Three-Dimensional Finite Volume Method of Triphasic Theory in Generalized Coordinates: Application to Human Intervertebral Disc During Compressive Stress Relaxation

2010 ◽  
Author(s):  
Xiangying Chen ◽  
Wei Yong Gu ◽  
Chun-Yuh Huang ◽  
Gecheng Zha
Keyword(s):  
Stress Relaxation ◽  
Intervertebral Disc ◽  
Compressive Stress ◽  
Three Dimensional ◽  
Spinal Column ◽  
Mesh Size ◽  
Commercial Software ◽  
Specific Geometry ◽  
Triphasic Theory ◽  
Volume Method

The intervertebral disc is an avascular cartilaginous structure that plays an important role in supporting loads through the spine and providing flexibility to the spinal column. The triphasic theory [1,2] has been used successfully to describe many of the mechanical, chemical and electrical behaviors of cartilaginous tissues. As an example of applying the triphasic theory, Yao and Gu [3] conducted a finite element simulation of human intervertebral disc during compressive stress relaxation using commercial software (FEMLAB). Due to the limitation of the commercial software, in the simulation reported in [3], the computational grid (mesh) is fixed throughout the simulation and the mesh size was not optimized for the specific geometry of the disc.

Stress relaxation at a gelatin hydrogel–glass interface in direct shear sliding

2018 ◽  
Vol 32 (02) ◽  
pp. 1750345 ◽  
Author(s):  
Vinit Gupta ◽  
Arun K. Singh
Keyword(s):  
Residual Stress ◽  
Stress Relaxation ◽  
Three Dimensional ◽  
Mesh Size ◽  
Friction Model ◽  
Direct Shear ◽  
Stick Slip ◽  
Strong Bond ◽  
Gelatin Concentration

In this paper, we study experimentally the stress relaxation behavior of soft solids such as gelatin hydrogels on a smooth glass surface in direct shear sliding. It is observed experimentally that irrespective of pulling velocity, the sliding block relaxes to the same level of nonzero residual stress. However, residual stress increases with increasing gelatin concentration in the hydrogels. We have also validated a friction model for strong bond formation during steady relaxation in light of the experimental observations. Our theoretical analysis establishes that population of dangling chains at the sliding interface significantly affects the relaxation process. As a result, residual stress increases with increasing gelatin concentration or decreasing mesh size of the three-dimensional structures in the hydrogels. It is also found that the transition time, at which a weak bond converts to strong bond, increases with increasing mesh size of the hydrogels. Moreover, relaxation time constant of a strong bond decreases with increasing mesh size. However, activation length of a strong bond increases with mesh size. Finally, this study signifies the role of residual strength in frictional shear sliding and it is believed that these results should be useful to understand the role of residual stress in stick-slip instability.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

scholarly journals Mesh size sensitivity analysis for interlaminar fracture of the fiber-reinforced laminated composites

2019 ◽  
Vol 14 ◽  
pp. 155892501988346 ◽  
Author(s):  
Fatih Daricik
Keyword(s):  
Crack Closure ◽  
Strain Energy ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Mesh Size ◽  
Strain Energy Release ◽  
Virtual Crack Closure Technique ◽  
Closure Technique ◽  
Interlaminar Fracture ◽  
Element Size

The virtual crack closure technique is a well-known finite element–based numerical method used to simulate fractures and it suits well to both of two-dimensional and three-dimensional interlaminar fracture analysis. In particular, strain energy release rate during a three-dimensional interlaminar fracture of laminated composite materials can successfully be computed using the virtual crack closure technique. However, the element size of a numerical model is an important concern for the success of the computation. The virtual crack closure technique analysis with a finer mesh converges the numerical results to experimental ones although such a model may need excessive modeling and computing times. Since, the finer element size through a crack path causes oscillation of the stresses at the free ends of the model, the plies in the delaminated zone may overlap. To eliminate this problem, the element size for the virtual crack closure technique should be adjusted to ascertain converged yet not oscillating results with an admissible processing time. In this study, mesh size sensitivity of the virtual crack closure technique is widely investigated for mode I and mode II interlaminar fracture analyses of laminated composite material models by considering experimental force and displacement responses of the specimens. Optimum sizes of the finite elements are determined in terms of the force, the displacement, and the strain energy release rate distribution along the width of the model.

scholarly journals Optimization of Polymer Extrusion Die Based on Response Surface Method

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1043 ◽  
Author(s):  
Amin Razeghiyadaki ◽  
Dichuan Zhang ◽  
Dongming Wei ◽  
Asma Perveen
Keyword(s):  
Three Dimensional ◽  
Theoretical Work ◽  
Optimization Method ◽  
Extrusion Die ◽  
Surface Method ◽  
Spline Fitting ◽  
Die Profile ◽  
Response Optimization ◽  
Geometric Variables ◽  
Volume Method

A coupled surface response optimization method with a three-dimensional finite volume method is adopted in this study to identify five independent geometric variables of the die interior that provides a design with the lowest velocity variance at the exit of the coat-hanger extrusion die. Two of these five geometric variables represent the manifold dimension while the other three variables represent the die profile. In this method, B-spline fitting with four points was used to represent the die profile. A comparison of the optimized die obtained in our study and the die with a geometry derived by a previous theoretical work shows a 20.07% improvement in the velocity distribution at the exit of the die.

Heat and Mass Diffusion Including Shrinkage and Hygrothermal Stress during Drying of Holed Ceramics Bricks

2011 ◽  
Vol 312-315 ◽  
pp. 971-976 ◽  
Author(s):  
J. Barbosa da Silva ◽  
G. Silva Almeida ◽  
W.C.P. Barbosa de Lima ◽  
Gelmires Araújo Neves ◽  
Antônio Gilson Barbosa de Lima
Keyword(s):  
Moisture Content ◽  
Three Dimensional ◽  
Average Moisture Content ◽  
Stress Distributions ◽  
Drying Process ◽  
Convective Boundary ◽  
Volume Method ◽  
Hygrothermal Stress ◽  
Thermo Physical Properties ◽  
Good Agreement

The Aim of this Work Is to Present a Three-Dimensional Mathematical Modelling to Predict Heat and Mass Transport inside the Industrial Brick with Rectangular Holes during the Drying Including Shrinkage and Hygrothermalelastic Stress Analysis. the Numerical Solution of the Diffusion Equation, Being Used the Finite-Volume Method, Considering Constant Thermo-Physical Properties and Convective Boundary Conditions at the Surface of the Solid, it Is Presented and Analyzed. Results of the Temperature, Moisture Content and Stress Distributions, and Drying and Heating Kinetics Are Shown and Analyzed. Results of the Average Moisture Content and Surface Temperature of the Brick along the Drying Process Are Compared with Experimental Data (T = 80.0oC and RH = 4.6 %) and Good Agreement Was Obtained. it Was Verified that the Largest Temperature, Moisture Content and Stress Gradients Are Located in the Intern and External Vertexes of the Brick.

Effect of the Separating Distance of Twin Buildings on the Generated Flow Structure

2010 ◽  
Vol 297-301 ◽  
pp. 924-929
Author(s):  
Inès Bhouri Baouab ◽  
Nejla Mahjoub Said ◽  
Hatem Mhiri ◽  
Georges Le Palec ◽  
Philippe Bournot
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Wind Flow ◽  
Turbulent Model ◽  
Navier Stokes Equations ◽  
Twin Buildings ◽  
Volume Method ◽  
Numerical Examination

The present work consists in a numerical examination of the dispersion of pollutants discharged from a bent chimney and crossing twin similar cubic obstacles placed in the lee side of the source. The resulting flow is assumed to be steady, three-dimensional and turbulent. Its modelling is based upon the resolution of the Navier Stokes equations by means of the finite volume method together with the RSM (Reynolds Stress Model) turbulent model. This examination aims essentially at detailing the wind flow perturbations, the recirculation and turbulence generated by the presence of the twin cubic obstacles placed tandem at different spacing distances (gaps): W = 4 h, W = 2 h and W = 1 h where W is the distance separating both buildings.

Thermohydrodynamic Behavior of a Slider Pocket Bearing

2005 ◽  
Vol 128 (2) ◽  
pp. 312-318 ◽  
Author(s):  
Mihai B. Dobrica ◽  
Michel Fillon
Keyword(s):  
Pressure Distribution ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Convective Boundary ◽  
Inertia Effects ◽  
Good Convergence ◽  
Bearing Design ◽  
The One ◽  
Volume Method ◽  
Generalized Reynolds Equation

Pocket-pads or steps are often used in journal bearing design, allowing improvement of the latter’s dynamic behavior. Similar “discontinuous” geometries are used in designing thrust bearing pads. A literature review shows that, to date, only isoviscous and adiabatic studies of such geometries have been performed. The present paper addresses this gap, proposing a complete thermohydrodynamic (THD) steady model, adapted to three-dimensional (3D) discontinuous geometries. The model is applied to the well-known geometry of a slider pocket bearing, operating with an incompressible viscous lubricant. A model based on the generalized Reynolds equation, with concentrated inertia effects, is used to determine the 2D pressure distribution. On this basis, a 3D field of velocities is constructed which, in turn, allows the resolution of the 3D energy equation. Using a variable-size grid improves the accuracy in the discontinuity region, allowing an evaluation of the magnitude of error induced by Reynolds assumptions. The equations are solved using the finite volume method. This ensures good convergence even when a significant reverse flow is present. Heat evacuation through the pad is taken into account by solving the Laplace equation with convective boundary conditions that are realistic. The runner’s temperature, assumed constant, is determined by imposing a zero value for the global heat flux balance. The constructed model gives the pressure distribution and velocity fields in the fluid, as well as the temperature distribution across the fluid and solid pad. Results show important transversal temperature gradients in the fluid, especially in the areas of minimal film thickness. This further justifies the use of a complete THD model such as the one employed.

Limit Load Analysis of Cracked Components Using the Reference Volume Method

2006 ◽  
Vol 129 (3) ◽  
pp. 391-399 ◽  
Author(s):  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Elastic Modulus ◽  
Three Dimensional ◽  
Local Limit ◽  
Limit Load ◽  
Multiple Cracks ◽  
Element Analysis ◽  
Limit Loads ◽  
Integrity Assessment ◽  
Reference Volume ◽  
Volume Method

Cracks and flaws occur in mechanical components and structures, and can lead to catastrophic failures. Therefore, integrity assessment of components with defects is carried out. This paper describes the Elastic Modulus Adjustment Procedures (EMAP) employed herein to determine the limit load of components with cracks or crack-like flaw. On the basis of linear elastic Finite Element Analysis (FEA), by specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible distributions can be generated, to obtain lower and upper bounds limit loads. Due to the expected local plastic collapse, the reference volume concept is applied to identify the kinematically active and dead zones in the component. The Reference Volume Method is shown to yield a more accurate prediction of local limit loads. The limit load values are then compared with results obtained from inelastic FEA. The procedures are applied to a practical component with crack in order to verify their effectiveness in analyzing crack geometries. The analysis is then directed to geometries containing multiple cracks and three-dimensional defect in pressurized components.

Chemical Stress Relaxation of NR Networks Prepared in the Swollen State

1986 ◽  
Vol 59 (4) ◽  
pp. 541-550 ◽  
Author(s):  
Kyung-Do Suh ◽  
Hidetoshi Oikawa ◽  
Kenkichi Murakami
Keyword(s):  
Stress Relaxation ◽  
Network Structure ◽  
Three Dimensional ◽  
Polymer Chains ◽  
Chemical Stress ◽  
Network Chain ◽  
Crosslinking Process ◽  
Dimensional Network ◽  
Chemical Relaxation ◽  
The Difference

Abstract From the experimental results of the present investigation, it is apparent that two kinds of networks which have a different three-dimensional network structure give quite different behavior of chemical stress relaxation, even if both networks have the same network chain density. The difference in three-dimensional network structure for the two kinds of rubber arises from the degree of entanglement, which changes with the concentration of the polymer chains prior to the crosslinking process. The direct cause of chemical relaxation is due to the scission of network chains by degradation, whereas the total relaxation is caused by the change of geometrical conformation of network chains. This then casts doubt on the basic concept of chemorheology which is represented by Equation 2.

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