Plain Strain Model Research Articles

Numerical simulation of hydraulic fracturing: A hybrid FEM‐based algorithm

AbstractIn this paper, a problem of numerical simulation of hydraulic fractures is considered. An efficient algorithm of solution is proposed for the plain strain model of hydraulic fracturing. The algorithm utilizes a FEM‐based subroutine to compute deformation of the fractured material. The flow of generalized Newtonian fluid in the fracture is modeled in the framework of lubrication theory. In this way, the architecture of the computational scheme is relatively simple and enables one to deal with advanced cases of the fractured material properties and configurations as well as various rheological models of fluid. In particular, the problems of poroelasticity, plasticity, and spatially varying properties of the fractured material can be analyzed. The accuracy and efficiency of the proposed algorithm are verified against analytical benchmark solutions. The algorithm capabilities are demonstrated using the example of the hydraulic fracture propagating in complex geological settings.

Multi thermal waves in a thermo diffusive piezo electric functionally graded rod via refined multi-dual phase-lag model

Abstract In the present work, a novel analytical model is provided for wave dispersion in a piezo-thermoelastic diffusive functionally graded rod through the multi-phase lag model and thermal activation. The plain strain model for thermo piezoelectric functionally graded rod is considered. The complex characteristic equations are obtained by using normal mode method which satisfies the nonlinear boundary conditions of piezo-thermoelastic functionally graded rod. The numerical calculations are carried out for copper material. The results of the variants stress, mechanical displacement, temperature and electric distribution, frequency are explored against the geometric parameters and some special parameters graded index, concentration constants are shown graphically. The observed results will be discuss elaborate. The results can be build reasonable attention in piezo-thermoelastic materials and smart materials industry.

Three-dimensional microstructure based model for evaluating the coefficient of thermal expansion and contraction of asphalt concrete

The coefficient of thermal expansion (CTE) and contraction (CTC) are critical parameters for pavement design and thermal analysis. This paper develops a 3-D microstructure-based FE model to evaluate the CTE and CTC of asphalt concrete. The 3-D random microstructure of asphalt concrete was generated with an image-aided algorithm. In the presented algorithm, the random 3-D geometry of a single aggregate was generated with a single 2-D image captured by Aggregate Image System 2 (AIMS2). The randomly generated 3-D aggregates were packaged with PFC 3D to construct the 3-D microstructure for asphalt concrete with prescribed gradation. Then the 3-D microstructure of asphalt concrete was imported into FE software ABAQUS to calculate the CTE and CTC. To validate the results from the numerical simulation, a laboratory experiment was conducted to test the CTE/CTC of the asphalt concrete with the same material composition. With the validated FE model, the effect of aggregate type, shape, and spatial orientation on the CTE/CTE was analyzed. Results show that the relative differences between the average values of numerical and experimental data were 1.63%∼4.64% for the CTE, and 3.01%∼7.20% for the CTC. With the increase of temperature, the CTE first decreased and then increased, while the CTC first increased and then decreased. Compared with the 3-D microstructure-based model, both the 2-D plain stress and plain strain models tended to overestimate the CTE of asphalt concrete. When the aggregate orientation tended to be inclined to a certain direction, the CTC and CTE of the asphalt concrete parallel to that direction tended to be smaller. Asphalt concrete prepared with quartz gravels and sand stones tended to have higher CTC and CTE. While the CTC and CTE of asphalt concrete could be reduced by using limestones.

Multi-leaf masonry walls: Load transfer mechanisms sensitivity to mechanic and geometric parameters

The apparent monolithic behaviour of multi-leaf walls is compromised by the discontinuity planes that the load transfer mechanisms generate for the following reasons: i) difference between mechanical characteristics of layers; ii) lack or weakness of the structural interaction between core and external layers. The goal of this paper is to evaluate through parametric analysis the dimensional ratios by reference to core confinement effects of multi-leaf masonry walls with several interface and mechanical characteristics of layers. The study was carried out through the finite element analysis performed in non-linear field on two-dimensional plain strain models calibrated on experimental basis and numerical results are presented and discussed. The horizontal interfaces hand the load transfer and structural performances of multi-leaf walls. The behaviour of short specimens is controlled by confinement of external layers while for slender masonry walls the out of plane mechanisms affect the confinement effect.

Theoretical analysis of equivalent hydrostatic stress attenuation in surrounding rocks after excavation

Energy concentration and redistribution are always accompanied by tunnel deformation and failure. This study uses a plain-strain model of circular openings under high in situ stress to derive the energy of the surrounding rocks before and after excavation based on elasticity. The study focuses on determining the areal extent of the surrounding rock significantly affected by the excavation. The relationship between dimensionless zonal radius ri/a and dimensionless stress σ0/R0 is determined based on two principles: (1) energy conservation and (2) the logarithmic relationship between consumed energy and the scale of fragmentation. The law of attenuation of stress in surrounding rock during the process of zonal fracture is theoretically explained. Preliminary values for the unknown parameters in the given formula are proposed using the data available, and the stress attenuation law corresponding to the given tunnels is presented.

Non-linear continuous model for three leaf masonry walls

Three-leaf brick masonry wall is a typical technique in historical buildings. Sensitivity of three-leaf brick masonry wall to core mechanical characteristics and interface between layers is studied by reference to an experimental campaign. Experimental activities were performed on three-leaf masonry panel under compressive loads and is used to identify mechanical characteristic of three-leaf masonry wall and calibrate a 2D plain strain model (without and with interfaces between layers) for cross section of panel. A parametric analysis on inner core and interface between layers mechanical characteristic sensitivity is proposed. Numerical modeling results are presented and discussed in comparison with experimental data.

Torsional complex impedance of pipe pile considering pile installation and soil plug effect

Torsional vibrations of pipe pile are more complicated compared to solid pile. In actual engineering, pile surrounding soil may be strengthened or weakened due to different pile installation methods, which is regarded as pile installation effect. At the same time, soil plug effect which describes the interaction between the soil plug and pile wall is also non-negligible in bearing analysis. Along the model of inhomogeneous medium, this paper subdivides the inhomogeneous soil region into certain sub-zones whose shear complex stiffness are derived by virtue of continuity conditions and plain strain model. To study the influence of soil plug effect, the additional mass model is raised and utilized in this paper. In this model, the pile-soil plug system is vertically split into infinite sections, and each pipe pile section and soil plug section is connected by distributed Voigt model. The analytical solution of torsional complex impedance is acquired and compared with results obtained from former studies to verify its rationality. Finally, a parametric research is presented to exhibit the influence of the pile installation and soil plug effect on the torsional complex impedance of pipe pile head.

Dynamic response of pipe pile embedded in layered visco elastic media with radial inhomogeneity under vertical excitation

A new mechanical model for predicting the vibration of a pipe pile embedded in longitudinally layered visco-elastic media with radial inhomogeneity is proposed by extending Novak\'s plain-strain model and complex stiffness method to consider viscous-type damping. The analytical solutions for the dynamic impedance, the velocity admittance and the reflected signal of wave velocity at the pile head are also derived and subsequently verified by comparison with existing solutions. An extensive parametric analysis is further performed to examine the effects of shear modulus, viscous damping coefficient, coefficient of disturbance degree, weakening or strengthening range of surrounding soil and longitudinal soft or hard interbedded layer on the velocity admittance and the reflected signal of wave velocity at the pile head. It is demonstrated that the proposed model and the obtained solutions provide extensive possibilities for practical application compared with previous related studies.

Analysis of the Thermomechanical Response of Structural Cables Subject to Fire

Cable-supported structures such as bridges and stadia are critical for the surrounding community and the consequences arising from a major fire event can be substantial. Previous computational studies into the thermal response of cables often employed simplistic heat transfer models that assumed lump capacitance or cross-sectional homogeneity without proof of validity. This paper proposes a methodology for calculating the thermal response of a cable cross-section allowing for heat transfer by conduction through each strand contact surface and radiation across inter-strand cavities. The methodology has been validated against two experiments of cables subjected to radiant heating and an input sensitivity analysis has been undertaken for the heat transfer and material parameters. The approach is compared against simple heat transfer lumped methods for a parallel-strand cable where it is shown that these lumped models are not always conservative. The model is then coupled with a two-dimensional generalised plain strain model to study the likely effect of the cross-sectional temperature gradients on the mechanical response. The study considers three qualitatively different hydrocarbon jet fire scenarios, both with and without external insulation for fire protection. It is shown that the proposed methodology can reproduce realistic cross-sectional temperature distributions with up to 50% temperature difference at the cable external surface and can capture the phenomenon of load shedding in a gradually heated cable. It is also shown that assuming a lumped thermal mass neglects the possibility of moment-inducing temperature gradients which are not considered in the ambient design of cables that is driven by tensile capacities. The proposed model and its predictions contribute towards an improved understanding and a more informed structural design of cable-supported structures in fire.

Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches

Virtual crack closure technique (VCCT), cohesive zone modeling (CZM) and extended finite element method (XFEM) are three well-known numerical methods frequently used for crack propagation modeling. It is often questioned by new researchers and engineers: which method is more appropriate for modeling of delamination propagation in composites? In this study, advantages, limitations, and challenges of each method are discussed with the goal of finding a suitable and cost-effective solution for modeling of delamination propagation in laminated composites. To this end, a composite double cantilever beam (DCB) specimen as a benchmark example is modeled in ABAQUS and delamination propagation is simulated using three above methods and the combination of XFEM with VCCT and CZM. Two-dimensional plain strain and three-dimensional DCB models are both considered. Finite element results are compared with experimental results available in the literature for unidirectional DCB specimens. Finally, the accuracy, convergence speed, run-time and mesh dependency of each method are discussed. The XFEM-CZM was found as a suitable method for simulation of delamination growth.

Static earth pressures on a pile supported excavation in Santiago gravel

Concrete soldier piles anchored in multiple levels are the most common method for supporting deep excavations in gravel. Their static design is based on limit equilibrium principles, although these procedures were originally developed for sheet piles or anchored walls on shallow excavations supporting medium-dense sand. The present study draws on the applicability of current design tools to model the static response of deep excavations in stiff gravels and their implications for design. For this purpose, the static response of an anchored pile system was evaluated with a detailed finite element model of a case study, and the results are compared with simplified hand-calculation procedures. The study unit was the 28 m deep excavation of the Beauchef Poniente building located in the fluvial deposits of the Mapocho River in Santiago. A plain strain model was developed in PLAXIS using the Hardening Soil constitutive model, with parameters determined from large-scale triaxial tests of local gravels, and the computed pile displacement were compared to actual displacement profiles measured with inclinometers. The analysis shows that the simplified procedures provide a reasonably good approximation to the computed earth pressures, internal forces on the piles, and stress in the anchors.

Improvement ratio and behavior of bearing capacity factors for strip skirt footing model resting on sand of different grain size distribution

Plain strain model tests were performed on beds of sands with different particle size distribution (Coarse, Medium and Fine) prepared at loose state (Relative density Dr. of 30%). A strip footing model with skirt was placed on the bed of sand and loaded vertically up to failure at different ratios of skirt depth to width D/B of (0.5, 1.0, 1.5, 2, and 3). The applied stress increments and the corresponding settlements were measured. The improvement ratio due to different skirt depth and the behavior of bearing capacity parameters Nγ and Nq at each depth were evaluated and compared with some theoretical approaches. The test results revealed that the improvement ratio increased linearly up to D/B of 1.5 then reduced. Two factors were introduce into the general bearing capacity equation where used to evaluate bearing capacity of skirt footing, there values are about 1.6 for skirt ratio ranged between 0.5 to 1.5, and 1.25 for skirt ratio more than 1.5. Also, it is found that the Nγ parameter for D/B=0 were very close to Vesic proposal for fine and medium grain size distribution, while it’s close to Biarez proposal for coarse sand. The behavior of Nq parameter with different skirt ratio shows slight increase up to D/B of 1.5 then decrease with increasing D/B ratio for different grain size distribution. While the behavior of theoretical Nq parameter (depending on angle of internal friction values) shows a linear increase with skirt ratio for different grain size distribution.

Material Flow Analysis in Indentation by Two-Dimensional Digital Image Correlation and Finite Elements Method.

The present work shows the material flow analysis in indentation by the numerical two dimensional Finite Elements (FEM) method and the experimental two-dimensional Digital Image Correlation (DIC) method. To achieve deep indentation without cracking, a ductile material, 99% tin, is used. The results obtained from the DIC technique depend predominantly on the pattern conferred to the samples. Due to the absence of a natural pattern, black and white spray painting is used for greater contrast. The stress-strain curve of the material has been obtained and introduced in the Finite Element simulation code used, DEFORM™, allowing for accurate simulations. Two different 2D models have been used: a plain strain model to obtain the load curve and a plain stress model to evaluate the strain maps on the workpiece surface. The indentation displacement load curve has been compared between the FEM and the experimental results, showing a good correlation. Additionally, the strain maps obtained from the material surface with FEM and DIC are compared in order to validate the numerical model. The Von Mises strain results between both of them present a 10–20% difference. The results show that FEM is a good tool for simulating indentation processes, allowing for the evaluation of the maximum forces and deformations involved in the forming process. Additionally, the non-contact DIC technique shows its potential by measuring the superficial strain maps, validating the FEM results.

Seismic response of shallow circular tunnels in two-layered ground

The effect of ground stratification on the seismic response of circular tunnels is investigated, as most practice-oriented studies consider homogeneous ground. A finite element plain-strain model of a circular tunnel cross-section embedded in a two-layered ground is used to highlight the influence of stratification on the tunnel׳s seismic response. The layers interface was placed at the crown, centre and invert level.It is proved that ground stratification has an important role in the lining seismic forces. When the tunnel is fully embedded in one of the layers, the seismic lining forces may vary significantly in comparison with the single-layer case. If the tunnel intercepts both layers, maximum lining forces aggravation occurs when the lower layer is very stiff.

Integrated finite element method and response surface methodology-based modelling and simulation of single point diamond turning of silicon

This paper presents an integrated finite element method-response surface methodology (FEM-RSM)-based approach for modelling and simulation of single point diamond turning (SPDT) operation of silicon. Initially, a two-dimensional nonlinear plain strain model of SPDT process has been developed by using FEM. The results predicted by the numerical model were validated with the experimental results available in the literature for similar process conditions and they found in good agreement. Detailed parametric studies were carried out using RSM to study the effect of cutting speed, rake angle, depth of cut and tool edge radius on machining forces. The RSM-based model was also validated by carrying out confirmation simulations and the model was found to be predicting good with mean prediction error of about 5%. It is felt that the proposed approach can be a good alternative to the costly, time consuming and tedious SPDT experimental study of silicon material.

Characterization and Modeling of Fine-Pitch Copper Ball Bonding on a Cu/Low-k Chip

Cu ball bonding faces more challenges than Au ball bonding, for example, excessive deformation of the bond pad and damage of Cu/low-k structures, because of the much greater hardness of Cu free air balls. In this study, dynamic finite-element analysis (FEA) modeling with displacement control was developed to simulate the ball-bonding process. The three-dimensional (3D) FEA simulation results were confirmed by use of stress-measurement data, obtained by use of stress sensors built into the test chip. Stress comparison between two-dimensional (2D) and 3D FEA models showed the 2D plain strain model to be a reasonable and effective model for simulation of the ball-bonding process without loss of accuracy; it also saves computing resources. The 2D FEA model developed was then used in studies of a Cu/low-k chip to find ways of reducing Al bond pad deformation and stresses of low-k structures. The variables studied included Al pad properties, capillary geometry, bond pad design (Al pad thickness, Al pad coated with Ni layer), and the effect of ultrasonic bonding power.

A physical and numerical investigation of the failure mechanism of weak rocks surrounding tunnels

The large-scale construction of railway tunnels in China is hindered by several challenges, including large depths, large tunnel cross-sections, and fragile geological conditions. In this paper, we explored a new physical and numerical simulation method that improves upon the currently used methods to investigate the deformation and failure modes of weak rocks surrounding a tunnel. We also compared the results from physical tests and numerical simulations with the field measurements to demonstrate the effectiveness of the proposed numerical simulation method. In the physical model test, an artificial speckle field was developed by staining quartz sand particles and mixing the particles with barite powder and petroleum jelly in preset proportions. The artificial speckle field was employed in the digital speckle correlation method (DSCM) to monitor the evolution of the strain field on the surface of the plain strain model for tunneling during loading. A secondary strain-softening constitutive model using the numerical modeling code FLAC3D was developed (degradation constitutive model) by considering the deformation modulus degradation in the numerical simulation. The failure mode of weak rocks surrounding a tunnel in the physical model test was examined using the developed degradation constitutive model. Both the physical and numerical results revealed that the least stable area was the shear wedge along the minimum principal stress, which was confirmed in the damage zone of the surrounding rocks. The results were consistent with previous research findings. The results of the DSCM in the physical model test indicated that the shear wedge in the middle part of the tunnel and the cracks around the arch of the tunnel were induced by shear strain, whereas the collapse of the arch was attributed to a combination of tensile strain and shear strain. A comparison of the physical and numerical simulation results demonstrated that the degradation constitutive model can be used to describe the extent and depth of the excavation damage zone of tunneling. A comparison of the displacements from the numerical simulation and field measurements indicated that the degradation model can be used to capture the displacement of weak rocks surrounding tunnels.

BOUNDARY ELEMENT METHOD MODELLING OF NANOCOMPOSITES

The paper deals with the numerical homogenization of polymer/clay nanocomposites reinforced by stacks of parallel clay sheets. The stacks can be modelled as effective particles, as it was shown in the literature. For a relatively small volume fraction of the reinforcement, the effective particles can be isotropic, while for greater values, the particles should be anisotropic. Other authors most commonly use analytical methods or the finite element method (FEM). In this work, the boundary element method (BEM) is applied. Two-dimensional plain strain models are analyzed. Two cases are considered, namely, isotropic and anisotropic (orthotropic) particles. The matrix of the composite is modelled as isotropic. The problem is solved by using a BEM formulation for plates containing many identical inclusions. The kernels of boundary integrals for the isotropic subdomains are the Kelvin solutions for plane elasticity. In the case of the orthotropic particles, fundamental solutions obtained by the Stroh formalism are applied. The results are compared to the Mori-Tanaka model. Acceptable agreement between the models is observed.

The Regression Analysis of Corresponding Crack in Asphalt Pavement under Temperature Load

By use of the theory of fracture mechanics, the plain-strain model is established to simulate the four-layer asphalt pavement of corresponding crack.. And then, applying the segmented integral method and power function form, the stretching stress intensify factors in the conditions that four limited layer combined status and different crack space are calculated and analyzed under the action of pavement and basement shrinkage. Moreover, the regression formulas are given which can meet requirements of the engineering regression equation precision.

The Regression Analysis of Corresponding Crack in Asphalt Pavement under Temperature Load

By use of the theory of fracture mechanics, the plain-strain model is established to simulate the four-layer asphalt pavement of corresponding crack.. And then, applying the segmented integral method and power function form, the stretching stress intensify factors in the conditions that four limited layer combined status and different crack space are calculated and analyzed under the action of pavement and basement shrinkage. Moreover, the regression formulas are given which can meet requirements of the engineering regression equation precision.