Timon Rabczuk

Bauhaus-University-Weimar, Faculty of Civil Engineering, Faculty Member

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Timon Rabczuk is professor of Computational Mechanics at Bauhaus University, Weimar, Germany. His major research area is Simulation Based Engineering Science and Computational Science. He is particularly interested in developing computational methods for the solution of partial differential equations (PDEs) and applying them to challenging problems in engineering and materials science such as the computational design of new materials, particularly composites, metamaterials and flexoelectric structures. One focus of his research is on computational methods for moving boundary/interface problems. He is also interested in machine learning solutions of PDEs such as PINNs, Deep Energy Methods, Physics Informed Neural Operators and diffusion models.

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Numerical integration over arbitrary surfaces in partition of unity finite elements

The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers

Icf13, Oct 22, 2013

The tensile and shear failure behavior dependence on chain length and temperature in amorphous po... more The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers are scrutinized using molecular dynamics simulations. A wide range chain length of alkane is tested under tension and shear with various temperatures. We find that the broken rate (the broken bond number to all polymer chain number ratios) under tension and shear increases with increasing chain length and temperature. For a given chain length and temperature, the broken rates under shear are always higher than those under tension at a same large strain. For a given chain length, the tensile and shear stresses decrease with increasing temperature. We propose three typical fracture mechanisms to effectively elucidate the ductile fracture response based on the predominance of chain scission process.

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Phonon Modes in Single-Walled Molybdenum Disulphide (MoS2) Nanotubes: Lattice Dynamics Calculation and Molecular Dynamics Simulation

We study the phonon modes in single-walled MoS$_{2}$ nanotubes via the lattice dynamics calculati... more We study the phonon modes in single-walled MoS$_{2}$ nanotubes via the lattice dynamics calculation and molecular dynamics simulation. The phonon spectra for tubes of arbitrary chiralities are calculated from the dynamical matrix constructed by the combination of an empirical potential with the conserved helical quantum numbers $(\kappa, n)$. In particular, we show that the frequency ($\omega$) of the radial breathing mode is inversely proportional to the tube diameter ($d$) as $\omega=665.3/d$ {cm$^{-1}$}. The eigen vectors of the first twenty lowest-frequency phonon modes are illustrated. Based on these eigen vectors, we demonstrate that the radial breathing oscillation is disturbed by phonon modes of three-fold symmetry initially, and the tube is squashed by the modes of two-fold symmetry eventually. Our study provides fundamental knowledge for further investigations of the thermal and mechanical properties of the MoS$_{2}$ nanotubes.

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On smoothed extended finite elements

Analysis of Reissner-Mindlin plates by iso-geometric finite element method

In this paper, non-uniform rational B-spline based iso-geometric finite element method is used to... more In this paper, non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on first order shear deformation plate theory. Two new techniques are proposed to avoid shear locking when the present formulation is applied to thin plates. The shear correction factors are evaluated employing the energy equivalence principle. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

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Smoothed extended finite element methods for modeling discontinuities

Composite structures yancheng ZHANG

A three-dimensional (3D) analytical solution is derived for homogeneous cylinder with the functio... more A three-dimensional (3D) analytical solution is derived for homogeneous cylinder with the functionally graded variation interphase (FGVI) at the inner surface. Based on the 3D solution, the dilute solution-based homogeneous model is adopted for the carbon nanotube (CNT)-reinforced nanocomposite considering FGVI and effective fibre modulus, in which the van der Waals-based cohesive law is adopted for the connection between CNT and the interphase. Parametric studies demonstrate that: (1) FGVI increases the composite stiffness, while it leads to the earlier debonding of the cohesive interface; (2) The peak strength of the macroscopic stress-strain is greatly influenced by the cohesive strength at the interface, higher cohesive strength leads to higher macroscopic peak strength. (3) The peak strength of the macroscopic stress-strain relation is underestimated without considering the effective fibre modulus, and the influence of the effective FGVI modulus is larger than that of the effective fibre; (4) CNTs of the large diameter bring the stress drop at a very small strain, especially for the large volume fraction of CNT. *

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ALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION

$Research paper thumbnail of Suppressing the need for meshing: Isogeometric Boundary Elements for linear-elastic fracture analysis$

Suppressing the need for meshing: Isogeometric Boundary Elements for linear-elastic fracture analysis

The interface strength and debonding for composite structures: Review and recent developments

Composite Structures, 2015

ABSTRACT

An adaptive continuum/discrete crack approach for meshfree particle methods

Latin American Journal of Solids and Structures

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Modelling cracks in meshfree methods

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

ABSTRACT

A Multiscale Model for the Quasi-Static Thermo-Plastic Behavior of Highly Cross-Linked Glassy Polymers

Macromolecules

We present experimentally validated molecular dynamics predictions of the quasistatic yield and p... more We present experimentally validated molecular dynamics predictions of the quasistatic yield and post-yield behavior for a highly cross-linked epoxy polymer under general stress states and for different temperatures. In addition, a hierarchical multiscale model is presented where the nano-scale simulations obtained from molecular dynamics were homogenized to a continuum thermoplastic constitutive model for the epoxy that can be used to describe the macroscopic behavior of the material.

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Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that inf... more Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation. We assume a transversely isotropic fashion at the macro-scale of dry woven fabric. This paper focuses on global sensitivity analysis; i.e. regression-and variance-based methods. The sensitivity of four meso-scale uncertain input parameters on the macro-scale response are investigated; i.e. the yarn height, the yarn spacing, the yarn width and the friction coefficient. The Pearson coefficients are adopted to measure the effect of each uncertain input variable on the structural response. Due to computational effectiveness, the sensitivity analysis is based on response surface models. The Sobol's variance-based method which consists of first-order and total-effect sensitivity indices are presented. The sensitivity analysis utilizes linear and quadratic correlation matrices, its corresponding correlation coefficients and the coefficients of determination of the response uncertainty criteria. The correlation analysis, the response surface model and Sobol's indices are presented and compared by means of uncertainty criteria influences on MataBerkait-dry woven fabric material properties. To anticipate, it is observed that the friction coefficient and yarn height are the most influential factors with respect to the specified macro-scale mechanical responses.

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A node-based smoothed finite element method (NS-FEM) for analysis of Reissner–Mindlin plates

Computational Mechanics

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular eleme... more In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.

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An alternative alpha finite element method (A$alpha$FEM) for free and forced vibration analysis of solid mechanics problems using triangular meshes

Journal of Computational and Applied Mathematics

An alternative alpha finite element method (Aαfem) free and forced vibration analysis of solids using triangular meshes

This paper presents a novel approach to modified a strain field of linear triangular FEM model wi... more This paper presents a novel approach to modified a strain field of linear triangular FEM model with an adjustable parameter α. Using meshes with the same aspect ratio, a preferable approach has been proposed to obtain a nearly exact solution in strain energy for linear problems. In this paper, it is extended to the free and forced analysis of two-dimensional dynamic for solid mechanics problems without increasing the computational cost. The numerical results show in AαFEM are more accurate results and higher convergence rates as compared to that of standard FEM when the same sets of nodes are used.

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On the Smoothed eXtended Finite Element Method for Continuum

Recovery-based error estimation in the dynamic analysis of offshore wind turbine monopile foundations

Computers and Geotechnics, 2015

Offshore wind turbine foundations are affected by cyclic loads due to oscillatory kinematic loads... more Offshore wind turbine foundations are affected by cyclic loads due to oscillatory kinematic loads, such as those from wind, waves, and earthquakes. Monopiles are often used as a foundation concept for offshore windmill turbines. In this study, coupled dynamic equations with the − formulation for low-frequency load are considered for an offshore wind turbine monopile foundation, to present the response in terms of pore water pressure (PWP), stress and strain distribution in an elastic porous medium at regions around the monopile foundation. Different stress recovery techniques based on the Zienkeiwicz-Zhu (ZZ) error estimator namely, super-convergent patch recovery (SPR), weighted super-convergent patch recovery (WSPR), and L 2 -projection techniques are also investigated to recover the stresses at nodal points in the finite element method. To estimate errors in the time domain when performing transient simulations, three recovery processes are used with different meshes. The convergence of the dynamic problem is also studied. The results are verified with findings in the literature, revealing that the time period of effective stresses follows the applied load frequency. In conclusion, the history of the shear stress can have an important effect on the shear stress distribution, making it asymmetric in the time domain.

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Timon Rabczuk

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