Search results for: Anisotropy

Authors: José Julio de C. Pituba

Abstract:

This work deals with the initial applications and formulation of an anisotropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

Keywords: Damage model, plastic strain, unilateral effect.

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Authors: Ashok K. Satapathy, Prerana Nashine

Abstract:

Radiative heat transfer in participating medium was carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab and by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient radiation equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: Participating media, finite volume method, radiation coupled with conduction, heat transfer.

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Authors: Amid Ranjkesh, Milan Ambrožič, Samo Kralj

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We study the typical domain size and configuration character of a randomly perturbed system exhibiting continuous symmetry breaking. As a model system we use rod-like objects within a cubic lattice interacting via a Lebwohl–Lasher-type interaction. We describe their local direction with a headless unit director field. An example of such systems represents nematic LC or nanotubes. We further introduce impurities of concentration p, which impose the random anisotropy field-type disorder to directors. We study the domain-type pattern of molecules as a function of p, anchoring strength w between a neighboring director and impurity, temperature, history of samples. In simulations we quenched the directors either from the random or homogeneous initial configuration. Our results show that a history of system strongly influences: i) the average domain coherence length; and ii) the range of ordering in the system. In the random case the obtained order is always short ranged (SR). On the contrary, in the homogeneous case, SR is obtained only for strong enough anchoring and large enough concentration p. In other cases, the ordering is either of quasi long range (QLR) or of long range (LR). We further studied memory effects for the random initial configuration. With increasing external ordering field B either QLR or LR is realized.

Keywords: Lebwohl-Lasher model, liquid crystals, disorder, memory effect, orientational order.

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Authors: J. P. Panda, K. Sasmal, H. V. Warrior

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Eddy viscosity models in turbulence modeling can be mainly classified as linear and nonlinear models. Linear formulations are simple and require less computational resources but have the disadvantage that they cannot predict actual flow pattern in complex geophysical flows where streamline curvature and swirling motion are predominant. A constitutive equation of Reynolds stress anisotropy is adopted for the formulation of eddy viscosity including all the possible higher order terms quadratic in the mean velocity gradients, and a simplified model is developed for actual oceanic flows where only the vertical velocity gradients are important. The new model is incorporated into the one dimensional General Ocean Turbulence Model (GOTM). Two realistic oceanic test cases (OWS Papa and FLEX' 76) have been investigated. The new model predictions match well with the observational data and are better in comparison to the predictions of the two equation k-epsilon model. The proposed model can be easily incorporated in the three dimensional Princeton Ocean Model (POM) to simulate a wide range of oceanic processes. Practically, this model can be implemented in the coastal regions where trasverse shear induces higher vorticity, and for prediction of flow in estuaries and lakes, where depth is comparatively less. The model predictions of marine turbulence and other related data (e.g. Sea surface temperature, Surface heat flux and vertical temperature profile) can be utilized in short term ocean and climate forecasting and warning systems.

Keywords: Eddy viscosity, turbulence modeling, GOTM, CFD.

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Authors: M. C. Cardoso, L. P. Moreira

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In this work, the plastic behaviour of cold-rolled zinc coated dual-phase steel sheets DP600 and DP800 grades is firstly investigated with the help of uniaxial, hydraulic bulge and Forming Limit Curve (FLC) tests. The uniaxial tensile tests were performed in three angular orientations with respect to the rolling direction to evaluate the strain-hardening and plastic anisotropy. True stressstrain curves at large strains were determined from hydraulic bulge testing and fitted to a work-hardening equation. The limit strains are defined at both localized necking and fracture conditions according to Nakajima’s hemispherical punch procedure. Also, an elasto-plastic localization model is proposed in order to predict strain and stress based forming limit curves. The investigated dual-phase sheets showed a good formability in the biaxial stretching and drawing FLC regions. For both DP600 and DP800 sheets, the corresponding numerical predictions overestimated and underestimated the experimental limit strains in the biaxial stretching and drawing FLC regions, respectively. This can be attributed to the restricted failure necking condition adopted in the numerical model, which is not suitable to describe the tensile and shear fracture mechanisms in advanced high strength steels under equibiaxial and biaxial stretching conditions.

Keywords: Advanced high strength steels, forming limit curve, numerical modeling, sheet metal forming.

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Authors: Talal S. Abdullah, Shahin Mehraban, Geraint Lodwig, Nicholas P. Lavery

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The defining property of Interstitial Free (IF) steels is formability, comprehensively measured using the Lankford coefficient (r-value) on uniaxial tensile test data. The contributing factors supporting this feature are grain size, orientation, and elemental additions. The processes that effectively modulate these factors are the casting procedure, hot rolling, and heat treatment. An existing methodology is well-practised in the steel industry; however, large-scale production and experimentation consume significant proportions of time, money, and material. Introducing small-scale rapid alloy prototyping (RAP) as an alternative process would considerably reduce the drawbacks relative to standard practices. The aim is to finetune the existing fundamental procedures implemented in the industrial plant to adapt to the RAP route. IF material is remelted in the 80-gram coil induction melting (CIM) glovebox. To birth small grains, maximum deformation must be induced onto the cast material during the hot rolling process. The rolled strip must then satisfy the polycrystalline behaviour of the bulk material by displaying a resemblance in microstructure, hardness, and formability to that of the literature and actual plant steel. A successful outcome of this work is that small-scale RAP can achieve target compositions with similar microstructures and statistically consistent mechanical properties which complements and accelerates the development of novel steel grades.

Keywords: Interstitial free, miniaturized tensile specimen, plastic anisotropy, rapid alloy prototyping.

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Authors: Lukas Horny, Rudolf Zitny, Hynek Chlup, Tomas Adamek, Michal Sara

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An inflation–extension test with human vena cava inferior was performed with the aim to fit a material model. The vein was modeled as a thick–walled tube loaded by internal pressure and axial force. The material was assumed to be an incompressible hyperelastic fiber reinforced continuum. Fibers are supposed to be arranged in two families of anti–symmetric helices. Considered anisotropy corresponds to local orthotropy. Used strain energy density function was based on a concept of limiting strain extensibility. The pressurization was comprised by four pre–cycles under physiological venous loading (0 – 4kPa) and four cycles under nonphysiological loading (0 – 21kPa). Each overloading cycle was performed with different value of axial weight. Overloading data were used in regression analysis to fit material model. Considered model did not fit experimental data so good. Especially predictions of axial force failed. It was hypothesized that due to nonphysiological values of loading pressure and different values of axial weight the material was not preconditioned enough and some damage occurred inside the wall. A limiting fiber extensibility parameter Jm was assumed to be in relation to supposed damage. Each of overloading cycles was fitted separately with different values of Jm. Other parameters were held the same. This approach turned out to be successful. Variable value of Jm can describe changes in the axial force – axial stretch response and satisfy pressure – radius dependence simultaneously.

Keywords: Constitutive model, damage, fiber reinforcedcomposite, limiting fiber extensibility, preconditioning, vena cavainferior.

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Authors: Syed Muzyan Shahzad, Liu Jianxin, Asim Shahzad, Muhammad Sharjeel Raza, Sun Ya, Fanidi Meryem

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Electrical resistivity investigation was conducted in vicinity of Tarbela Ghazi, in order to study the subsurface layer with a view of determining the depth to the aquifer and thickness of groundwater potential zones. Vertical Electrical Sounding (VES) using Schlumberger array was carried out at 16 VES stations. Well logging data at four tube wells have been used to mark the super saturated zones with great discharge rate. The present paper shows a geoelectrical identification of the lithology and an estimate of the relationship between the resistivity and Dar Zarrouk parameters (transverse unit resistance and longitudinal unit conductance). The VES results revealed both homogeneous and heterogeneous nature of the subsurface strata. Aquifer is unconfined to confine in nature, and at few locations though perched aquifer has been identified, groundwater potential zones are developed in unconsolidated deposits layers and more than seven geo-electric layers are observed at some VES locations. Saturated zones thickness ranges from 5 m to 150 m, whereas at few area aquifer is beyond 150 m thick. The average anisotropy, transvers resistance and longitudinal conductance values are 0.86 %, 35750.9821 Ω.m², 0.729 Siemens, respectively. The transverse unit resistance values fluctuate all over the aquifer system, whereas below at particular depth high values are observed, that significantly associated with the high transmissivity zones. The groundwater quality in all analyzed samples is below permissible limit according to World Health Standard (WHO).

Keywords: Geoelectric layers, Dar Zarrouk parameters, Aquifer, Electro-stratigraphic.

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