@article{GuoAlajlanZhuangetal.,
  author    = {Guo, Hongwei and Alajlan, Naif and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials},
  series = {Computational Mechanics},
  volume    = {2023},
  journal   = {Computational Mechanics},
  publisher = {Springer},
  address   = {Berlin},
  doi       = {10.1007/s00466-023-02287-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230517-63666},
  pages     = {1 -- 12},
  abstract  = {We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge-Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge-Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.},
  subject      = {W{\"a}rme{\"u}bergang},
  language  = {en}
}
@article{RabczukZhuangOterkus,
  author    = {Rabczuk, Timon and Zhuang, Xiaoying and Oterkus, Erkan},
  title     = {Editorial: Computational modeling based on nonlocal theory},
  series = {Engineering with Computers},
  volume    = {2023},
  journal   = {Engineering with Computers},
  number    = {Volume 39, issue 3},
  publisher = {Springer},
  address   = {London},
  doi       = {https://doi.org/10.1007/s00366-022-01775-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230517-63658},
  pages     = {1},
  abstract  = {Nonlocal theories concern the interaction of objects, which are separated in space. Classical examples are Coulomb's law or Newton's law of universal gravitation. They had signficiant impact in physics and engineering. One classical application in mechanics is the failure of quasi-brittle materials. While local models lead to an ill-posed boundary value problem and associated mesh dependent results, nonlocal models guarantee the well-posedness and are furthermore relatively easy to implement into commercial computational software.},
  subject      = {Computersimulation},
  language  = {en}
}
@article{GuoZhuangChenetal.,
  author    = {Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif and Rabczuk, Timon},
  title     = {Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-022-01633-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46764},
  pages     = {1 -- 22},
  abstract  = {In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.},
  subject      = {Deep learning},
  language  = {en}
}
@article{ChakrabortyAnitescuZhuangetal.,
  author    = {Chakraborty, Ayan and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Domain adaptation based transfer learning approach for solving PDEs on complex geometries},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-022-01661-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46776},
  pages     = {1 -- 20},
  abstract  = {In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.},
  subject      = {Maschinelles Lernen},
  language  = {en}
}
@article{RabczukGuoZhuangetal.,
  author    = {Rabczuk, Timon and Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif},
  title     = {Stochastic deep collocation method based on neural architecture search and transfer learning for heterogeneous porous media},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  publisher = {Springer},
  address   = {London},
  doi       = {10.1007/s00366-021-01586-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45835},
  pages     = {1 -- 26},
  abstract  = {We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.},
  subject      = {Maschinelles Lernen},
  language  = {en}
}
@article{RenZhuangOterkusetal.,
  author    = {Ren, Huilong and Zhuang, Xiaoying and Oterkus, Erkan and Zhu, Hehua and Rabczuk, Timon},
  title     = {Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method},
  series = {Engineering with Computers},
  volume    = {2021},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-021-01502-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20211207-45388},
  pages     = {1 -- 22},
  abstract  = {The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.},
  subject      = {Bruchmechanik},
  language  = {en}
}
@article{NooriMortazaviKeshtkarietal.,
  author    = {Noori, Hamidreza and Mortazavi, Bohayra and Keshtkari, Leila and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Nanopore creation in MoS2 and graphene monolayers by nanoparticles impact: a reactive molecular dynamics study},
  series = {Applied Physics A},
  volume    = {2021},
  journal   = {Applied Physics A},
  number    = {volume 127, article 541},
  publisher = {Springer},
  address   = {Heidelberg},
  doi       = {10.1007/s00339-021-04693-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44756},
  pages     = {1 -- 13},
  abstract  = {In this work, extensive reactive molecular dynamics simulations are conducted to analyze the nanopore creation by nano-particles impact over single-layer molybdenum disulfide (MoS2) with 1T and 2H phases. We also compare the results with graphene monolayer. In our simulations, nanosheets are exposed to a spherical rigid carbon projectile with high initial velocities ranging from 2 to 23 km/s. Results for three different structures are compared to examine the most critical factors in the perforation and resistance force during the impact. To analyze the perforation and impact resistance, kinetic energy and displacement time history of the projectile as well as perforation resistance force of the projectile are investigated. Interestingly, although the elasticity module and tensile strength of the graphene are by almost five times higher than those of MoS2, the results demonstrate that 1T and 2H-MoS2 phases are more resistive to the impact loading and perforation than graphene. For the MoS2nanosheets, we realize that the 2H phase is more resistant to impact loading than the 1T counterpart. Our reactive molecular dynamics results highlight that in addition to the strength and toughness, atomic structure is another crucial factor that can contribute substantially to impact resistance of 2D materials. The obtained results can be useful to guide the experimental setups for the nanopore creation in MoS2or other 2D lattices.},
  subject      = {Nanomechanik},
  language  = {en}
}
@article{FaizollahzadehArdabiliNajafiAlizamiretal.,
  author    = {Faizollahzadeh Ardabili, Sina and Najafi, Bahman and Alizamir, Meysam and Mosavi, Amir and Shamshirband, Shahaboddin and Rabczuk, Timon},
  title     = {Using SVM-RSM and ELM-RSM Approaches for Optimizing the Production Process of Methyl and Ethyl Esters},
  series = {Energies},
  journal   = {Energies},
  number    = {11, 2889},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/en11112889},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20181025-38170},
  pages     = {1 -- 20},
  abstract  = {The production of a desired product needs an effective use of the experimental model. The present study proposes an extreme learning machine (ELM) and a support vector machine (SVM) integrated with the response surface methodology (RSM) to solve the complexity in optimization and prediction of the ethyl ester and methyl ester production process. The novel hybrid models of ELM-RSM and ELM-SVM are further used as a case study to estimate the yield of methyl and ethyl esters through a trans-esterification process from waste cooking oil (WCO) based on American Society for Testing and Materials (ASTM) standards. The results of the prediction phase were also compared with artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS), which were recently developed by the second author of this study. Based on the results, an ELM with a correlation coefficient of 0.9815 and 0.9863 for methyl and ethyl esters, respectively, had a high estimation capability compared with that for SVM, ANNs, and ANFIS. Accordingly, the maximum production yield was obtained in the case of using ELM-RSM of 96.86\% for ethyl ester at a temperature of 68.48 °C, a catalyst value of 1.15 wt. \%, mixing intensity of 650.07 rpm, and an alcohol to oil molar ratio (A/O) of 5.77; for methyl ester, the production yield was 98.46\% at a temperature of 67.62 °C, a catalyst value of 1.1 wt. \%, mixing intensity of 709.42 rpm, and an A/O of 6.09. Therefore, ELM-RSM increased the production yield by 3.6\% for ethyl ester and 3.1\% for methyl ester, compared with those for the experimental data.},
  subject      = {Biodiesel},
  language  = {en}
}
@article{MosaviNajafiFaizollahzadehArdabilietal.,
  author    = {Mosavi, Amir and Najafi, Bahman and Faizollahzadeh Ardabili, Sina and Shamshirband, Shahaboddin and Rabczuk, Timon},
  title     = {An Intelligent Artificial Neural Network-Response Surface Methodology Method for Accessing the Optimum Biodiesel and Diesel Fuel Blending Conditions in a Diesel Engine from the Viewpoint of Exergy and Energy Analysis},
  series = {Energies},
  volume    = {2018},
  journal   = {Energies},
  number    = {11, 4},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/en11040860},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20180507-37467},
  pages     = {18},
  abstract  = {Biodiesel, as the main alternative fuel to diesel fuel which is produced from renewable and available resources, improves the engine emissions during combustion in diesel engines. In this study, the biodiesel is produced initially from waste cooking oil (WCO). The fuel samples are applied in a diesel engine and the engine performance has been considered from the viewpoint of exergy and energy approaches. Engine tests are performed at a constant 1500 rpm speed with various loads and fuel samples. The obtained experimental data are also applied to develop an artificial neural network (ANN) model. Response surface methodology (RSM) is employed to optimize the exergy and energy efficiencies. Based on the results of the energy analysis, optimal engine performance is obtained at 80\% of full load in presence of B10 and B20 fuels. However, based on the exergy analysis results, optimal engine performance is obtained at 80\% of full load in presence of B90 and B100 fuels. The optimum values of exergy and energy efficiencies are in the range of 25-30\% of full load, which is the same as the calculated range obtained from mathematical modeling.},
  subject      = {Biodiesel},
  language  = {en}
}
@article{NanthakumarLahmerRabczuk,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Detection of flaws in piezoelectric structures using extended FEM},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  pages     = {373 -- 389},
  abstract  = {Detection of flaws in piezoelectric structures using extended FEM},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{VuBacRafieeZhuangetal.,
  author    = {Vu-Bac, N. and Rafiee, Roham and Zhuang, Xiaoying and Lahmer, Tom and Rabczuk, Timon},
  title     = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters},
  series = {Composites Part B: Engineering},
  journal   = {Composites Part B: Engineering},
  pages     = {446 -- 464},
  abstract  = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhangWangLahmeretal.,
  author    = {Zhang, Chao and Wang, Cuixia and Lahmer, Tom and He, Pengfei and Rabczuk, Timon},
  title     = {A dynamic XFEM formulation for crack identification},
  series = {International Journal of Mechanics and Materials in Design},
  journal   = {International Journal of Mechanics and Materials in Design},
  pages     = {427 -- 448},
  abstract  = {A dynamic XFEM formulation for crack identification},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{VuBacLahmerZhuangetal.,
  author    = {Vu-Bac, N. and Lahmer, Tom and Zhuang, Xiaoying and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {A software framework for probabilistic sensitivity analysis for computationally expensive models},
  series = {Advances in Engineering Software},
  journal   = {Advances in Engineering Software},
  pages     = {19 -- 31},
  abstract  = {A software framework for probabilistic sensitivity analysis for computationally expensive models},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerZhuangetal.,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Park, Harold S. and Rabczuk, Timon},
  title     = {Topology optimization of piezoelectric nanostructures},
  series = {Journal of the Mechanics and Physics of Solids},
  journal   = {Journal of the Mechanics and Physics of Solids},
  pages     = {316 -- 335},
  abstract  = {Topology optimization of piezoelectric nanostructures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerZhuangetal.,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Zi, Goangseup and Rabczuk, Timon},
  title     = {Detection of material interfaces using a regularized level set method in piezoelectric structures},
  series = {Inverse Problems in Science and Engineering},
  journal   = {Inverse Problems in Science and Engineering},
  pages     = {153 -- 176},
  abstract  = {Detection of material interfaces using a regularized level set method in piezoelectric structures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerRabczuk,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  pages     = {960},
  abstract  = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{GhorashiLahmerBagherzadehetal.,
  author    = {Ghorashi, Seyed Shahram and Lahmer, Tom and Bagherzadeh, Amir Saboor and Zi, Goangseup and Rabczuk, Timon},
  title     = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials},
  series = {Engineering Geology},
  journal   = {Engineering Geology},
  abstract  = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhangNanthakumarLahmeretal.,
  author    = {Zhang, Chao and Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Multiple cracks identification for piezoelectric structures},
  series = {International Journal of Fracture},
  journal   = {International Journal of Fracture},
  pages     = {1 -- 19},
  abstract  = {Multiple cracks identification for piezoelectric structures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThanhRabczukNguyenXuanetal.,
  author    = {Nguyen-Thanh, Nhon and Rabczuk, Timon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain},
  title     = {An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes},
  series = {Journal of Computational and Applied Mathematics},
  journal   = {Journal of Computational and Applied Mathematics},
  pages     = {2112 -- 2135},
  abstract  = {An alternative alpha finite element method (A?FEM) free and forced vibration analysis of solids using triangular meshes},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenXuanRabczukNguyenThanhetal.,
  author    = {Nguyen-Xuan, Hung and Rabczuk, Timon and Nguyen-Thanh, Nhon and Nguyen-Thoi, T. and Bordas, St{\´e}phane Pierre Alain},
  title     = {A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates},
  series = {Computational Mechanics},
  journal   = {Computational Mechanics},
  pages     = {679 -- 701},
  abstract  = {A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThanhThaiHoangNguyenXuanetal.,
  author    = {Nguyen-Thanh, Nhon and Thai-Hoang, C. and Nguyen-Xuan, Hung and Rabczuk, Timon},
  title     = {A smoothed finite element method for the static and free vibration analysis of shells},
  series = {Journal of Civil Engineering and Architecture},
  journal   = {Journal of Civil Engineering and Architecture},
  pages     = {13 -- 25},
  abstract  = {A smoothed finite element method for the static and free vibration analysis of shells},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThanhRabczukNguyenXuanetal.,
  author    = {Nguyen-Thanh, Nhon and Rabczuk, Timon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain},
  title     = {An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates},
  series = {Finite Elements in Analysis \& Design},
  journal   = {Finite Elements in Analysis \& Design},
  pages     = {519 -- 535},
  abstract  = {An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThanhNguyenXuanBordasetal.,
  author    = {Nguyen-Thanh, Nhon and Nguyen-Xuan, Hung and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon},
  title     = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {1892 -- 1908},
  abstract  = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThanhKiendlNguyenXuanetal.,
  author    = {Nguyen-Thanh, Nhon and Kiendl, J. and Nguyen-Xuan, Hung and W{\"u}chner, R. and Bletzinger, Kai-Uwe and Bazilevs, Yuri and Rabczuk, Timon},
  title     = {Rotation free isogeometric thin shell analysis using PHT-splines},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {3410 -- 3424},
  abstract  = {Rotation free isogeometric thin shell analysis using PHT-splines},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{SimpsonBordasTrevelyanetal.,
  author    = {Simpson, R. and Bordas, St{\´e}phane Pierre Alain and Trevelyan, J. and Kerfriden, Pierre and Rabczuk, Timon},
  title     = {An Isogeometric Boundary Element Method for elastostatic analysis},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  doi       = {10.1016/j.cma.2011.08.008},
  abstract  = {The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ChauDinhZiLeeetal.,
  author    = {Chau-Dinh, T. and Zi, Goangseup and Lee, P.S. and Song, Jeong-Hoon and Rabczuk, Timon},
  title     = {Phantom-node method for shell models with arbitrary cracks},
  series = {Computers \& Structures},
  journal   = {Computers \& Structures},
  doi       = {10.1016/j.compstruc.2011.10.021},
  abstract  = {A phantom-node method is developed for three-node shell elements to describe cracks. This method can treat arbitrary cracks independently of the mesh. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Several numerical examples are presented to illustrate the proposed method.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{TalebiSamaniegoSamaniegoetal.,
  author    = {Talebi, Hossein and Samaniego, C. and Samaniego, Esteban and Rabczuk, Timon},
  title     = {On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  doi       = {10.1002/nme.3275},
  pages     = {1009 -- 1027},
  abstract  = {Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ChenRabczukLiuetal.,
  author    = {Chen, Lei and Rabczuk, Timon and Liu, G.R. and Zeng, K.Y. and Kerfriden, Pierre and Bordas, St{\´e}phane Pierre Alain},
  title     = {Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  doi       = {10.1016/j.cma.2011.08.013},
  abstract  = {This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenXuanRabczukNguyenThoietal.,
  author    = {Nguyen-Xuan, Hung and Rabczuk, Timon and Nguyen-Thoi, T. and Tran, T. and Nguyen-Thanh, Nhon},
  title     = {Computation of limit and shakedown loads using a node-based smoothed finite element method},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  doi       = {10.1002/nme.3317},
  pages     = {287 -- 310},
  abstract  = {This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal-dual algorithm. An associated primal-dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal-dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczukDiasdaCostaetal.,
  author    = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D. and Piresh, E.B.},
  title     = {Implicit solutions with consistent additive and multiplicative components},
  series = {Finite Elements in Analysis and Design},
  journal   = {Finite Elements in Analysis and Design},
  doi       = {10.1016/j.finel.2012.03.007},
  pages     = {15 -- 31},
  abstract  = {This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudo-elements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{JiangZhaoZhouetal.,
  author    = {Jiang, Jin-Wu and Zhao, Jun-Hua and Zhou, K. and Rabczuk, Timon},
  title     = {Superior thermal conductivity and extremely high mechanical strength in polyethylene chains from ab initio calculation},
  series = {Journal of Applied Physics},
  journal   = {Journal of Applied Physics},
  doi       = {10.1063/1.4729489},
  abstract  = {The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the ab initio calculation and applying the quantum mechanical non-equilibrium Green's function approach. Specially, there are two main findings from our calculation: (1) the thermal conductivity can reach a high value of 310 Wm-1 K-1 in a 100 nm polyethylene chain at room temperature and the thermal conductivity increases with the length of the chain; (2) the Young's modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain 32.85\%±0.05\% (ultimate) strain before undergoing structural phase transition into gaseous ethylene.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{JiangWangRabczuk,
  author    = {Jiang, Jin-Wu and Wang, Bing-Shen and Rabczuk, Timon},
  title     = {Acoustic and breathing phonon modes in bilayer graphene with Moire-acute patterns},
  series = {Applied Physics Letters},
  journal   = {Applied Physics Letters},
  doi       = {10.1063/1.4735246},
  abstract  = {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.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{TalebiZiSilanietal.,
  author    = {Talebi, Hossein and Zi, Goangseup and Silani, Mohammad and Samaniego, Esteban and Rabczuk, Timon},
  title     = {A simple circular cell method for multilevel finite element analysis},
  series = {Journal of Applied Mathematics},
  journal   = {Journal of Applied Mathematics},
  doi       = {10.1155/2012/526846},
  abstract  = {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.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenVinhBakarMsekhetal.,
  author    = {Nguyen-Vinh, H. and Bakar, I. and Msekh, Mohammed Abdulrazzak and Song, Jeong-Hoon and Muthu, Jacob and Zi, Goangseup and Le, P. and Bordas, St{\´e}phane Pierre Alain and Simpson, R. and Natarajan, S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Extended Finite Element Method for Dynamic Fracture of Piezo-Electric Materials},
  series = {Engineering Fracture Mechanics},
  journal   = {Engineering Fracture Mechanics},
  doi       = {10.1016/j.engfracmech.2012.04.025},
  pages     = {19 -- 31},
  abstract  = {We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NatarajanChakrabortyThangaveletal.,
  author    = {Natarajan, S. and Chakraborty, S. and Thangavel, M. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon},
  title     = {Size dependent free flexural vibration behavior of functionally graded nanoplates},
  series = {Computational Materials Science},
  journal   = {Computational Materials Science},
  pages     = {74 -- 80},
  abstract  = {Size dependent free flexural vibration behavior of functionally graded nanoplates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ThaiNguyenXuanNguyenThanhetal.,
  author    = {Thai, Chien H. and Nguyen-Xuan, Hung and Nguyen-Thanh, Nhon and Le, T.H. and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {Static, free vibration and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  doi       = {10.1002/nme.4282},
  pages     = {571 -- 603},
  abstract  = {This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoGuoRabczuk,
  author    = {Zhao, Jun-Hua and Guo, Wanlin and Rabczuk, Timon},
  title     = {An analytical molecular mechanics model for the elastic properties of crystalline polyethylene},
  series = {Journal of Applied Physics},
  journal   = {Journal of Applied Physics},
  doi       = {10.1063/1.4745035},
  abstract  = {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.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{JiangParkRabczuk,
  author    = {Jiang, Jin-Wu and Park, Harold S. and Rabczuk, Timon},
  title     = {Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism},
  series = {Nanotechnology},
  journal   = {Nanotechnology},
  abstract  = {Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenXuanLiuBordasetal.,
  author    = {Nguyen-Xuan, Hung and Liu, G.R. and Bordas, St{\´e}phane Pierre Alain and Natarajan, S. and Rabczuk, Timon},
  title     = {An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {252 -- 273},
  abstract  = {An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhangZhaoWeietal.,
  author    = {Zhang, Yancheng and Zhao, Jiyun and Wei, Ning and Jiang, Jin-Wu and Rabczuk, Timon},
  title     = {Effects of the dispersion of polymer wrapped two neighbouring single walled carbon nanotubes (SWNTs) on nanoengineering load transfer},
  series = {Composites Part B: Engineering},
  journal   = {Composites Part B: Engineering},
  pages     = {1714 -- 1721},
  abstract  = {Effects of the dispersion of polymer wrapped two neighbouring single walled carbon nanotubes (SWNTs) on nanoengineering load transfer},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AreiasRabczukDiasdaCosta,
  author    = {Areias, Pedro and Rabczuk, Timon and Dias-da-Costa, D.},
  title     = {Assumed-metric spherically-interpolated quadrilateral shell element},
  series = {Finite Elements in Analysis and Design},
  journal   = {Finite Elements in Analysis and Design},
  pages     = {53 -- 67},
  abstract  = {Assumed-metric spherically-interpolated quadrilateral shell element},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ValizadehNatarajanGonzalezEstradaetal.,
  author    = {Valizadeh, Navid and Natarajan, S. and Gonzalez-Estrada, O.A. and Rabczuk, Timon and Tinh Quoc, Bui and Bordas, St{\´e}phane Pierre Alain},
  title     = {NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter},
  series = {Composite Structures},
  journal   = {Composite Structures},
  pages     = {309 -- 326},
  abstract  = {NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{KerfridenGouryRabczuketal.,
  author    = {Kerfriden, Pierre and Goury, O. and Rabczuk, Timon and Bordas, St{\´e}phane Pierre Alain},
  title     = {A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics},
  series = {Computer Methods in Applied Mechanics and Engineering},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  pages     = {169 -- 188},
  abstract  = {A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoWeiFanetal.,
  author    = {Zhao, Jun-Hua and Wei, Ning and Fan, Z. and Jiang, Jin-Wu and Rabczuk, Timon},
  title     = {Mechanical properties of three types of carbon allotropes},
  series = {Nanotechnology},
  journal   = {Nanotechnology},
  abstract  = {Mechanical properties of three types of carbon allotropes},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhaoWangJiangetal.,
  author    = {Zhao, Jun-Hua and Wang, L. and Jiang, Jin-Wu and Wang, Z. and Guo, Wanlin and Rabczuk, Timon},
  title     = {A comparative study of two molecular mechanics models based on harmonic potentials},
  series = {Journal of Applied Physics},
  journal   = {Journal of Applied Physics},
  abstract  = {A comparative study of two molecular mechanics models based on harmonic potentials},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{BakarKramerBordasetal.,
  author    = {Bakar, I. and Kramer, O. and Bordas, St{\´e}phane Pierre Alain and Rabczuk, Timon},
  title     = {Optimization of Elastic Properties and Weaving Patterns of Woven Composites},
  series = {Composite Structures},
  journal   = {Composite Structures},
  pages     = {575 -- 591},
  abstract  = {Optimization of Elastic Properties and Weaving Patterns of Woven Composites},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{PhanDaoNguyenXuanThaiHoangetal.,
  author    = {Phan-Dao, H. and Nguyen-Xuan, Hung and Thai-Hoang, C. and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {An edge-based smoothed finite element method for analysis of laminated composite plates},
  series = {International Journal of Computational Methods},
  journal   = {International Journal of Computational Methods},
  abstract  = {An edge-based smoothed finite element method for analysis of laminated composite plates},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThoiPhungVanRabczuketal.,
  author    = {Nguyen-Thoi, T. and Phung-Van, P. and Rabczuk, Timon and Nguyen-Xuan, Hung and Le-Van, C.},
  title     = {An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems},
  series = {International Journal of Computational Methods},
  journal   = {International Journal of Computational Methods},
  abstract  = {An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{LeNguyenXuanAskesetal.,
  author    = {Le, C.V. and Nguyen-Xuan, Hung and Askes, H. and Rabczuk, Timon and Nguyen-Thoi, T.},
  title     = {Computation of limit load using edge-based smoothed finite element method and second-order cone programming},
  series = {International Journal of Computational Methods},
  journal   = {International Journal of Computational Methods},
  abstract  = {Computation of limit load using edge-based smoothed finite element method and second-order cone programming},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenThoiPhungVanRabczuketal.,
  author    = {Nguyen-Thoi, T. and Phung-Van, P. and Rabczuk, Timon and Nguyen-Xuan, Hung and Le-Van, C.},
  title     = {Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)},
  series = {International Journal of Computational Methods},
  journal   = {International Journal of Computational Methods},
  abstract  = {Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)},
  subject      = {Angewandte Mathematik},
  language  = {en}
}