problem comprising a square box representing the fluid domain with a flexible bottom modeled with structural shell elements. We compared data from previously published work whose authors used the same numerical approach, i.e., a partitioned approach coupling a finite volume solver (for the fluid domain) and a finite element solver (for the solid domain). Specifically, we established several benchmarks and made comparisons with respect to fluid and solid meshes, structural element types, and structural damping, as well as solution algorithms. Moreover, we compared our method with a monolithic finite element solution method. Our comparisons of new and old results provide an outline of best practices for such simulations.
Keywords: ADINA™ - benchmark - finite element method - finite volume method - fluid-structure interaction - monolithic - partitioned
Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder
Khanafer, K.1, Aithal, S.M.2
1 Mechanical Engineering Department, Australian College of Kuwait, Safat, 13060, Kuwait
2 Computing and Life Sciences Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, United States
International Communications in Heat and Mass Transfer: Volume 86, August 2017, Pages 131-142
Abstract: Mixed convection heat transfer in a lid-driven cavity with a rotating cylinder was analyzed numerically for two important parameters - Richardson number, the non-dimensional angular velocity of the cylinder, and the direction of rotation using the commercial software, ADINA. The results from these simulations were validated using an open-source spectral element code, Nek5000. The results of this investigation were presented in terms of streamlines, isotherms, and average and local Nusselt numbers. The present results illustrated that the average Nusselt number was found to depend on the direction of the angular velocity. The average Nusselt number increased with an increase in the clockwise angular velocity of the cylinder for various Richardson numbers. However, it decreased with an increase in the counterclockwise until reached a critical velocity where average Nusselt number increased with an increase in the angular velocity. This study illustrated that the maximum heat transfer can be achieved when placing a rotating cylinder inside a cavity compared with non-rotating cylinder.
Keywords: Heat transfer - Laminar - Lid-driven - Mixed convection - Rotating cylinder
Modelling of wave phenomena in the Zahorski material based on modified library for ADINA software
Major, M., Major, I.
Czestochowa University of Technology, Faculty of Civil Engineering, ul. Akademicka 3, Częstochowa, 42-200, Poland
Applied Mathematical Modelling: Volume 46, June 2017, Pages 727-735
Abstract: This paper presents numerical modelling of wave phenomena in simple elastic structures such as rods and shields made of hyperelastic Zahorski material. The main difference between the Zahorski material, which is an elastic material in the Green sense, and the commonly used Mooney–Rivlin material lies in the non-linear term including the constant C3. Consequently, qualitative and quantitative differences are observed compared to the Mooney–Rivlin material, for example in the values of effective stresses. The extension to the ADINA software developed by the author, which helps create 2D and 3D libraries, significantly facilitates modelling of the Zahorski material. The modification can be used for comparison of wave phenomena that are observed during the propagation of disturbances in the Mooney–Rivlin and Zahorski materials. It should be emphasised that the Zahorski material behaves much better at high strains during the analysis of incompressible rubber and rubber-like hyperelastic materials and can be used in various fields of science wherever the model of Mooney–Rivlin material is successfully applied. The results of numerical computations for both Mooney–Rivlin and Zahorski materials were presented in a graphical form and compared in order to illustrate the differences.
Keywords: FEM - Hyperelastic Zahorski material - Nonlinear wave - Wave phenomena
Dynamic Response of Curved Wall LTSLS Under the Interaction of Rainwater Seepage and Earthquake
Cheng, X., Feng, H., Qi, S., Zhang, X., Liu, B.
School of Civil Engineering, Lanzhou University of Technology, Lanzhou, China
Geotechnical and Geological Engineering: Volume 35, Issue 3, 1 June 2017, Pages 903-914
Abstract: When water permeates the loess, the strength of the loess will be greatly reduced; thus, it is necessary to study the effect of seepage on the seismic response of a loess tunnel. Fields of structure and fluid are simulated using ADINA, and the calculation model of a curved wall loess tunnel with a super-large section (LTSLS) is established. Rainwater is simulated using an incompressible constant parameter model. Considering the action of near- and far-field earthquake and pulse effects, the Galerkin method is used to solve the interaction of stress and seepage fields. By contrasting and analyzing the maximum principal stress, the minimum principal stress, the maximum displacement of lining and the internal force of the tunnel structure, the influence of rainwater seepage on the mechanical properties of LTSLS is studied, and meanwhile, dynamic responses of LTSLS under the interaction of rainwater seepage and earthquakes are studied. The results show that if rainwater seepage is only considered for shallow buried LTSLS, the pore water pressure of a tunnel is so small that it may be neglected. The damage degree of LTSLS under the interaction of rainwater seepage and earthquakes is more than that under a single field. When considering the interaction effect of rainwater and earthquakes, the pore water pressure, principal stress and displacement under a near-field earthquake with pulse effect are greater than those under a near-field earthquake without pulse effect and a far-field earthquake under the same condition.
Keywords: Curved wall - Dynamic response - Earthquake - Loess - Seepage - Super-large section - Tunnel
Comparison of FEM calculated heat transfer coefficient in a minichannel using two approaches: Trefftz base functions and ADINA software
Maciejewska, B.1, łabȩdzki, P.a, Piasecki, A.2, Piasecka, M.3
1 Faculty of Management and Computer Modelling, Kielce University of Technology, Al. 1000-lecia P.P. 7, Kielce, 25-314, Poland
2 Contractor of Project from Polish National Science Centre (No. DEC-2013/09/B/ST8/02825), Kielce University of Technology, Al. 1000-lecia P.P. 7, Kielce, 25-314, Poland
3 Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, Al. 1000-lecia P.P. 7, Kielce, 25-314, Poland
EPJ Web of Conferences: Volume 143, 12 May 2017, Article number 02070
Abstract: The paper presents the methods of heat transfer coefficient determination for boiling research during FC-72 flow in a minichannel. The boundary condition in the form of distributions of temperature on the outer side of the minichannel heated wall was obtained using infrared thermography. It was assumed two-dimensional steady-state heat flow. The local values of the heat transfer coefficients on the surface between the heated foil and boiling liquid, were determined from the Robin boundary condition. Data necessary for the heat transfer coefficient evaluation were obtained from numerical computations using two approaches: calculation procedure based on the Trefftz functions and FEM simulations by ADINA software. The shape functions were linear combinations of the Trefftz functions. Combinations of the Trefftz functions exactly satisfy the differential equation. Coefficients of the linear combination of the shape function in the approximate solution were chosen to minimize residuals on domain boundary and along common edges of adjacent elements. Temperature measurement points were located in boundary nodes. During FEM simulations 4-node FCBI elements were used, fluid flow was assumed to be laminar, incompressible and material constants of the fluid and of the foil were independent on temperature. The results of the comparative analysis were presented and discussed
Tuned mass damper system of high-rise intake towers optimized by improved harmony search algorithm
Zhang, H.Y., Zhang, L.J.
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, Jiangsu, China
Engineering Structures: Volume 138, 1 May 2017, Pages 270-282
Abstract: The seismic safety and proper functioning of intake towers in a major earthquake are very crucial to the whole hydraulic project, since the controlled release of the reservoir could help to prevent catastrophic failure of a dam after an earthquake by reducing the water pressure. In this study, the tuned mass damper (TMD) system was introduced into the seismic design of high-rise intake towers. The installation of TMD can effectively dissipate the seismic energy acting on the intake tower and thus overcome the whiplash effect of the hoist room. The 3D finite element model of the intake tower was simplified into a 2D MDOF model. Improved harmony search (IHS) algorithm was used to determine the optimal parameters for the TMD systems using Matlab, and the robustness of the TMD systems was investigated. The simulation elements of the TMD system were incorporated into ADINA to simulate and evaluate the effect of the TMD system on the dynamic displacement and stress responses of various key points of the intake tower to different seismic excitations.
Keywords: Earthquake - Improved harmony search - Intake towers - Structural control - Structural dynamics - Tuned mass damper
Foundations for low cost buildings
Salam, S.A., El-kady, M.S.
Structural Engineering Department, Faculty of Engineering, Zagazig University, Egypt
Journal of Computational Design and Engineering: Volume 4, Issue 2, 1 April 2017, Pages 143-149
Abstract: Attaining an economical and safe design of structures is regarded as a prerequisite for the structural engineer. The market prices of reinforcing steels have dramatically soared in recent years internationally. Therefore, the purpose of the current paper is not just reducing the ratio of reinforcing steel in the foundations for skeleton structures, but rather minimizing this ratio through choosing the most effective footing shape (folded strip footings). Folded footings have been used as an alternative to the conventional rectangular strip footings. The height of the studied model is ten floors. Two different foundation systems are used in the analysis namely; rectangular strip footings, and folded strip footings respectively. Both footing shapes will be designed as continuous footings with grid shape under the building. Comparison between the two systems is also presented regarding the concrete sections and reinforcement ratio under the same applied loads. The finite element analysis software ADINA is used in modeling and analysis of the structural and geotechnical behavior of both types of footings, with emphasis on the effect of changing the footing shape on the stresses in the footing concrete body and the underlying soils. Research results presents the internal stresses within the footing and soil domains, as well as the contact pressure distribution for a reinforced folded strip footing resting on different soil types. The influence of folding inclination angle, and soil type on the results are also studied. Results showed that folded strip footings are efficient in reducing the amount of needed reinforcements, and such efficiency in reducing the required steel reinforcement in the footings is depending on the applied footing loads, and to some degree on the soil type and properties. Reduction in the reinforcement ratio between the rectangular and folded footing types is about 26% in favor of the folded strip footings. A comparative economical study shows that the total cost of the reinforced concrete section for the folded strip footings is less than the traditional one by about 18%. This difference in cost of both types of footings is mainly due to the relatively smaller in steel reinforcement ratio needed for the folded type as compared with the rectangular ones. So, the folded strip footing is more economical than the rectangular strip footing.
Keywords: ADINA - Finite element - Folded strip footing - Settlement - Stress
Experimental and numerical analyses of the effectiveness of high-frequency peening processes
Mangerig, I.1, Kroyer, R.2, Koller, M.3
1 Faculty of Civil Engineering & Environmental Sciences, Institute & Laboratory for Structural Engineering, University of the German Armed Forces Munich, Werner-Heisenberg-Weg 39, Neubiberg, 85577, Germany
2 Senior Expert for Structural Mechanics/Dynamics, System Design, MBDA Deutschland GmbH, Hagenauer Forst 27, Schrobenhausen, 86529, Germany
3 Rübezahlstraße 108, München, 81739, Germany
Steel Construction: Volume 10, Issue 1, February 2017, Pages 54-66
Abstract: Dedicated to Prof. Dr. Akimitsu Kurita on his 70th birthday. To assess fatigue behaviour, experimental tests were conducted on material specimens furnished with hammer peening tracks, with two different types of treatment being employed. The results of fatigue tests on treated specimens were compared with those of untreated specimens and assessed. Non-linear analyses with the FE program ADINA, taking into account the stress–distortion behaviour of a material subjected to fatigue, were conducted as part of the test concept, specimen analysis, evaluation of the test results and probing the mode of action of both techniques.
Keywords: fatigue test - FEM - high-frequency peening process - material fatigue - plasticity
A fluid structure interaction model for hydraulic fracture simulation on Vaca Muerta Argentina shale formation
Alderete, I.D., Sosa-Massaro, A., D'Hers, S.
Instituto Tecnológico de Buenos Aires, Argentina
SPE Latin American and Caribbean Petroleum Engineering Conference Proceedings 2017
Abstract: Vaca Muerta Formation in Neuquén Basin, Argentina, is one of the great worldwide promises given its potential as a non-conventional reservoir. Because of the intrinsic heterogeneity and low permeability, hydraulic fracturing is a required operation to stimulate the reservoir for better production. Simulation becomes a desirable tool to make fractures more efficient and get predictable outcomes. For this purpose, a 3D finite element analysis is performed using ADINA software to model reservoir response during the hydraulic fracturing process. This iterative, fully coupled model uses fluid structure interaction (FSI), porous elastic media and stratified materials with transversely isotropic (TI) properties. The allowed fracture distribution is proposed beforehand. A cohesive model is added via non linear springs placed along the fracture proposed path. Material models are calibrated using data from well logs and microseismics taken from one well located in the field. All the information obtained from that well is then filtered for a particular region of interest in depth, determined by the mechanical properties observed. Regarding the calculation procedure, as initial condition for the stimulated reservoir volume (SRV) the stress strain state measured in the field is adopted. Then hydraulic fracture process is simulated pumping fluid through punched holes and then fracture opening is analyzed, based on nodes displacement along the proposed path, to characterize fracture's opening and extension. The resulting state of stress developed after the fracture is updated at every calculation step. Key information such as resulting pore pressure and effective stresses can be easily computed along the fracturing process. Once obtained results are compared to analytical solutions and experimental data obtained from fractures performed in similar soil conditions with good agreement. The developed model can tackle a variety of reservoir volumes, considering stratification, geomechanical properties, fracture fluid, fracture paths and the initial state of stress. Natural cracks can be added in a rather simple fashion by adding fractures to the proposed distribution with adequate fracture strengths.
Passive prosthetic foot shape and size optimization using lower leg trajectory error
Olesnavage, K.M.Email Author, Winter, A.G.V.
Global Engineering and Research (GEAR) Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
Proceedings of the ASME Design Engineering Technical Conference, Volume 5A-2017, 2017
Abstract: A method is presented to optimize the shape and size of a passive prosthetic foot using the Lower Leg Trajectory Error (LLTE) as the design objective. The LLTE is defined as the root-mean-square error between the lower leg trajectory calculated for a given prosthetic foot by finding the deformed shape of the foot under typical ground reaction forces and a target physiological lower leg trajectory obtained from published gait data for able-bodied walking. In previous work, the design of simple two degree-of-freedom analytical models consisting of rigid structures, rotational joints with constant stiffness, and uniform cantilevered beams, have been optimized for LLTE. However, prototypes built to replicate these simple models were large, heavy, and overly complex. In this work, the size and shape of a singlepart compliant prosthetic foot keel made out of nylon 6/6 was optimized for LLTE to produce a light weight, low cost, and easily manufacturable prosthetic foot design. The shape of the keel was parameterized as a wide Bézier curve, with constraints ensuring that only physically meaningful shapes were considered. The LLTE value for each design was evaluated using a custom MATLAB script, which ran ADINA finite element analysis software to find the deformed shape of the prosthetic keel under multiple loading scenarios. The optimization was performed by MATLAB's built-in genetic algorithm. After the optimal design for the keel was found, a heel was added to structure, sized such that when the user's full weight acted on the heel, the structure had a factor of safety of two. The resulting optimal design has a lower LLTE value than the two degree-of-freedom analytical models, at 0.154 compared to 0.172, 0.187, and 0.269 for the two degree-of-freedom models. At 412 g, the optimal wide curve foot is nearly half the mass of the lightest prototype built from the previous models, which was 980 g. The design found through this compliant mechanism optimization method is thus far superior to the two degree-of-freedom models previously considered.
Recent progress on air-bearing slumping of segmented thin-shell mirrors for X-ray telescopes: Experiments and numerical analysis
Zuo, H.E.1, Yao, Y.b, Chalifoux, B.D.3, Detienne, M.D.4, Heilmann, R.K.2, Schattenburg, M.L.2
1 MIT Dept. of Aeronautics and Astronautics Engineering, 70 Vassar St. 37-411, Cambridge, MA 02139, United States
2 Space Nanotechnology Lab, MIT Kavli Institute, Cambridge, MA 02139, United States
3 MIT Dept. of Mechanical Engineering, Cambridge, MA 02139, United States
4 Izentis LLC, Cambridge, MA 02139, United States
Proceedings of SPIE - The International Society for Optical Engineering, Volume 10399, 2017, Article number 1039910
Abstract: Slumping (or thermal-shaping) of thin glass sheets onto high precision mandrels was used successfully by NASA Goddard Space Flight Center to fabricate the NuSTAR telescope. But this process requires long thermal cycles and produces mid-range spatial frequency errors due to the anti-stick mandrel coatings. Over the last few years, we have designed and tested non-contact horizontal slumping of round flat glass sheets floating on thin layers of nitrogen between porous air-bearings using fast position control algorithms and precise fiber sensing techniques during short thermal cycles. We recently built a finite element model with ADiNA to simulate the viscoelastic behavior of glass during the slumping process. The model utilizes fluid-structure interaction (FSI) to understand the deformation and motion of glass under the influence of air flow. We showed that for the 2D axisymmetric model, experimental and numerical approaches have comparable results. We also investigated the impact of bearing permeability on the resulting shape of the wafers. A novel vertical slumping set-up is also under development to eliminate the undesirable influence of gravity. Progress towards generating mirrors for good angular resolution and low mid-range spatial frequency errors is reported.
Keywords: air-bearing - deformations - lumping - uid-structure interaction - viscoelastic - X-ray mirrors
Finite Element Analysis of Mechanical Characteristics of Dropped Eggs Based on Fluid-Solid Coupling Theory
Haiyan, S.1,2, Fang, W.3, Jianguo, Z.3, Yinong, Z.3, Shugang, Y.3
1 College of Packaging and Printing Engineering, Tianjin University of Science and Technology, Tianjin, 300222, China
2 China Key Laboratory of Food Packaging Materials and Technology in Light Industry, Tianjin, 300222, China
3 College of Mechanical Engineering, Tianjin University of Science and Technology, Key Lab. of Intgd. Des. and Online Monitoring of Light Indust. and Food Mach. and Equip. in Tianjin, Tianjin, 300222, China
Shock and Vibration, Volume 2017, 2017, Article number 4512497
Abstract: It is important to study the properties and mechanics of egg drop impacts in order to reduce egg loss during processing and logistics and to provide a basis for the protective packaging of egg products. In this paper, we present the results of our study of the effects of the structural parameters on the mechanical properties of an egg using a finite element model of the egg. Based on Fluid-Solid coupling theory, a finite element model of an egg was constructed using ADINA, a finite element calculation and analysis software package. To simplify the model, the internal fluid of the egg was considered to be a homogeneous substance. The egg drop impact was simulated by the coupling solution, and the feasibility of the model was verified by comparison with the experimental results of a drop test. In summary, the modeling scheme was shown to be feasible and the simulation results provide a theoretical basis for the optimum design of egg packaging and egg processing equipment.
A new elastohydrodynamic lubricated spherical joint model for rigid-flexible multibody dynamics
Tian, Q.1, Lou, J.1, Mikkola, A.2
1 MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China
2 Department of Mechanical Engineering, Lappeenranta University of Technology, Lappeenranta, Finland
Mechanism and Machine Theory, Volume 107, 1 January 2017, Pages 210-228
Abstract: In a unified global coordinate system frame, a new elastohydrodynamic (EHD) lubricated spherical joint model for flexible multibody dynamics is proposed. The proposed joint can be further used to model the human gait artificial hip joints. To mesh the flexible spherical socket of the joint, an isoparametric fifteen-node pentahedron finite element with global nodal position coordinates is introduced. The element elastic forces and their Jacobians are derived using a continuum mechanics approach. The ball within the spherical joint is assumed to be rigid, and it is described using the absolute nodal coordinate formulation reference node (ANCF-RN). The spherical joint lubricant pressure is obtained by solving the Reynolds’ equation using the successive over relaxation (SOR) algorithm. To address the lubrication interface non-conformance problem that exists between the lubricant grid and the socket inner surface node grid, a novel lubricant finite-difference grid rotation scheme is introduced. The assembled equations of motion for the constrained rigid-flexible multibody system with a large number of degrees of freedom are solved using the generalized-alpha algorithm. Finally, four numerical examples are studied to validate the proposed EHD lubricated spherical joint model. Some numerical results are also verified using the commercial software ADINA.
Keywords: ANCF-RN - Elastohydrodynamic (EHD) - Hip joint - Isoparametric pentahedron element - Spherical joint
Analysis of Stress and Strain of Fatigue Specimens Localised in the Cross-sectional Area of the Gauge Section Testing on Bi-axial Fatigue Machine Loaded in the High-cycle Fatigue Region
Handrik, M., Kopas, P., Baniari, V., Vaško, M., Saga, M.
University of Zilina, Faculty of Mechanical Engineering, Department of Applied Mechanics, Univerzitna 1, Zilina, 010 26, Slovakia
Procedia Engineering, Volume 177, 2017, Pages 516-519
Abstract: Fatigue is a progressive, localized, permanent structural change that occurs in materials subjected to fluctuating stresses and strains that may result in cracks or fracture after a sufficient number of fluctuations. Fatigue fractures are caused by the simultaneous action of cyclic stress, tensile stress and plastic strain. If one of these three acting phenomena is not present, fatigue cracking will not initiate and propagate. Small geometrical changes in the specimens, or specifically, test conditions by invariable angular displacement cannot significantly allow analytical calculation of stresses and strains. Therefore a numerical analysis of stresses generated through bending and torsion fatigue specimens has been performed using available FEM-program ADINA. Computer simulation has been performed on fatigue specimens made of high-strength steel DOMEX 700 MC D.
Keywords: bi-axial high-cycle fatigue - finite element method - high-strength steel