Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.

SEMI-ANALYTICAL FINITE ELEMENT METHOD FOR FICTITIOUS CRACK MODEL IN FRACTURE MECHANICS OF CONCRETE

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.

Study on hot deformation behavior of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy using a combination of strain-compensated Arrhenius constitutive model and finite element simulation method

Isothermal hot compression experiments were conducted on homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy to investigate hot deformation behavior at the temperature range of 673-773 K and the strain rate range of 0.001-1 s^(-1)by using a Gleeble-1500D thermo mechanical simulator.Metallographic characterization on samples deformed to true strain of 0.70 illustrates the occurrence of flow localization and/or microcrack at deformation conditions of 673 K/0.01 s^(-1),673 K/1 s^(-1)and 698 K/1 s^(-1),indicating that these three deformation conditions should be excluded during hot working of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy.Based on the measured true stress-strain data,the strain-compensated Arrhenius constitutive model was constructed and then incorporated into UHARD subroutine of ABAQUS software to study hot deformation process of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy.By comparison with measured force-displacement curves,the predicted results can describe well the rheological behavior of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy,verifying the validity of finite element simulation of hot compression process with this complicated constitutive model.Numerical results demonstrate that the distribution of values of material parameters(α,n,Q and ln A)within deformed sample is inhomogeneous.This issue is directly correlated to the uneven distribution of equivalent plastic strain due to the friction effect.Moreover,at a given temperature the increase of strain rate would result in the decrease of equivalent plastic strain within the central region of deformed sample,which hinders the occurrence of dynamic recrystallization(DRX).

The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives

In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.

The Modeling of 2D Controlled Source Audio Magnetotelluric (Csamt) Responses Using Finite Element Method

This paper presents the modeling of 2D CSAMT responses generated by horizontal electric dipole using the separation of primary and secondary field technique. The primary field is calculated using 1D analytical solution for homogeneous earth and it is used to calculate the secondary electric field in the inhomogeneous Helmholtz Equation. Calculation of Helmholtz Equation is carried out using the finite element method. Validation of this modeling is conducted by comparison of numerical results with 1D analytical response for the case of homogeneous and layered earth. The comparison of CSAMT responses are also provided for 2D cases of vertical contact and anomalous conductive body with the 2D magnetotelluric (MT) responses. The results of this study are expected to provide better interpretation of the 2D CSAMT data.

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

Multiple linear system techniques for 3D finite element method modeling of direct current resistivity

The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.

A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus

In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

Finite element method for coupled diffusion-deformation theory in polymeric gel based on slip-link model

A polymeric gel is an aggregate of polymers and solvent molecules, which can retain its shape after a large deformation. The deformation behavior of polymeric gels was often described based on the Flory-Rehner free energy function without considering the influence of chain entanglements on the mechanical behavior of gels. In this paper,a new hybrid free energy function for gels is formulated by combining the EdwardsVilgis slip-link model and the Flory-Huggins mixing model to quantify the time-dependent concurrent process of large deformation and mass transport. The finite element method is developed to analyze examples of swelling-induced deformation. Simulation results are compared with available experimental data and show good agreement. The influence of entanglements on the time-dependent deformation behavior of gels is also demonstrated.The study of large deformation kinetics of polymeric gel is useful for diverse applications.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Deformation Stability of GH4033 Superalloy in the Hot Continuous Rolling Process Based on Dynamic Material Model and Finite Element Model

The flow stress behavior of GH4033 superalloy was determined by the hot compression tests at the temperatures of 1223-1473 K and the total strains of 0.6 with the strain rates of 0.001-30.0 s^(-1) by using cylindrical samples.The processing maps based on the dynamic material model(DMM)combined with the corresponding microstructure observations indicate the reasonable processing domain locating at the strain rates of 0.1-1.0 s^(-1) and the deformation temperature of 1273-1423 K.Meanwhile,the numerical simulation based on finite element model(FEM)described the variation of the effective strain,effective strain rate and the temperature for the core node,and unveiled the influence of the hot rolling parameters considering the initial temperature(T_(0))range of 1223-1473 K and the first-stand biting velocity(v_(0))range of 0.15-0.35 m·s^(-1).Furthermore,the deformation stability of GH4033 superalloy in the round rod hot continuous rolling(HCR)process is described and analyzed by coupling the three-dimensional(3-D)processing map,and the spatial trajectory lines were determined by the numerically simulated temperatures,the strains and the strain rates.Finally,the results show that the hot deformation stability of GH4033 can be achieved by the rolling process parameters located at T_(0)=1423 K and v_(0)=0.25 m·s^(-1).Additionally,the practical HCR processes as T_(0)=1423 K and v_(0)=0.15,0.25,0.35 m·s^(-1) were operated to verify the influence of the hot rolling parameters on the hot deformation stability by the microstructure observation of the final products.

Finite Element Simulation of Radial Tire Building and Shaping Processes Using an Elasto-Viscoplastic Model

The comprehensive tire building and shaping processes are investigated through the finite element method(FEM)in this article.The mechanical properties of the uncured rubber from different tire components are investigated through cyclic loading-unloading experiments under different strain rates.Based on the experiments,an elastoviscoplastic constitutive model is adopted to describe themechanical behaviors of the uncured rubber.The distinct mechanical properties,including the stress level,hysteresis and residual strain,of the uncured rubber can all be well characterized.The whole tire building process(including component winding,rubber bladder inflation,component stitching and carcass band folding-back)and the shaping process are simulated using this constitutive model.The simulated green tire profile is in good agreement with the actual profile obtained through 3D scanning.The deformation and stress of the rubber components and the cord reinforcements during production can be obtained fromthe FE simulation,which is helpful for judging the rationality of the tire construction design.Finally,the influence of the parameter“drum width”is investigated,and the simulated result is found to be consistent with the experimental observations,which verifies the effectiveness of the simulation.The established simulation strategy provides some guiding significance for the improvement of tire design parameters and the elimination of tire production defects.

A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model.The model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi levels.We propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction equations.The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations.Moreover,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi levels.The Poisson equation of electrical potential is solved with standard Lagrangian finite elements.We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete problem.Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory:development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.

Surrounding rock deformation analysis of underground caverns with multi-body finite element method

Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.

Rutting Resistance of Asphalt Pavement Mixes by Finite Element Modelling and Optimisation

Asphalt pavement rtting is a major safety concem and is one of the main distress modes of asphalt pavement.Research into asphalt pavement mixes that provide strong resistance for nutting is considered of great significance as it can help provide extended pavement life and significant cost savings in pavement maintenance and rehabilitation.The objectives of this study are to develop numernical models to investigate the ntting of asphalt concrete pavements and to find optimal design of asphalt pave-ment mix for nutting resistance.Three-dimensional Finite Element mod-els were first developed to simulate both the axial compression and wheel track testing in which a visco elastic-plastic material model was used to predict the ntting of the asphalt concrete pavements.A strain hardening creep model with the material parameters developed from experimental testing was employed to model the time-dependent characteristics of the asphalt concrete pavements.The results were validated against the pre-vious experimental wheel track test results of different pavement mixes.Finally,optimisation techniques using the Design Of Experiments method were applied to the simulation rutting results by varying creep parameters to identify their effects on rutting resistance in order to obtain an optimal asphalt pavements mixes.The results of this paper clearly demonstrate an efficient and effective experimental-numerical method and tool set towards optimal design for asphalt concrete pavements for rutting resis-tance.

Modal and Thermal Analysis of a Modified Connecting Rod of an Internal Combustion Engine Using Finite Element Method

The connecting rod is one of the most important moving components in an internal combustion engine. The present work determined the possibility of using aluminium alloy 7075 material to design and manufacture a connecting rod for weight optimisation without losing the strength of the connecting rod. It considered modal and thermal analyses to investigate the suitability of the material for connecting rod design. The parameters that were considered under the modal analysis were: total deformation, and natural frequency, while the thermal analysis looked at the temperature distribution, total heat flux and directional heat flux of the four connecting rods made with titanium alloy, grey cast iron, structural steel and aluminium 7075 alloy respectively. The connecting rod was modelled using Autodesk inventor2017 software using the calculated parameters. The steady-state thermal analysis was used to determine the induced heat flux and directional heat flux. The study found that Aluminium 7075 alloy deformed more than the remaining three other materials but has superior qualities in terms of vibrational natural frequency, total heat flux and lightweight compared to structural steel, grey cast iron and titanium alloy.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Texture evolution and inhomogeneous deformation of polycrystalline Cu based on crystal plasticity finite element method and particle swarm optimization algorithm

Texture evolution and inhomogeneous deformation of polycrystalline Cu during uniaxial compression are investigated at the grain scale by combining crystal plasticity finite element method(CPFEM) with particle swarm optimization(PSO) algorithm. The texture-based representative volume element(TBRVE) is used in the crystal plasticity finite element model, where a given number of crystallographic orientations are obtained by means of discretizing the orientation distribution function(ODF) based on electron backscattered diffraction(EBSD) experiment data. Three-dimensional grains with different morphologies are generated on the basis of Voronoi tessellation. The PSO algorithm plays a significant role in identifying the material parameters and saving computational time. The macroscopic stress–strain curve is predicted based on CPFEM, where the simulation results are in good agreement with the experimental ones. Therefore, CPFEM is a powerful candidate for capturing the texture evolution and clarifying the inhomogeneous plastic deformation of polycrystalline Cu. The simulation results indicate that the <110> fiber texture is generated finally with the progression of plastic deformation. The inhomogeneous distribution of rotation angles lays the foundation for the inhomogeneous deformation of polycrystalline Cu in terms of grain scale.