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doc. Ing. Radek Kolman, Ph.D.

2023, Vol. 42 (2023): 18th Youth Symposium on Experimental Solid Mechanics, Praha, České vysoké učení technické v Praze), p. 6-11), ISBN 978-80-01-07237-0, ISSN 2336-5382

This contribution deals with an asynchronous direct time integration of the finite-element model. The proposed method is applied to the phenomenon of wave propagation through an elastic linear continuum. The numerical model is partitioned into individual subdomains using the domain decomposition method by means of localized Lagrange multipliers. For each subdomain, different time discretizations are used. No restrictions for relation between subdomain’s time steps are imposed. The coupling of the subdomains is forced by an acceleration continuity condition. Additionally, we use the a posteriori technique to also provide the displacement and velocity continuity at the interfaces, and hence we obtain exact continuity of all three kinematic fields. The proposed method is experimentally validated using the modified SHPB (split Hopkinson pressure bar) setup.

2023, Proceedings of the 9 th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Athens, Institute of Structural Analysis and Antiseismic Research, NTUA)

2023, Computer Methods in Applied Mechanics and Engineering, 413, p. 1-26), ISSN 1879-2138

The derivation and implementation of an asynchronous direct time integration scheme for domain-decomposed finite element models is presented. To maximize clarity in the description of the proposed asynchronous integration, the scheme is restricted to the linear-elastic stress wave propagation case. The proposed method allows the integration of individual subdomains with independent time steps. There is no requirement for an integer time steps ratio of the interacting domains while maintaining zero interface energy. The subdomains are connected by the condition of the continuity of the acceleration field at the interface. In addition, the a posteriori technique is applied to satisfy the continuity of the displacement and velocity fields. Another important contribution of this paper lies in the description of the implementation — we offer the reader a general description of the implementation of the case of any number of subdomains with any number of constraints between them, while the basics of the algorithm are explained on a single domain pair. The functionality of the asynchronous integrator is verified by solving selected problems and comparing with analytical solutions and experimental measurements obtained using a Split Hopkinson pressure bar setup. © 2023 Elsevier B.V.

2023, Wave Motion, 121, ISSN 0165-2125

This is a presentation of robust and accurate explicit time-stepping strategy for finite element modeling of elastic discontinuous wave propagation in strongly heterogeneous, multi-material and graded one-dimensional media. One of the major issues in FEM modeling is the existence of spurious numerical stress oscillations close to theoretical wave fronts due to temporal-spatial dispersion behavior of FE discretization. The numerical strategy presented for modeling of 1D discontinuous elastic waves is based on (a) pushforward-pullback local stepping — ensuring the elimination of dispersion due to different critical time step sizes of finite elements, (b) domain decomposition via localized Lagrange multipliers — to satisfy coupling kinematics and dynamic equations , (c) asynchronous time scheme — ensuring the correct information transfer of quantities for the case of integer ratios of time step size for all domain pairs. Dispersion behaviors, existence of spurious stress oscillations, and sensitivity of the dispersion to time step size are then suppressed. The proposed method is numerically tested with regard to the rectangular step pulse elastic propagation problem considering in-space varying Young’s modulus. To prove robustness and accuracy, a comparison with results from commercial software, an analytical solution, and experimental data from partial assembly of a split Hopkinson pressure bar (SHPB) setup is provided.

2023, Proceedings of the 1st Conference on INAM 2023, Jihlava, Vysoká škola polytechnická Jihlava)

2022, DD27 abstract book, Praha, CESKE VYSOKE UCENI TECHNICKE V PRAZE)

The problem of the linear elastodynamics including domain decomposition via localized Lagrange multipliers method is solved using nite element method and direct time integration. Time integration of domains is performed separately with dierent time steps. The asynchronous integrator scheme is generalized for multiple domains problem and enhanced by the use of a local variant of the pushforward-pullback method, which eectively avoids spurious oscillation in steep stress pulses response. The proposed method is applied to the rectangular step pulse propagation problem considering the linearly varying Young modulus in space as well as the bi-material interface problem. To prove the robustness and the accuracy, the comparison with analytical solution and commercial soft- ware outputs is provided.

2022, International Conference on Nonlinear Solid Mechanics, abstract book, International Research Center on Mathematics and Mechanics of Complex Systems), p. 35-35)

The problem of the linear elastodynamics including domain decomposition via localized La- grange multipliers method [2] is solved using finite element method and direct time integration. Time integration of domains is performed separately with different time steps with integer ra- tio. The known asynchronous integrator scheme [1] is generalized for multiple domains prob- lem and enhanced by the use of a local variant of the pushforward-pullback method, which effectively avoids spurious oscillation in steep stress pulses response. The proposed method is applied to the rectangular step pulse propagation problem considering the linearly varying Young modulus in space as well as the bi-material interface problem. To prove the robustness and the accuracy, the comparison with analytical solution and commercial software outputs is provided.

2022, International Conference on Nonlinear Solid Mechanics, abstract book, International Research Center on Mathematics and Mechanics of Complex Systems)

The problem of the linear elastodynamics including domain decomposition via localized Lagrange multipliers method [2] is solved using finite element method and direct time integration. Time integration of domains is performed separately with different time steps with integer ratio. The known asynchronous integrator scheme [1] is generalized for multiple domains problem and enhanced by the use of a local variant of the pushforward-pullback method, which effectively avoids spurious oscillation in steep stress pulses response. The proposed method is applied to the rectangular step pulse propagation problem considering the linearly varying Young modulus in space as well as the bi-material interface problem. To prove the robustness and the accuracy, the comparison with analytical solution and commercial software outputs is provided.