A New Perspective on the Mathematical Modeling of Highly Nonlinear Anisotropic Plastic Flows in a Heterogeneous Solid

2005 ◽  
Vol 105 ◽  
pp. 271-276 ◽  
Author(s):  
Wei Tong
Keyword(s):  
Biaxial Tension ◽  
Flow Behavior ◽  
Plastic Anisotropy ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Mathematical Representation ◽  
Principal Stresses ◽  
Anisotropic Plasticity ◽  
Highly Nonlinear ◽  
Anisotropic Plastic

A new mathematical formulation is presented for describing the three-dimensional anisotropic plastic flow behavior of a heterogeneous polycrystalline solid. By using three principal stresses, three loading orientation angles, and a generally non-quadratic, real-valued stress exponent, a mathematical theory of anisotropic plasticity is formulated as two coupled orthogonal series expansions in both the 3D principal stress space (the p–plane) and the 3D loading orientation space. A geometrical interpretation of the new mathematical representation of anisotropic plasticity is offered. Specific examples are given to illustrate the application of the proposed theory for modeling the plastic anisotropy of orthotropic polycrystalline sheets under uniaxial and biaxial tension.

scholarly journals On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 170
Author(s):  
Panayiotis Vafeas ◽  
Eleftherios Protopapas ◽  
Maria Hadjinicolaou
Keyword(s):  
Stokes Flow ◽  
Cell Model ◽  
Flow Behavior ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Flow Fields ◽  
Particle In Cell ◽  
Embedded Particles ◽  
Type Particle ◽  
Spheroidal Geometry

Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.

Constitutive Modeling of Advanced High Strength Steels Characterized by Uniaxial and Biaxial Experiments

2013 ◽  
Vol 849 ◽  
pp. 207-211
Author(s):  
Sansot Panich
Keyword(s):  
Experimental Data ◽  
Biaxial Tension ◽  
Flow Behavior ◽  
Plastic Anisotropy ◽  
High Strength Steels ◽  
High Strength ◽  
Uniaxial Tensile ◽  
Plastic Behavior ◽  
Yield Criteria ◽  
Von Mises

Anisotropic plastic behavior of advanced high strength steel sheets of grade DP780 and DP980 were investigated using three different yield functions, namely, the von Mises, Hills 48 and Barlat2000 (Yld2000-2d) criteria. Uniaxial tensile and balanced biaxial (hydraulic bulge) tests were conducted for the examined steels in order to characterize flow behavior and plastic anisotropy for different stress states. Additionally, disk compression and In-plane biaxial tension tests were performed for obtaining balanced r-value of DP780 and DP980, respectively. All these data were used to determine the anisotropic coefficients. According to the different yield criteria, yield stresses and r-values for different directions were calculated corresponding to these yield criteria. The results were compared with experimental data. It was found that the Yld2000-2d model precisely predict well with experimental data than the other models.

scholarly journals Effects of Plastic Anisotropy and Void Shape on Full Three-Dimensional Void Growth

2018 ◽  
Vol 85 (5) ◽  
Author(s):  
Brian Nyvang Legarth ◽  
Viggo Tvergaard
Keyword(s):  
Void Growth ◽  
Volume Fraction ◽  
Plastic Anisotropy ◽  
Three Dimensional ◽  
Stress Triaxiality ◽  
Principal Stresses ◽  
Unit Cells ◽  
3D Effects ◽  
Void Shape ◽  
Transverse Stresses

Void growth in an anisotropic ductile solid is studied by numerical analyses for three-dimensional (3D) unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include the effects of different void shapes, including oblate, prolate, or general ellipsoidal voids. Also, other 3D effects such as those of different spacings of voids in different material directions and the effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the response is very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.

Comparison of Conventional and Pontic Fixed Partial Dentures Over Implants Using the Finite Element Method: Three-Dimensional Analysis of Cortical and Medullary Bone Stress

2020 ◽  
Vol 46 (3) ◽  
pp. 175-181
Author(s):  
Marcelo Bighetti Toniollo ◽  
Mikaelly dos Santos Sá ◽  
Fernanda Pereira Silva ◽  
Giselle Rodrigues Reis ◽  
Ana Paula Macedo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Medullary Bone ◽  
Principal Stresses ◽  
Bone Stress ◽  
Bone Damage ◽  
Rehabilitation System ◽  
Minimum Requirements

Rehabilitation with implant prostheses in posterior areas requires the maximum number of possible implants due to the greater masticatory load of the region. However, the necessary minimum requirements are not always present in full. This project analyzed the minimum principal stresses (TMiP, representative of the compressive stress) to the friable structures, specifically the vestibular face of the cortical bone and the vestibular and internal/lingual face of the medullary bone. The experimental groups were as follows: the regular splinted group (GR), with a conventional infrastructure on 3 regular-length Morse taper implants (4 × 11 mm); and the regular pontic group (GP), with a pontic infrastructure on 2 regular-length Morse taper implants (4 × 11 mm). The results showed that the TMiP of the cortical and medullary bones were greater for the GP in regions surrounding the implants (especially in the cervical and apical areas of the same region) but they did not reach bone damage levels, at least under the loads applied in this study. It was concluded that greater stress observed in the GP demonstrates greater fragility with this modality of rehabilitation; this should draw the professional's attention to possible biomechanical implications. Whenever possible, professionals should give preference to use of a greater number of implants in the rehabilitation system, with a focus on preserving the supporting tissue with the generation of less intense stresses.

Computational and Experimental Study of Enhanced Laminar Flow Heat Transfer in Three-Dimensional Sinusoidal Wavy-Plate-Fin Channels

2003 ◽  
Author(s):  
Jiehai Zhang ◽  
Arun Muley ◽  
Joseph B. Borghese ◽  
Raj M. Manglik
Keyword(s):  
Heat Transfer ◽  
Flow Behavior ◽  
Computational Simulation ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Staggered Grid ◽  
Uniform Heat Flux ◽  
Complex Flow ◽  
Constant Property ◽  
Fin Efficiency

Enhanced heat transfer characteristics of low Reynolds number airflows in three-dimensional sinusoidal wavy plate-fin channels are investigated. For the computational simulation, steady state, constant property, periodically developed, laminar forced convection is considered with the channel surface at the uniform heat flux condition; the wavy-fin is modeled by its two asymptotic limits of 100% and zero fin efficiency. The governing equations are solved numerically using finite-volume techniques for a non-orthogonal, non-staggered grid. Computational results for velocity and temperature distribution, isothermal Fanning friction factor f and Colburn factor j are presented for airflow rates in the range of 10 ≤ Re ≤ 1500. The numerical results are further compared with experimental data, with excellent agreement, for two different wavy-fin geometries. The influence of fin density on the flow behavior and the enhanced convection heat transfer are highlighted. Depending on the flow rate, a complex flow structure is observed, which is characterized by the generation, spatial growth and dissipation of vortices in the trough region of the wavy channel. The thermal boundary layers on the fin surface are periodically disrupted, resulting in high local heat fluxes. The overall heat transfer performance is improved considerably, compared to the straight channel with the same cross-section, with a relatively smaller increase in the associated pressure drop penalty.

The Use of Photogrammetry in Piping Design

1983 ◽  
Vol 197 (2) ◽  
pp. 125-138 ◽  
Author(s):  
P A Bracewell ◽  
U R Klement
Keyword(s):  
Information Retrieval ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cost Effective ◽  
Process Industry ◽  
Process Plant ◽  
Definition Of ◽  
High Degree ◽  
Positional Data

Piping design for ‘revamp’ projects in the process industry requires the retrieval of large amounts of ‘as-built’ data from existing process plant installations. Positional data with a high degree of accuracy are required. Photogrammetry, the science of measurement from photographs, was identified in Imperial Chemical Industries plc (ICI) as a suitable tool for information retrieval. The mathematical formulation enabling the definition of three-dimensional positions from photographic information is described. The process of using ICI's photogrammetric system for the definition of complete objects such as structures and pipes is illustrated. The need for specialized photogrammetric software for design purposes is explained. A case study describing how the photogrammetric system has been applied is described and graphical outputs from this exercise are shown. It is concluded that this particular photogrammetric system has proved to be a cost effective and accurate tool for the retrieval of ‘as-built’ information.

The Measurement of Stresses in Composites

1986 ◽  
Vol 1 (2) ◽  
pp. 15-21 ◽  
Author(s):  
J. B. Cohen
Keyword(s):  
Three Dimensional ◽  
Stress System ◽  
Principal Stresses ◽  
Reasonable Time ◽  
Complete Measurement ◽  
Useful Life ◽  
Diffraction Peaks ◽  
The Difference ◽  
Full Investigation ◽  
Hydrostatic Component

AbstractAlthough there is mounting interest in the measurement of stresses in composite materials after fabrication and/or use, few measurements to date have not taken into account the three dimensional nature of the stress system in such materials. Most data give only the net stress, that is, the difference between principal stresses. A procedure for a more complete measurement (in a reasonable time) is developed here, including the separation of macrostresses and microstresses. If time does not permit a full investigation, measurements of the lattice parameters of the component phases provide a simple way to sample the hydrostatic component due to differential thermal contraction. The Barrett-Predecki method of adding filler is particularly promising for stress measurements in those composites whose component phases do not give appropriate diffraction peaks. This procedure could also be used for monitoring stresses during the useful life of such materials.

Effect of Outer Fin Axial Gap on the Sealing Effectiveness and Fluid Dynamics of Radial Rim Seal

2017 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Liming Song ◽  
Qing Gao ◽  
Xin Yan ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Flow Rate ◽  
Gas Turbines ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Coolant Flow ◽  
Coolant Flow Rate ◽  
Navier Stokes ◽  
Hot Gas

The modern gas turbine is widely applied in the aviation propulsion and power generation. The rim seal is usually designed at the periphery of the wheel-space and prevented the hot gas ingestion in modern gas turbines. The high sealing effectiveness of rim seal can improve the aerodynamic performance of gas turbines and avoid of the disc overheating. Effect of outer fin axial gap of radial rim seal on the sealing effectiveness and fluid dynamics was numerically investigated in this work. The sealing effectiveness and fluid dynamics of radial rim seal with three different outer fin axial gaps was conducted at different coolant flow rates using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) and SST turbulent model solutions. The accuracy of the presented numerical approach for the prediction of the sealing performance of the turbine rim seal was demonstrated. The obtained results show that the sealing effectiveness of radial rim seal increases with increase of coolant flow rate at the fixed axial outer fin gap. The sealing effectiveness increases with decrease of the axial outer fin gap at the fixed coolant flow rate. Furthermore, at the fixed coolant flow rate, the hot gas ingestion increases with the increase of the axial outer fin gap. This flow behavior intensifies the interaction between the hot gas and coolant flow at the clearance of radial rim seal. The preswirl coefficient in the wheel-space cavity is also illustrated to analyze the flow dynamics of radial rim seal at different axial outer fin gaps.

Computation of Flow Through a Three-Dimensional Periodic Array of Porous Structures by a Parallel Immersed-Boundary Method

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhenglun Alan Wei ◽  
Zhongquan Charlie Zheng ◽  
Xiaofan Yang
Keyword(s):  
Porous Media ◽  
Parallel Implementation ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Periodic Array ◽  
Immersed Boundary ◽  
Navier Stokes Equation ◽  
Flow Through ◽  
Ib Method

A parallel implementation of an immersed-boundary (IB) method is presented for low Reynolds number flow simulations in a representative elementary volume (REV) of porous media that are composed of a periodic array of regularly arranged structures. The material of the structure in the REV can be solid (impermeable) or microporous (permeable). Flows both outside and inside the microporous media are computed simultaneously by using an IB method to solve a combination of the Navier–Stokes equation (outside the microporous medium) and the Zwikker–Kosten equation (inside the microporous medium). The numerical simulation is firstly validated using flow through the REVs of impermeable structures, including square rods, circular rods, cubes, and spheres. The resultant pressure gradient over the REVs is compared with analytical solutions of the Ergun equation or Darcy–Forchheimer law. The good agreements demonstrate the validity of the numerical method to simulate the macroscopic flow behavior in porous media. In addition, with the assistance of a scientific parallel computational library, PETSc, good parallel performances are achieved. Finally, the IB method is extended to simulate species transport by coupling with the REV flow simulation. The species sorption behaviors in an REV with impermeable/solid and permeable/microporous materials are then studied.

Anisotropic Plastic Behavior of TRIP 780 Steel Sheet in Hole Expansion Test

2012 ◽  
Vol 504-506 ◽  
pp. 89-94 ◽  
Author(s):  
Sansot Panich ◽  
Vitoon Uthaisangsuk ◽  
Surasak Suranuntchai ◽  
Suwat Jirathearanat
Keyword(s):  
Steel Sheet ◽  
Flow Behavior ◽  
Plastic Anisotropy ◽  
Yield Potential ◽  
Uniaxial Tensile ◽  
Plastic Behavior ◽  
Biaxial Test ◽  
Hole Expansion ◽  
Expansion Test ◽  
Hole Expansion Test

Plastic behavior of advanced high strength steel sheet of grade TRIP780 (Transformation Induced Plasticity) was investigated using three different yield functions, namely, the von Mises’s isotropic, Hill’s anisotropic (Hill’48), and Barlat’s anisotropic (Yld2000-2d) criterion. Uniaxial tensile and balanced biaxial test were conducted for the examined steel in order to characterize flow behavior and plastic anisotropy in different stress states. Additionally, disk compression test was performed for obtaining the balanced r-value. According to the different yield criteria, yield stresses and r-values were calculated for different directions and then compared with experimental data. To verify the modeling accuracy, a hole expansion test was carried out experimentally and numerically by FE simulation. Stress-strain curve from the biaxial test was described using voce and swift hardening models. Punch load and stroke, final hole radius, and strain distribution on specimen surface along the hole circumference and the specimen diameter in rolling and transverse directions were determined and compared with the experimental results. It was found that the simulations applying Yld2000-2d yield function provided an acceptable agreement. Consequently, it is noted that the anisotropic yield potential significantly affects the accuracy of the predicted deformation behavior of sheet metal subjected to hole expanding load.

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