Papers by Soheil Mohammadi
International Journal of Solids and Structures
Brain Structure and Function, 2022
doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by pee... more doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.
Computational Materials Science, 2019
Linking atomistic and continuum zones in multiscale methods is a necessity in order to overcome t... more Linking atomistic and continuum zones in multiscale methods is a necessity in order to overcome the deficiencies of the conventional molecular and continuum-based methods. In this paper, a novel approach is presented to bind the atomistic and continuum zones together based on the combined concepts of the finite element method and the radial point interpolation meshfree method. This variable node multiscale method (VNMM) introduces a new way to couple the finite element method with the molecular solutions with nodes coinciding with the atoms. In contrast to QC methods, VNMM does not need a mesh refinement in the vicinity of the molecular zone, nor it requires an overlapping zone in the continuum/atomistic interface which is necessary in bridging schemes. In VNMM, the total displacement of each atom is decomposed into coarse and fine displacements, in which the coarse displacement is computed using the finite element solution over the whole domain, while the fine displacement is calculated just in a limited atomistic zone with the use of molecular statics. Integration of the finite element method within the VNMM formulation potentially allows for enrichment of any field over the entire domain. Conventional interatomic potentials could be employed at the atomistic zone. The results are compared with the fully atomistic simulation, conducted with the molecular statics, and the multiscale quasicontinuum method. A good agreement is observed with substantially reduced degrees of freedom and computational costs.
Burns, 2017
Please cite this article in press as: A.A. Mohammadi, S. Mohammadi, Hand aesthetic, an annoying p... more Please cite this article in press as: A.A. Mohammadi, S. Mohammadi, Hand aesthetic, an annoying problem for the burn patients, but commonly overlooked issue by the burn surgeons, Burns (2017),
Dynamic analysis of stationary cracks is investigated in the framework of the extended finite ele... more Dynamic analysis of stationary cracks is investigated in the framework of the extended finite element method. The Generalized-α (G-α) method is adopted for solving the dynamic equation as the time integration scheme. The G-α method has shown to provide better numerical dissipation characteristics, smaller period and lower displacement errors compared with other time integration methods such as the Newmark algorithm. Finally, numerical examples are solved using the extended finite element method and the predicted dynamic intensity factors for stationary cracks are verified by available analytical solutions.
Computational Materials Science, 2015
An extended three-dimensional multi-scale framework is presented to model plasticity in precipita... more An extended three-dimensional multi-scale framework is presented to model plasticity in precipitate containing materials in the presence of cracks. The present framework is constructed in two scales. At the micro scale, plasticity is computed via the line dislocation dynamics (DD) methodology in which the penetrable and impenetrable precipitates are modeled. At the macro scale, application of the extended finite element method (XFEM) allows for accurate analysis of mixed-mode cohesive crack propagation without the need for any remeshing procedure. This is a significant improvement especially when two different scales are involved. While the former simulations have so far been limited to the study of only mode-I crack propagation to avoid the expensive remeshing procedure, in the present work, the effects of loading rates and precipitate density on general crack propagations are studied by utilizing the XFEM-DD multi-scale framework to illustrate the efficiency and capability of the proposed approach.
Petroleum Science, 2015
High energy gas fracturing is a simple approach of applying high pressure gas to stimulate wells ... more High energy gas fracturing is a simple approach of applying high pressure gas to stimulate wells by generating several radial cracks without creating any other damages to the wells. In this paper, a numerical algorithm is proposed to quantitatively simulate propagation of these fractures around a pressurized hole as a quasi-static phenomenon. The gas flow through the cracks is assumed as a one-dimensional transient flow, governed by equations of conservation of mass and momentum. The fractured medium is modeled with the extended finite element method, and the stress intensity factor is calculated by the simple, though sufficiently accurate, displacement extrapolation method. To evaluate the proposed algorithm, two field tests are simulated and the unknown parameters are determined through calibration. Sensitivity analyses are performed on the main effective parameters. Considering that the level of uncertainty is very high in these types of engineering problems, the results show a good agreement with the experimental data. They are also consistent with the theory that the final crack length is mainly determined by the gas pressure rather than the initial crack length produced by the stress waves.
Theoretical and Applied Fracture Mechanics, 2014
An XFEM multiscale approach is adopted in order to investigate the mechanical properties and frac... more An XFEM multiscale approach is adopted in order to investigate the mechanical properties and fracture behavior of carbon nanotube reinforced concrete specimen. At the nanoscale, molecular dynamics simulation is used to find the mechanical properties of carbon nanotube (CNTs). Afterwards, a hydration model is adopted to find the chemical composition of cement paste. The hydrated model and CNTs are then converted into a finite element mesh for further analysis. Finally, at the meso scale the fracture behavior of the CNT reinforced concrete is simulated by the XFEM approach. The results indicate that the fracture energy of samples with similar volume fractions but reinforced by longer CNTs increase significantly, but addition of CNTs has little influence on the elastic modulus. In addition, the extent of crack propagation under a similar load level becomes considerably lower for the concrete samples reinforce by longer CNTs.
Thin-Walled Structures, 2006
An extended finite element method has been proposed for modeling crack in orthotropic media. To a... more An extended finite element method has been proposed for modeling crack in orthotropic media. To achieve this aim a discontinuous function and two-dimensional asymptotic crack-tip displacement fields are used in a classical finite element approximation enriched with the framework of partition of unity. It allows modeling crack by standard finite element method without explicitly defining and remeshing of surfaces of the crack. In this study, fracture properties of the models are defined by the mixed-mode stress intensity factors (SIFs), which are obtained by means of the domain form of the interaction integral (M-integral). Numerical simulations are performed to verify the approach, and the accuracy of the results is discussed by comparison with other numerical or (semi-) analytical methods.
XFEM Fracture Analysis of Composites, 2012
International Journal of Rock Mechanics and Mining Sciences, 2009
The validity of three-dimensional discontinuous deformation analysis (3-D DDA) is examined by com... more The validity of three-dimensional discontinuous deformation analysis (3-D DDA) is examined by comparing its solution for dynamic block displacement with an analytical solution. Displacement of a single block on inclined planes subjected to dynamic loadings is studied for analytical solutions derived with respect to the frictional resistance offered by the planes. 3-D DDA predicts accurately the analytical displacements, and the results were found sensitive to the maximum displacement ratio, and the size of the time step, which are defined by the user. Best results were achieved when the actual displacements were approximately equal to the assumed maximum displacements per time step. Furthermore, edgeto-edge contact constraints have been improved by using the augmented Lagrangian method instead of the penalty method. Using the augmented Lagrangian method to enforce contact restraints retains the simplicity of the penalty method, and reduces its disadvantages. The new formulation of edge-to-edge contact using the augmented Lagrangian method is implemented in 3-D DDA and has been programmed in VC++. Finally two illustrative examples are presented for demonstrating this new approach.
International Journal for Numerical Methods in Engineering, 2011
SUMMARYA novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is... more SUMMARYA novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B‐splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two‐dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichm...
Finite Elements in Analysis and Design, 2008
One of the most important problems in solution of partial differential equations in their strong ... more One of the most important problems in solution of partial differential equations in their strong form with particle methods is the instability of results. A number of methods have been developed for elimination of this deficiency in past decade. Many of them, however, cannot be efficiently applied to all general engineering problems.In this paper, two new methods for removing the instability in particle methods are presented. The first method is based on an incremental form of the Navier equation in small deformations combined with the Newmark time integration scheme. The second method is based on the concept of field smoothing. This method stabilizes the solution by removing high frequency vibrations of field variables with a number of field smoothing techniques. This method is more general than the first one and may be applied to various engineering problems. The proposed methods have no requirements of considering any stabilizing terms in the main equations. Although the proposed approaches can be applied to any particle method, the CSPM particle method is adopted for detail discussion. Several illustrative examples are analyzed to assess the capability of the proposed approaches to enhance the stability of particle methods.
Geomechanics and Geoengineering, 2009
This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons wi... more This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the 'Common-Plane' method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.
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Papers by Soheil Mohammadi