Search results for: Fluid Mechanics.

Authors: Monika Neda, Elena Nikonova

Abstract:

We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.

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Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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Authors: Satya Pilla

Abstract:

This study explores how the mechanics of learning paves the way to engineering innovation. Theories related to learning in the new product/service innovation are reviewed from an organizational perspective, behavioral perspective, and engineering perspective. From this, an engineering team-s external interactions for knowledge brokering and internal composition for skill balance are examined from a learning and innovation viewpoints. As a result, an integrated learning model is developed by reconciling the theoretical perspectives as well as developing propositions that emphasize the centrality of learning, and its drivers, in the engineering product/service development. The paper also provides a review and partial validation of the propositions using the results of a previously published field study in the aerospace industry.

Keywords: Engineering Services, Integrated Learning, NewProduct Development, Service Innovation

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Authors: M. Malek Yarand, H. Saebi Monfared

Abstract:

This study aimed at designing and developing a mechanical force gauge for the square watermelon mold for the first time. It also tried to introduce the square watermelon characteristics and its production limitations. The mechanical force gauge performance and the product itself were also described. There are three main designable gauge models: a. hydraulic gauge, b. strain gauge, and c. mechanical gauge. The advantage of the hydraulic model is that it instantly displays the pressure and thus the force exerted by the melon. However, considering the inability to measure forces at all directions, complicated development, high cost, possible hydraulic fluid leak into the fruit chamber and the possible influence of increased ambient temperature on the fluid pressure, the development of this gauge was overruled. The second choice was to calculate pressure using the direct force a strain gauge. The main advantage of these strain gauges over spring types is their high precision in measurements; but with regard to the lack of conformity of strain gauge working range with water melon growth, calculations were faced with problems. Finally the mechanical pressure gauge has advantages, including the ability to measured forces and pressures on the mold surface during melon growth; the ability to display the peak forces; the ability to produce melon growth graph thanks to its continuous force measurements; the conformity of its manufacturing materials with the required physical conditions of melon growth; high air conditioning capability; the ability to permit sunlight reaches the melon rind (no yellowish skin and quality loss); fast and straightforward calibration; no damages to the product during assembling and disassembling; visual check capability of the product within the mold; applicable to all growth environments (field, greenhouses, etc.); simple process; low costs and so forth.

Keywords: Mechanical Force Gauge, Mold, Reshaped Fruit, Square Watermelon.

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Authors: Gozel Judakova, Markus Bause

Abstract:

We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: Discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, two-phase flow.

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Authors: Lubis A., Widayanti R., Hikmah Z., Endaryanto A., Harsono A., Harianto A., Etika R., Handayani D. K., Sampurna M.

Abstract:

Neonatal lupus erythematous (NLE) is a rare disease marked by clinical characteristic and specific maternal autoantibody. Many cutaneous, cardiac, liver, and hematological manifestations could happen with affect of one organ or multiple. In this case, both babies were premature, low birth weight (LBW), small for gestational age (SGA) and born through caesarean section from a systemic lupus erythematous (SLE) mother. In the first case, we found a baby girl with dyspnea and grunting. Chest X ray showed respiratory distress syndrome (RDS) great I and echocardiography showed small atrial septal defect (ASD) and ventricular septal defect (VSD). She also developed anemia, thrombocytopenia, elevated C-reactive protein, hypoalbuminemia, increasing coagulation factors, hyperbilirubinemia, and positive blood culture of Klebsiella pneumonia. Anti-Ro/SSA and Anti-nRNP/sm were positive. Intravenous fluid, antibiotic, transfusion of blood, thrombocyte concentrate, and fresh frozen plasma were given. The second baby, male presented with necrotic tissue on the left ear and skin rashes, erythematous macula, athropic scarring, hyperpigmentation on all of his body with various size and facial haemorrhage. He also suffered from thrombocytopenia, mild elevated transaminase enzyme, hyperbilirubinemia, anti-Ro/SSA was positive. Intravenous fluid, methyprednisolone, intravenous immunoglobulin (IVIG), blood, and thrombocyte concentrate transfution were given. Two cases of neonatal lupus erythematous had been presented. Diagnosis based on clinical presentation and maternal auto antibody on neonate. Organ involvement in NLE can occur as single or multiple manifestations.

Keywords: Neonatus lupus erythematous, maternal autoantibody, clinical characteristic.

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Authors: Trevor Sabiston, Mohsen Mohammadi, Mohammed Cherkaoui, Kaan Inal

Abstract:

A new micromechanics framework is developed for long fibre reinforced composites using a single fibre surrounded by a functionally graded interphase and matrix as a representative unit cell. The unit cell is formulated to represent any number of aligned fibres by a single fibre. Using this model the elastic response of long fibre composites is predicted in all directions. The model is calibrated to experimental results and shows very good agreement in the elastic regime. The differences between the proposed model and existing models are discussed.

Keywords: Computational mechanics, functionally graded interphase, long fibre composites, micromechanics.

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Authors: M. Nabeel Rashin, J. Hemalatha

Abstract:

Novel Coconut oil nanofluids of various concentrations have been prepared through ultrasonically assisted sol-gel method. The structural and morphological properties of the copper oxide nanoparticle have been analyzed with respectively and it revealed the monoclinic end-centered structure of crystallite and shuttle like flake morphology of agglomerates. Ultrasonic studies have been made for the nanofluids at different temperatures. The molecular interactions responsible for the changes in acoustical parameter with respect to concentration and temperature are discussed.

Keywords: Cutting Fluid, Molecular Interaction, Nanofluids, Ultrasonic

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Authors: Yohei Saika

Abstract:

On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

Keywords: Bayesian inference, generalized mean-field theory, phase unwrapping, statistical mechanics.

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Authors: Ilma Robo, Saimir Heta, Nedja Hysi, Vera Ostreni

Abstract:

Introduction: Marginal gingivitis is a disease with considerable frequency among patients who present routinely for periodontal control and treatment. In fact, this disease may not have alarming symptoms in patients and may go unnoticed by themselves when personal hygiene conditions are optimal. The aim of this study was to collect retrograde data on the prevalence of marginal gingiva in the respective group of patients, evaluated according to specific periodontal diagnostic tools. Materials and methods: The study was conducted in two patient groups. The first group was with 34 patients, during December 2019-January 2020, and the second group was with 64 patients during 2010-2018 (each year in the mentioned monthly period). Bacterial plaque index, hemorrhage index, amount of gingival fluid, presence of xerostomia and candidiasis were recorded in patients. Results: Analysis of the collected data showed that susceptibility to marginal gingivitis shows higher values according to retrograde data, compared to cross-sectional ones. Susceptibility to candidiasis and the occurrence of xerostomia, even in the combination of both pathologies, as risk factors for the occurrence of marginal gingivitis, show higher values ​​according to retrograde data. The female are presented with a reduced bacterial plaque index than the males, but more importantly, this index in the females is also associated with a reduced index of gingival hemorrhage, in contrast to the males. Conclusions: Cross-sectional data show that the prevalence of marginal gingivitis is more reduced, compared to retrograde data, based on the hemorrhage index and the bacterial plaque index together. Changes in production in the amount of gingival fluid show a higher prevalence of marginal gingivitis in cross-sectional data than in retrograde data; this is based on the sophistication of the way data are recorded, which evolves over time and also based on professional sensitivity to this phenomenon.

Keywords: Marginal gingivitis, cross-sectional, retrograde, prevalence.

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Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

This paper treats different aspects of entropy measure in classical information theory and statistical quantum mechanics, it presents the possibility of extending the definition of Von Neumann entropy to image and array processing. In the first part, we generalize the quantum entropy using singular values of arbitrary rectangular matrices to measure the randomness and the quality of denoising operation, this new definition of entropy can be implemented to compare the performance analysis of filtering methods. In the second part, we apply the concept of pure state in quantum formalism to generalize the maximum entropy method for narrowband and farfield source localization problem. Several computer simulation results are illustrated to demonstrate the effectiveness of the proposed techniques.

Keywords: Von Neumann entropy, Filtering, array, DoA, Maximum Entropy Method.

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Authors: Shilpa N. Kulkarni, Sujata R. Patrikar

Abstract:

In the present work, an attempt is made to understand electromagnetic field confinement in a subwavelength waveguide structure using concepts of quantum mechanics. Evanescent field in the waveguide is looked as inability of the photon to get confined in the waveguide core and uncertainty of position is assigned to it. The momentum uncertainty is calculated from position uncertainty. Schrödinger wave equation for the photon is written by incorporating position-momentum uncertainty. The equation is solved and field distribution in the waveguide is obtained. The field distribution and power confinement is compared with conventional waveguide theory. They were found in good agreement with each other.

Keywords: photon localization in waveguide, photon tunneling, quantum confinement of light, Schrödinger wave equation, uncertainty principle.

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Authors: Hadi Niknami Esfahani , Hossein Shokouhmand, Fahim Faraji

Abstract:

The forced convection heat transfer in high porosity metal-foam filled tube heat exchangers are studied in this paper. The Brinkman Darcy momentum model and two energy equations for both solid and fluid phases in porous media are employed .The study shows that using metal-foams can significantly improve the heat transfer in heat exchangers.

Keywords: Metal foam, Nusselt number, heat exchanger, heat flux.

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Authors: Abdelrahman Elsehsah, Hany Madkour, Khalid Farah

Abstract:

This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.

Keywords: 3-D numerical analysis, damage mechanics, RC slab with opening.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

Abstract:

A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.

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Authors: Imran Siddique

Abstract:

This paper deals with the helical flow of a Newtonian fluid in an infinite circular cylinder, due to both longitudinal and rotational shear stress. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms and satisfy all imposed initial and boundary conditions. For large times, these solutions reduce to the well-known steady-state solutions.

Keywords: Newtonian fluids, Velocity field, Exact solutions, Shear stress, Cylindrical domains.

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Authors: Sharfi Dirar, Shihab Elhaj, Ahmed El Fatih

Abstract:

Computational fluid dynamics were used to simulate and study the heated water boiler tube for both normal and rifled tube with a refinement of the mesh to check the convergence. The operation condition was taken from GARRI power station and used in a boundary condition accordingly. The result indicates the rifled tube has higher heat transfer efficiency than the normal tube.

Keywords: Boiler tube, Convergence Check, Normal Tube, Rifled Tube.

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Authors: Hans H. Diel

Abstract:

In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Problem, Models of Physics.

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Authors: A. Tavangari, N. Salehzadeh

Abstract:

In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny- Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: Penny-shaped crack, Stress intensity factor, Fracture mechanics, Ritz method.

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Authors: Vicente F. P. Aleixo, Augusto C. F. Saraiva, Jordan Del Nero

Abstract:

The production of devices in nanoscale with specific molecular rectifying function is one of the most significant goals in state-of-art technology. In this work we show by ab initio quantum mechanics calculations coupled with non-equilibrium Green function, the design of an organic two-terminal device. These molecular structures have molecular source and drain with several bridge length (from five up to 11 double bonds). Our results are consistent with significant features as a molecular rectifier and can be raised up as: (a) it can be used as bi-directional symmetrical rectifier; (b) two devices integrated in one (FET with one operational region, and Thyristor thiristor); (c) Inherent stability due small intrinsic capacitance under forward/reverse bias. We utilize a scheme for the transport mechanism based on previous properties of ¤Ç bonds type that can be successfully utilized to construct organic nanodevices.

Keywords: ab initio, Carotenoid, Charge Transfer, Nanodevice

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Authors: Nabli L., Dhouibi H., Collart Dutilleul S., Craye E.

Abstract:

The indistinctness of the manufacturing processes makes that a parts cannot be realized in an absolutely exact way towards the specifications on the dimensions. It is thus necessary to assume that the effectively realized product has to belong in a very strict way to compatible intervals with a correct functioning of the parts. In this paper we present an approach based on mixing tow different characteristics theories, the fuzzy system and Petri net system. This tool has been proposed to model and control the quality in an assembly system. A robust command of a mechanical assembly process is presented as an application. This command will then have to maintain the specifications interval of parts in front of the variations. It also illustrates how the technique reacts when the product quality is high, medium, or low.

Keywords: Petri nets, production rate, performance evaluation, tolerant system, fuzzy sets.

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Authors: Rohit, S. Vishnuvardhan, P. Gandhi, Nagesh R. Iyer

Abstract:

The evaluation of energy release rate and centre Crack Opening Displacement (COD) for circumferential Through-Wall Cracked (TWC) pipes is an important issue in the assessment of critical crack length for unstable fracture. The ability to predict crack growth continues to be an important component of research for several structural materials. Crack growth predictions can aid the understanding of the useful life of a structural component and the determination of inspection intervals and criteria. In this context, studies were carried out at CSIR-SERC on Nuclear Power Plant (NPP) piping components subjected to monotonic as well as cyclic loading to assess the damage for crack growth due to low-cycle fatigue in circumferentially TWC pipes.

Keywords: 304LN stainless steel, cyclic J-integral, Elastic- Plastic Fracture Mechanics, J-integral, Through-wall crack

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Authors: R. O. Ocaya, J. J. Terblans

Abstract:

The laws of Newtonian mechanics allow ab-initio molecular dynamics to model and simulate particle trajectories in material science by defining a differentiable potential function. This paper discusses some considerations for the coding of ab-initio programs for simulation on a standalone computer and illustrates the approach by C language codes in the context of embedded metallic atoms in the face-centred cubic structure. The algorithms use velocity-time integration to determine particle parameter evolution for up to several thousands of particles in a thermodynamical ensemble. Such functions are reusable and can be placed in a redistributable header library file. While there are both commercial and free packages available, their heuristic nature prevents dissection. In addition, developing own codes has the obvious advantage of teaching techniques applicable to new problems.

Keywords: C-language, molecular dynamics, simulation, embedded atom method.

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Authors: Saimir Heta, Ilma Robo, Rialda Xhizdari, Kers Kapaj

Abstract:

The stability of an ideal disinfectant should be constant regardless of the change in the atmospheric conditions of the environment where it is kept. If the conditions such as temperature or humidity change, it is understood that it will also be necessary to approach possible changes in the holding materials such as plastic or glass bottles with the aim of protecting the disinfectant, for example, from the excessive lighting of the environment, which can also be translated as an increase in the temperature of disinfectant as a fluid. In this study, an attempt was made to find the most recent published data about the best possible combination of disinfectants indicated for use after dental procedures. This purpose of the study was realized by comparing the basic literature that is studied in the field of dentistry by students with the most published data in the literature of recent years about this topic. Each disinfectant is represented by a number called the disinfectant count, in which different factors can influence the increase or reduction of variables whose production remains a specific statistic for a specific disinfectant. The changes in the atmospheric conditions where the disinfectant is deposited and stored in the environment are known to affect the stability of the disinfectant as a fluid; this fact is known and even cited in the leaflets accompanying the manufactured boxes of disinfectants. It is these cares, in the form of advice, which are based not only on the preservation of the disinfectant but also on the application in order to have the desired clinical result. Aldehydes have the highest constant among the types of disinfectants, followed by acids. The lowest value of the constant belongs to the class of glycols, the predecessors of which were the halogens, in which class there are some representatives with disinfection applications. The class of phenols and acids have almost the same intervals of constants. If the goal were to find the ideal disinfectant among the large variety of disinfectants produced, a good starting point would be to find something unchanging or a fixed, unchanging element on the basis of which the comparison can be made properties of different disinfectants. Precisely based on the results of this study, the role of the specific constant according to the specific disinfectant is highlighted. Finding an ideal disinfectant, like finding a medication or the ideal antibiotic, is an ongoing but unattainable goal.

Keywords: Different disinfectants, phenols, aldehydes, specific constant, dental procedures.

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Authors: Philippe Jorrand

Abstract:

Research in quantum computation is looking for the consequences of having information encoding, processing and communication exploit the laws of quantum physics, i.e. the laws which govern the ultimate knowledge that we have, today, of the foreign world of elementary particles, as described by quantum mechanics. This paper starts with a short survey of the principles which underlie quantum computing, and of some of the major breakthroughs brought by the first ten to fifteen years of research in this domain; quantum algorithms and quantum teleportation are very biefly presented. The next sections are devoted to one among the many directions of current research in the quantum computation paradigm, namely quantum programming languages and their semantics. A few other hot topics and open problems in quantum information processing and communication are mentionned in few words in the concluding remarks, the most difficult of them being the physical implementation of a quantum computer. The interested reader will find a list of useful references at the end of the paper.

Keywords: Quantum information processing, quantum algorithms, quantum programming languages.

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Authors: Djamal Hamadi, Oussama Temami, Abdallah Zatar, Sifeddine Abderrahmani

Abstract:

The analysis and design of thin shell structures is a topic of interest in a variety of engineering applications. In structural mechanics problems the analyst seeks to determine the distribution of stresses throughout the structure to be designed. It is also necessary to calculate the displacements of certain points of the structure to ensure that specified allowable values are not exceeded. In this paper a comparative study between displacement and strain based finite elements applied to the analysis of some thin shell structures is presented. The results obtained from some examples show the efficiency and the performance of the strain based approach compared to the well known displacement formulation.

Keywords: Displacement formulation, Finite elements, Strain based approach, Shell structures.

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Authors: Mohammad Hamdan, Emad Elnajjar

Abstract:

The LHP is a two-phase device with extremely high effective thermal conductivity that utilizes the thermodynamic pressure difference to circulate a cooling fluid. A thermodynamics analytical model is developed to explore different parameters effects on a Loop Heat Pipe (LHP).. The effects of pipe length, pipe diameter, condenser temperature, and heat load are reported. As pipe length increases and/or pipe diameter decreases, a higher temperature is expected in the evaporator.

Keywords: Loop Heat Pipe, LHP, Passive Cooling, CapillaryForce.

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Authors: Alibek Issakhov

Abstract:

In this paper developed and realized absolutely new algorithm for solving three-dimensional Poisson equation. This equation used in research of turbulent mixing, computational fluid dynamics, atmospheric front, and ocean flows and so on. Moreover in the view of rising productivity of difficult calculation there was applied the most up-to-date and the most effective parallel programming technology - MPI in combination with OpenMP direction, that allows to realize problems with very large data content. Resulted products can be used in solving of important applications and fundamental problems in mathematics and physics.

Keywords: MPI, OpenMP, three dimensional Poisson equation

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Authors: L. Nguyen, V. Golubev, R. Mankbadi

Abstract:

We consider here the subsonic impinging jet representing the flow field of a vertical take-off aircraft or the initial stage of rocket launching. Implicit Large-Eddy Simulation (ILES) is used to calculate the time-dependent flow field and the radiate sound pressure associated with jet impinging. With proper boundary treatments and high-order numerical scheme, the near field sound pressure is successfully obtained. Results are presented for both a rectangular as well a circular jet.

Keywords: Aeroacoustics, Large-Eddy Simulations, Jets, Fluid Dynamics.

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Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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