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A cell-based smoothed finite element method for three dimensional solid structures (2014)
Nguyen-Xuan, Hung ; Nguyen, Hiep Vinh ; Bordas, Stéphane Pierre Alain ; Rabczuk, Timon ; Duflot, Marc
This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation.
A comparative study of two molecular mechanics models based on harmonic potentials (2013)
Zhao, Jun-Hua ; Wang, L. ; Jiang, Jin-Wu ; Wang, Z. ; Guo, Wanlin ; Rabczuk, Timon
A comparative study of two molecular mechanics models based on harmonic potentials
A comparison of approximate response functions in structural reliability analysis (2008)
Bucher, Christian ; Most, Thomas
A comparison of approximate response functions in structural reliability analysis
A computational library for multiscale modeling of material failure (2014)
Talebi, Hossein ; Silani, Mohammad ; Bordas, Stéphane Pierre Alain ; Kerfriden, Pierre ; Rabczuk, Timon
A computational library for multiscale modeling of material failure
A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage (2014)
Zhuang, Xiaoying ; Huang, Runqiu ; Rabczuk, Timon ; Liang, C.
A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage
A dynamic XFEM formulation for crack identification (2016)
Zhang, Chao ; Wang, Cuixia ; Lahmer, Tom ; He, Pengfei ; Rabczuk, Timon
A dynamic XFEM formulation for crack identification
A four-node plane EAS-element for stochastic nonlinear materials (2003)
Brehm, Maik ; Most, Thomas
A four-node plane EAS-element for stochastic nonlinear materials
A Meshless Adaptive Multiscale Method for Fracture (2015)
Yang, Shih-Wei ; Budarapu, Pattabhi Ramaiah ; Mahapatra, D.R. ; Bordas, Stéphane Pierre Alain ; Zi, Goangseup ; Rabczuk, Timon
A Meshless Adaptive Multiscale Method for Fracture
A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions (2005)
Most, Thomas ; Bucher, Christian
A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions
A multigrid finite element method for the mesoscale analysis of concrete (2004)
Häfner, Stefan ; Könke, Carsten
A multigrid finite element method for the mesoscale analysis of concrete
A natural neighbour-based moving least-squares approach for the element-free Galerkin method (2007)
Most, Thomas
A natural neighbour-based moving least-squares approach for the element-free Galerkin method
A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates (2010)
Nguyen-Xuan, Hung ; Rabczuk, Timon ; Nguyen-Thanh, Nhon ; Nguyen-Thoi, T. ; Bordas, Stéphane Pierre Alain
A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates
A Novel Dynamic Multilevel Technique for Image Registration (2015)
Jia, Yue ; Zhang, Yongjie ; Rabczuk, Timon
A Novel Dynamic Multilevel Technique for Image Registration
A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses (2016)
Nguyen-Tuan, Long ; Lahmer, Tom ; Datcheva, Maria ; Stoimenova, Eugenia ; Schanz, Tom
A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses
A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics (2013)
Kerfriden, Pierre ; Goury, O. ; Rabczuk, Timon ; Bordas, Stéphane Pierre Alain
A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading (2003)
Döring, R. ; Hoffmeyer, J. ; Seeger, T. ; Vormwald, M.
A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading
A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites (2014)
Silani, Mohammad ; Ziaei-Rad, S. ; Talebi, Hossein ; Rabczuk, Timon
A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites
A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares (2015)
Areias, Pedro ; Rabczuk, Timon ; Cesar de Sa, J.M. ; Jorge, R.N.
A semi-implicit _nite strain shell algorithm using in-plane strains based on least-squares
A Short Crack Growth Model for the Prediction of Fatigue Lives under Multiaxial Nonproportional Loading (2001)
Döring, R. ; Hoffmeyer, J. ; Seeger, T. ; Vormwald, M.
A Short Crack Growth Model for the Prediction of Fatigue Lives under Multiaxial Nonproportional Loading
A simple circular cell method for multilevel finite element analysis (2012)
Talebi, Hossein ; Zi, Goangseup ; Silani, Mohammad ; Samaniego, Esteban ; Rabczuk, Timon
A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.
A smoothed finite element method for the static and free vibration analysis of shells (2010)
Nguyen-Thanh, Nhon ; Thai-Hoang, C. ; Nguyen-Xuan, Hung ; Rabczuk, Timon
A smoothed finite element method for the static and free vibration analysis of shells
A software framework for probabilistic sensitivity analysis for computationally expensive models (2016)
Vu-Bac, N. ; Lahmer, Tom ; Zhuang, Xiaoying ; Nguyen-Thoi, T. ; Rabczuk, Timon
A software framework for probabilistic sensitivity analysis for computationally expensive models
A Stillinger-Weber Potential for Single-Layer Black Phosphorus, and the Importance of Cross-Pucker Interactions for Negative Poisson's Ratio and Edge Stress-Induced Bending (2015)
Jiang, Jin-Wu ; Rabczuk, Timon ; Park, Harold S.
The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger–Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.
A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials (2016)
Ghorashi, Seyed Shahram ; Lahmer, Tom ; Bagherzadeh, Amir Saboor ; Zi, Goangseup ; Rabczuk, Timon
A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials
A Surface Stacking Fault Energy Approach to Predicting Defect Nucleation in Surface-Dominated Nanostructures (2013)
Jiang, Jin-Wu ; Park, Harold S. ; Gall, K. ; Leach, A. ; Rabczuk, Timon
A Surface Stacking Fault Energy Approach to Predicting Defect Nucleation in Surface-Dominated Nanostructures
A theoretical analysis of cohesive energy between carbon nanotubes, graphene and substrates (2014)
Zhao, Jun-Hua ; Jiang, Jin-Wu ; Jia, Yue ; Guo, Wanlin ; Rabczuk, Timon
Explicit solutions for the cohesive energy between carbon nanotubes, graphene and substrates are obtained through continuum modeling of the van der Waals interaction between them. The dependence of the cohesive energy on their size, spacing and crossing angles is analyzed. Checking against full atom molecular dynamics calculations and available experimental results shows that the continuum solution has high accuracy. The equilibrium distances between the nanotubes, graphene and substrates with minimum cohesive energy are also provided explicitly. The obtained analytical solution should be of great help for understanding the interaction between the nanostructures and substrates, and designing composites and nanoelectromechanical systems.
A three dimensional Extended Arlequin Method for Dynamic Fracture (2015)
Silani, Mohammad ; Talebi, Hossein ; Ziaei-Rad, S. ; Hamouda, A.M.S. ; Zi, Goangseup ; Rabczuk, Timon
A three dimensional Extended Arlequin Method for Dynamic Fracture
A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs) (2015)
Vu-Bac, N. ; Silani, Mohammad ; Lahmer, Tom ; Zhuang, Xiaoying ; Rabczuk, Timon
A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs)
ABAQUS implementation of phase_field model for brittle fracture (2015)
Msekh, Mohammed Abdulrazzak ; Sargado, M. ; Jamshidian, M. ; Areias, Pedro ; Rabczuk, Timon
ABAQUS implementation of phase_field model for brittle fracture
Acoustic and breathing phonon modes in bilayer graphene with Moire-acute patterns (2012)
Jiang, Jin-Wu ; Wang, Bing-Shen ; Rabczuk, Timon
The lattice dynamics properties are investigated for twisting bilayer graphene. There are big jumps for the inter-layer potential at twisting angle θ=0° and 60°, implying the stability of Bernal-stacking and the instability of AA-stacking structures, while a long platform in [8,55]° indicates the ease of twisting bilayer graphene in this wide angle range. Significant frequency shifts are observed for the z breathing mode around θ=0° and 60°, while the frequency is a constant in a wide range [8,55]°. Using the z breathing mode, a mechanical nanoresonator is proposed to operate on a robust resonant frequency in terahertz range.
Adaptation of the natural element method for crack growth simulations (2004)
Unger, Jörg F. ; Most, Thomas ; Bucher, Christian ; Könke, Carsten
Adaptation of the natural element method for crack growth simulations
Adaptive damage simulation of concrete using heterogeneous multiscale models (2008)
Eckardt, Stefan ; Könke, Carsten
Adaptive damage simulation of concrete using heterogeneous multiscale models
Adaptive excitation for selective sensitivity-based structural identification (2006)
Pham, Hoang Anh
Adaptive excitation for selective sensitivity-based structural identification
Adaptive multiscale methods for fracture (2015)
Budarapu, Pattabhi Ramaiah
One major research focus in the Material Science and Engineering Community in the past decade has been to obtain a more fundamental understanding on the phenomenon 'material failure'. Such an understanding is critical for engineers and scientists developing new materials with higher strength and toughness, developing robust designs against failure, or for those concerned with an accurate estimate of a component's design life. Defects like cracks and dislocations evolve at nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. In engineering applications, the global response of the system is often governed by the behaviour at the smaller length scales. Hence, the sub-scale behaviour must be computed accurately for good predictions of the full scale behaviour. Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. Since the atomistic dimensions are of the order of Angstroms ( A), approximately 85 billion atoms are required to model a 1 micro- m^3 volume of Copper. Therefore, pure atomistic models are prohibitively expensive with everyday engineering computations involving macroscopic cracks and shear bands, which are much larger than the atomistic length and time scales. To reduce the computational effort, multiscale methods are required, which are able to couple a continuum description of the structure with an atomistic description. In such paradigms, cracks and dislocations are explicitly modeled at the atomistic scale, whilst a self-consistent continuum model elsewhere. Many multiscale methods for fracture are developed for "fictitious" materials based on "simple" potentials such as the Lennard-Jones potential. Moreover, multiscale methods for evolving cracks are rare. Efficient methods to coarse grain the fine scale defects are missing. However, the existing multiscale methods for fracture do not adaptively adjust the fine scale domain as the crack propagates. Most methods, therefore only "enlarge" the fine scale domain and therefore drastically increase computational cost. Adaptive adjustment requires the fine scale domain to be refined and coarsened. One of the major difficulties in multiscale methods for fracture is to up-scale fracture related material information from the fine scale to the coarse scale, in particular for complex crack problems. Most of the existing approaches therefore were applied to examples with comparatively few macroscopic cracks. Key contributions The bridging scale method is enhanced using the phantom node method so that cracks can be modeled at the coarse scale. To ensure self-consistency in the bulk, a virtual atom cluster is devised providing the response of the intact material at the coarse scale. A molecular statics model is employed in the fine scale where crack propagation is modeled by naturally breaking the bonds. The fine scale and coarse scale models are coupled by enforcing the displacement boundary conditions on the ghost atoms. An energy criterion is used to detect the crack tip location. Adaptive refinement and coarsening schemes are developed and implemented during the crack propagation. The results were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale method is one of the first adaptive multiscale method for fracture. A robust and simple three dimensional coarse graining technique to convert a given atomistic region into an equivalent coarse region, in the context of multiscale fracture has been developed. The developed method is the first of its kind. The developed coarse graining technique can be applied to identify and upscale the defects like: cracks, dislocations and shear bands. The current method has been applied to estimate the equivalent coarse scale models of several complex fracture patterns arrived from the pure atomistic simulations. The upscaled fracture pattern agree well with the actual fracture pattern. The error in the potential energy of the pure atomistic and the coarse grained model was observed to be acceptable. A first novel meshless adaptive multiscale method for fracture has been developed. The phantom node method is replaced by a meshless differential reproducing kernel particle method. The differential reproducing kernel particle method is comparatively more expensive but allows for a more "natural" coupling between the two scales due to the meshless interpolation functions. The higher order continuity is also beneficial. The centro symmetry parameter is used to detect the crack tip location. The developed multiscale method is employed to study the complex crack propagation. Results based on the meshless adaptive multiscale method were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale methods are applied to study the fracture in practical materials like Graphene and Graphene on Silicon surface. The bond stretching and the bond reorientation were observed to be the net mechanisms of the crack growth in Graphene. The influence of time step on the crack propagation was studied using two different time steps. Pure atomistic simulations of fracture in Graphene on Silicon surface are presented. Details of the three dimensional multiscale method to study the fracture in Graphene on Silicon surface are discussed.
Adaptive response surface approach for reliability analysis using advanced meta-models (2007)
Most, Thomas ; Bucher, Christian
Adaptive response surface approach for reliability analysis using advanced meta-models
Adaptive response surface approach using artificial neural networks and Moving Least Squares (2006)
Most, Thomas ; Bucher, Christian
Adaptive response surface approach using artificial neural networks and Moving Least Squares
Adaptive Response Surfaces for Structural Reliability of Nonlinear Finite Element Structures (2003)
Roos, Dirk ; Bucher, Christian
Adaptive Response Surfaces for Structural Reliability of Nonlinear Finite Element Structures
Algorithms for structural identification and damage detection of steel-concrete composite bridges (2009)
De Roeck, G. ; Zabel, Volkmar ; Brehm, Maik ; Liu, K. ; Reynders, E.
Algorithms for structural identification and damage detection of steel-concrete composite bridges
Algorithms for vibration-based structural identification and damage detection (2010)
Zabel, Volkmar ; Brehm, Maik
Algorithms for vibration-based structural identification and damage detection
Ambient modal analysis and model updating of a twin composite filler beam railway bridge for high-speed trains with continuous ballast (2008)
Cantieni, Reto ; Brehm, Maik ; Zabel, Volkmar ; Rauert, T. ; Hoffmeister, B.
Ambient modal analysis and model updating of a twin composite filler beam railway bridge for high-speed trains with continuous ballast
Ambient Testing and Model Updating of a Filler Beam Bridge for High-Speed Trains (2008)
Cantieni, Reto ; Brehm, Maik ; Zabel, Volkmar ; Rauert, T. ; Hoffmeister, B.
Ambient Testing and Model Updating of a Filler Beam Bridge for High-Speed Trains
An adaptive multiscale method for quasi-static crack growth (2014)
Budarapu, Pattabhi Ramaiah ; Gracie, Robert ; Bordas, Stéphane Pierre Alain ; Rabczuk, Timon
This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom–atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.
An adaptive response surface approach for reliability analyses of high-dimensional problems (2008)
Most, Thomas
An adaptive response surface approach for reliability analyses of high-dimensional problems
An adaptive response surface approach for structural reliability analyses based on support vector machines (2007)
Most, Thomas
An adaptive response surface approach for structural reliability analyses based on support vector machines
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order (2013)
Nguyen-Xuan, Hung ; Liu, G.R. ; Bordas, Stéphane Pierre Alain ; Natarajan, S. ; Rabczuk, Timon
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics (2014)
Nguyen-Thanh, Nhon ; Muthu, Jacob ; Zhuang, Xiaoying ; Rabczuk, Timon
An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics
An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes (2009)
Nguyen-Thanh, Nhon ; Rabczuk, Timon ; Nguyen-Xuan, Hung ; Bordas, Stéphane Pierre Alain
An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes
An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates (2011)
Nguyen-Thanh, Nhon ; Rabczuk, Timon ; Nguyen-Xuan, Hung ; Bordas, Stéphane Pierre Alain
An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates
An alternative formulation for quasi-static frictional and cohesive contact problems (2014)
Areias, Pedro ; Pinto da Costa, A. ; Rabczuk, Timon ; Queiros de Melo, F. J. M. ; Dias-da-Costa, D.
An alternative formulation for quasi-static frictional and cohesive contact problems
An analytical molecular mechanics model for the elastic properties of crystalline polyethylene (2012)
Zhao, Jun-Hua ; Guo, Wanlin ; Rabczuk, Timon
We present an analytical model to relate the elastic properties of crystalline polyethylene based on a molecular mechanics approach. Along the polymer chains direction, the united-atom (UA) CH2-CH2 bond stretching, angle bending potentials are replaced with equivalent Euler-Bernoulli beams. Between any two polymer chains, the explicit formulae are derived for the van der Waals interaction represented by the linear springs of different stiffness. Then, the nine independent elastic constants are evaluated systematically using the formulae. The analytical model is finally validated by present united-atom molecular dynamics (MD) simulations and against available all-atom molecular dynamics results in the literature. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials.
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