[{"type":"journal_article","publication":"Computational Mechanics","abstract":[{"lang":"eng","text":"ELDIRK methods are defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge-Kutta</jats:italic> methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes,  e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability."}],"status":"public","_id":"52233","user_id":"335","department":[{"_id":"154"},{"_id":"321"}],"keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"language":[{"iso":"eng"}],"publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0178-7675","1432-0924"]},"year":"2024","citation":{"chicago":"Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit Last-Stage Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>, 2024. <a href=\"https://doi.org/10.1007/s00466-024-02442-y\">https://doi.org/10.1007/s00466-024-02442-y</a>.","ieee":"R. Mahnken and H. Westermann, “Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods,” <i>Computational Mechanics</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>.","ama":"Mahnken R, Westermann H. Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>","apa":"Mahnken, R., &#38; Westermann, H. (2024). Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>. <a href=\"https://doi.org/10.1007/s00466-024-02442-y\">https://doi.org/10.1007/s00466-024-02442-y</a>","bibtex":"@article{Mahnken_Westermann_2024, title={Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}, DOI={<a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf and Westermann, Hendrik}, year={2024} }","mla":"Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit Last-Stage Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00466-024-02442-y\">10.1007/s00466-024-02442-y</a>.","short":"R. Mahnken, H. Westermann, Computational Mechanics (2024)."},"date_updated":"2024-03-19T12:14:07Z","publisher":"Springer Science and Business Media LLC","author":[{"last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf","first_name":"Rolf"},{"last_name":"Westermann","orcid":"0000-0002-5034-9708","full_name":"Westermann, Hendrik","id":"60816","first_name":"Hendrik"}],"date_created":"2024-03-03T13:23:28Z","title":"Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods","doi":"10.1007/s00466-024-02442-y"},{"_id":"48465","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"article_number":"116545","type":"journal_article","status":"public","date_updated":"2023-11-07T14:34:56Z","author":[{"last_name":"Westermann","orcid":"0000-0002-5034-9708","full_name":"Westermann, Hendrik","id":"60816","first_name":"Hendrik"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"volume":418,"doi":"10.1016/j.cma.2023.116545","publication_status":"published","publication_identifier":{"issn":["0045-7825"]},"citation":{"ieee":"H. Westermann and R. Mahnken, “On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems,” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 418, Art. no. 116545, 2023, doi: <a href=\"https://doi.org/10.1016/j.cma.2023.116545\">10.1016/j.cma.2023.116545</a>.","chicago":"Westermann, Hendrik, and Rolf Mahnken. “On the Accuracy, Stability and Computational Efficiency of Explicit Last-Stage Diagonally Implicit Runge–Kutta Methods (ELDIRK) for the Adaptive Solution of Phase-Field Problems.” <i>Computer Methods in Applied Mechanics and Engineering</i> 418 (2023). <a href=\"https://doi.org/10.1016/j.cma.2023.116545\">https://doi.org/10.1016/j.cma.2023.116545</a>.","ama":"Westermann H, Mahnken R. On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems. <i>Computer Methods in Applied Mechanics and Engineering</i>. 2023;418. doi:<a href=\"https://doi.org/10.1016/j.cma.2023.116545\">10.1016/j.cma.2023.116545</a>","apa":"Westermann, H., &#38; Mahnken, R. (2023). On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems. <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>418</i>, Article 116545. <a href=\"https://doi.org/10.1016/j.cma.2023.116545\">https://doi.org/10.1016/j.cma.2023.116545</a>","short":"H. Westermann, R. Mahnken, Computer Methods in Applied Mechanics and Engineering 418 (2023).","mla":"Westermann, Hendrik, and Rolf Mahnken. “On the Accuracy, Stability and Computational Efficiency of Explicit Last-Stage Diagonally Implicit Runge–Kutta Methods (ELDIRK) for the Adaptive Solution of Phase-Field Problems.” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 418, 116545, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.cma.2023.116545\">10.1016/j.cma.2023.116545</a>.","bibtex":"@article{Westermann_Mahnken_2023, title={On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems}, volume={418}, DOI={<a href=\"https://doi.org/10.1016/j.cma.2023.116545\">10.1016/j.cma.2023.116545</a>}, number={116545}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Westermann, Hendrik and Mahnken, Rolf}, year={2023} }"},"intvolume":"       418","keyword":["Computer Science Applications","General Physics and Astronomy","Mechanical Engineering","Mechanics of Materials","Computational Mechanics"],"language":[{"iso":"eng"}],"publication":"Computer Methods in Applied Mechanics and Engineering","publisher":"Elsevier BV","date_created":"2023-10-25T10:47:23Z","title":"On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems","quality_controlled":"1","year":"2023"},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"45757","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Three prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge–Kutta</jats:italic> (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown.\r\n</jats:p>","lang":"eng"}],"type":"journal_article","publication":"Computational Mechanics","doi":"10.1007/s00466-023-02347-2","title":"Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation","author":[{"id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"}],"date_created":"2023-06-23T06:47:36Z","date_updated":"2023-06-23T06:48:42Z","publisher":"Springer Science and Business Media LLC","citation":{"mla":"Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.” <i>Computational Mechanics</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>.","short":"R. Mahnken, Computational Mechanics (2023).","bibtex":"@article{Mahnken_2023, title={Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}, DOI={<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf}, year={2023} }","apa":"Mahnken, R. (2023). Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation. <i>Computational Mechanics</i>. <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">https://doi.org/10.1007/s00466-023-02347-2</a>","ama":"Mahnken R. Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation. <i>Computational Mechanics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>","ieee":"R. Mahnken, “Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation,” <i>Computational Mechanics</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>.","chicago":"Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.” <i>Computational Mechanics</i>, 2023. <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">https://doi.org/10.1007/s00466-023-02347-2</a>."},"year":"2023","publication_status":"published","publication_identifier":{"issn":["0178-7675","1432-0924"]},"quality_controlled":"1"},{"keyword":["Mechanical Engineering","Computational Mechanics"],"language":[{"iso":"eng"}],"publication":"Acta Mechanica","abstract":[{"text":"Galvanic corrosion is a destructive process between dissimilar metals. The present paper presents a constructed numerical test case to simulate galvanic corrosion of two dissimilar metals. This test case is used to study the accuracy of different implementations to track the dissolving anode boundary. One technique is to numerically simulate a mesh displacement based on the prescribed displacement at the anode boundary. The second method is to adjust only the boundary elements. Re-meshing after a certain number of time steps is applied to both implementations. They produce similar results for an electrical and electrochemical field problem. This work shows that mesh smoothing does not result in higher accuracy when modeling a moving anode front. Adjusting only the boundary elements is sufficient when frequent re-meshing is used.","lang":"eng"}],"publisher":"Springer Science and Business Media LLC","date_created":"2022-12-06T20:47:16Z","title":"Comparison of two mesh-moving techniques for finite element simulations of galvanic corrosion","issue":"11","year":"2022","_id":"34257","project":[{"grant_number":"418701707","_id":"130","name":"TRR 285: TRR 285"},{"name":"TRR 285 – B03: TRR 285 - Subproject B03","_id":"142"}],"department":[{"_id":"630"}],"user_id":"14931","type":"journal_article","status":"public","date_updated":"2023-01-02T11:07:28Z","oa":"1","volume":233,"author":[{"first_name":"Sven","last_name":"Harzheim","full_name":"Harzheim, Sven"},{"full_name":"Hofmann, Martin","last_name":"Hofmann","first_name":"Martin"},{"first_name":"Thomas","last_name":"Wallmersperger","full_name":"Wallmersperger, Thomas"}],"doi":"10.1007/s00707-022-03326-z","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00707-022-03326-z","open_access":"1"}],"publication_identifier":{"issn":["0001-5970","1619-6937"]},"publication_status":"published","intvolume":"       233","page":"4427-4439","citation":{"chicago":"Harzheim, Sven, Martin Hofmann, and Thomas Wallmersperger. “Comparison of Two Mesh-Moving Techniques for Finite Element Simulations of Galvanic Corrosion.” <i>Acta Mechanica</i> 233, no. 11 (2022): 4427–39. <a href=\"https://doi.org/10.1007/s00707-022-03326-z\">https://doi.org/10.1007/s00707-022-03326-z</a>.","ieee":"S. Harzheim, M. Hofmann, and T. Wallmersperger, “Comparison of two mesh-moving techniques for finite element simulations of galvanic corrosion,” <i>Acta Mechanica</i>, vol. 233, no. 11, pp. 4427–4439, 2022, doi: <a href=\"https://doi.org/10.1007/s00707-022-03326-z\">10.1007/s00707-022-03326-z</a>.","ama":"Harzheim S, Hofmann M, Wallmersperger T. Comparison of two mesh-moving techniques for finite element simulations of galvanic corrosion. <i>Acta Mechanica</i>. 2022;233(11):4427-4439. doi:<a href=\"https://doi.org/10.1007/s00707-022-03326-z\">10.1007/s00707-022-03326-z</a>","apa":"Harzheim, S., Hofmann, M., &#38; Wallmersperger, T. (2022). Comparison of two mesh-moving techniques for finite element simulations of galvanic corrosion. <i>Acta Mechanica</i>, <i>233</i>(11), 4427–4439. <a href=\"https://doi.org/10.1007/s00707-022-03326-z\">https://doi.org/10.1007/s00707-022-03326-z</a>","mla":"Harzheim, Sven, et al. “Comparison of Two Mesh-Moving Techniques for Finite Element Simulations of Galvanic Corrosion.” <i>Acta Mechanica</i>, vol. 233, no. 11, Springer Science and Business Media LLC, 2022, pp. 4427–39, doi:<a href=\"https://doi.org/10.1007/s00707-022-03326-z\">10.1007/s00707-022-03326-z</a>.","short":"S. Harzheim, M. Hofmann, T. Wallmersperger, Acta Mechanica 233 (2022) 4427–4439.","bibtex":"@article{Harzheim_Hofmann_Wallmersperger_2022, title={Comparison of two mesh-moving techniques for finite element simulations of galvanic corrosion}, volume={233}, DOI={<a href=\"https://doi.org/10.1007/s00707-022-03326-z\">10.1007/s00707-022-03326-z</a>}, number={11}, journal={Acta Mechanica}, publisher={Springer Science and Business Media LLC}, author={Harzheim, Sven and Hofmann, Martin and Wallmersperger, Thomas}, year={2022}, pages={4427–4439} }"}},{"page":"847-863","intvolume":"        69","citation":{"ama":"Ju X, Mahnken R, Xu Y, Liang L. Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>. 2022;69(3):847-863. doi:<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>","chicago":"Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, and Lihua Liang. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i> 69, no. 3 (2022): 847–63. <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">https://doi.org/10.1007/s00466-021-02117-y</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, and L. Liang, “Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua,” <i>Computational Mechanics</i>, vol. 69, no. 3, pp. 847–863, 2022, doi: <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>.","apa":"Ju, X., Mahnken, R., Xu, Y., &#38; Liang, L. (2022). Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>, <i>69</i>(3), 847–863. <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">https://doi.org/10.1007/s00466-021-02117-y</a>","bibtex":"@article{Ju_Mahnken_Xu_Liang_2022, title={Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}, volume={69}, DOI={<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>}, number={3}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}, year={2022}, pages={847–863} }","short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, Computational Mechanics 69 (2022) 847–863.","mla":"Ju, Xiaozhe, et al. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i>, vol. 69, no. 3, Springer Science and Business Media LLC, 2022, pp. 847–63, doi:<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>."},"year":"2022","issue":"3","quality_controlled":"1","publication_identifier":{"issn":["0178-7675","1432-0924"]},"publication_status":"published","doi":"10.1007/s00466-021-02117-y","title":"Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua","volume":69,"date_created":"2022-03-28T13:23:17Z","author":[{"first_name":"Xiaozhe","last_name":"Ju","full_name":"Ju, Xiaozhe"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"},{"first_name":"Yangjian","full_name":"Xu, Yangjian","last_name":"Xu"},{"first_name":"Lihua","last_name":"Liang","full_name":"Liang, Lihua"}],"date_updated":"2023-01-24T13:10:56Z","publisher":"Springer Science and Business Media LLC","status":"public","publication":"Computational Mechanics","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","_id":"30655"},{"publication":"Computer Methods in Applied Mechanics and Engineering","type":"journal_article","status":"public","_id":"30657","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","keyword":["Computer Science Applications","General Physics and Astronomy","Mechanical Engineering","Mechanics of Materials","Computational Mechanics"],"article_number":"114790","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0045-7825"]},"quality_controlled":"1","publication_status":"published","year":"2022","intvolume":"       393","citation":{"chicago":"Henkes, Alexander, Henning Wessels, and Rolf Mahnken. “Physics Informed Neural Networks for Continuum Micromechanics.” <i>Computer Methods in Applied Mechanics and Engineering</i> 393 (2022). <a href=\"https://doi.org/10.1016/j.cma.2022.114790\">https://doi.org/10.1016/j.cma.2022.114790</a>.","ieee":"A. Henkes, H. Wessels, and R. Mahnken, “Physics informed neural networks for continuum micromechanics,” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 393, Art. no. 114790, 2022, doi: <a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>.","ama":"Henkes A, Wessels H, Mahnken R. Physics informed neural networks for continuum micromechanics. <i>Computer Methods in Applied Mechanics and Engineering</i>. 2022;393. doi:<a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>","apa":"Henkes, A., Wessels, H., &#38; Mahnken, R. (2022). Physics informed neural networks for continuum micromechanics. <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>393</i>, Article 114790. <a href=\"https://doi.org/10.1016/j.cma.2022.114790\">https://doi.org/10.1016/j.cma.2022.114790</a>","mla":"Henkes, Alexander, et al. “Physics Informed Neural Networks for Continuum Micromechanics.” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 393, 114790, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>.","bibtex":"@article{Henkes_Wessels_Mahnken_2022, title={Physics informed neural networks for continuum micromechanics}, volume={393}, DOI={<a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>}, number={114790}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Henkes, Alexander and Wessels, Henning and Mahnken, Rolf}, year={2022} }","short":"A. Henkes, H. Wessels, R. Mahnken, Computer Methods in Applied Mechanics and Engineering 393 (2022)."},"publisher":"Elsevier BV","date_updated":"2023-01-24T13:09:40Z","volume":393,"author":[{"first_name":"Alexander","last_name":"Henkes","full_name":"Henkes, Alexander"},{"first_name":"Henning","full_name":"Wessels, Henning","last_name":"Wessels"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"date_created":"2022-03-28T13:24:32Z","title":"Physics informed neural networks for continuum micromechanics","doi":"10.1016/j.cma.2022.114790"},{"author":[{"first_name":"X.","last_name":"Ju","full_name":"Ju, X."},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"},{"first_name":"Y.","last_name":"Xu","full_name":"Xu, Y."},{"full_name":"Liang, L.","last_name":"Liang","first_name":"L."}],"volume":398,"date_updated":"2023-04-27T10:04:01Z","doi":"10.1016/j.cma.2022.115199","publication_status":"published","publication_identifier":{"issn":["0045-7825"]},"citation":{"apa":"Ju, X., Mahnken, R., Xu, Y., &#38; Liang, L. (2022). NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems. <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>398</i>, Article 115199. <a href=\"https://doi.org/10.1016/j.cma.2022.115199\">https://doi.org/10.1016/j.cma.2022.115199</a>","short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, Computer Methods in Applied Mechanics and Engineering 398 (2022).","bibtex":"@article{Ju_Mahnken_Xu_Liang_2022, title={NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems}, volume={398}, DOI={<a href=\"https://doi.org/10.1016/j.cma.2022.115199\">10.1016/j.cma.2022.115199</a>}, number={115199}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Ju, X. and Mahnken, Rolf and Xu, Y. and Liang, L.}, year={2022} }","mla":"Ju, X., et al. “NTFA-Enabled Goal-Oriented Adaptive Space–Time Finite Elements for Micro-Heterogeneous Elastoplasticity Problems.” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 398, 115199, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cma.2022.115199\">10.1016/j.cma.2022.115199</a>.","chicago":"Ju, X., Rolf Mahnken, Y. Xu, and L. Liang. “NTFA-Enabled Goal-Oriented Adaptive Space–Time Finite Elements for Micro-Heterogeneous Elastoplasticity Problems.” <i>Computer Methods in Applied Mechanics and Engineering</i> 398 (2022). <a href=\"https://doi.org/10.1016/j.cma.2022.115199\">https://doi.org/10.1016/j.cma.2022.115199</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, and L. Liang, “NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems,” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 398, Art. no. 115199, 2022, doi: <a href=\"https://doi.org/10.1016/j.cma.2022.115199\">10.1016/j.cma.2022.115199</a>.","ama":"Ju X, Mahnken R, Xu Y, Liang L. 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Kohlmeier. “Finite Element Simulation for Rock Salt with Dilatancy Boundary Coupled to Fluid Permeation.” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 190, no. 32–33, Elsevier BV, 2002, pp. 4259–78, doi:<a href=\"https://doi.org/10.1016/s0045-7825(00)00317-0\">10.1016/s0045-7825(00)00317-0</a>.","bibtex":"@article{Mahnken_Kohlmeier_2002, title={Finite element simulation for rock salt with dilatancy boundary coupled to fluid permeation}, volume={190}, DOI={<a href=\"https://doi.org/10.1016/s0045-7825(00)00317-0\">10.1016/s0045-7825(00)00317-0</a>}, number={32–33}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Mahnken, Rolf and Kohlmeier, M.}, year={2002}, pages={4259–4278} }","short":"R. Mahnken, M. Kohlmeier, Computer Methods in Applied Mechanics and Engineering 190 (2002) 4259–4278.","apa":"Mahnken, R., &#38; Kohlmeier, M. (2002). 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Kohlmeier. “Finite Element Simulation for Rock Salt with Dilatancy Boundary Coupled to Fluid Permeation.” <i>Computer Methods in Applied Mechanics and Engineering</i> 190, no. 32–33 (2002): 4259–78. <a href=\"https://doi.org/10.1016/s0045-7825(00)00317-0\">https://doi.org/10.1016/s0045-7825(00)00317-0</a>."},"page":"4259-4278","intvolume":"       190","publication_status":"published","publication_identifier":{"issn":["0045-7825"]},"doi":"10.1016/s0045-7825(00)00317-0","author":[{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"},{"last_name":"Kohlmeier","full_name":"Kohlmeier, M.","first_name":"M."}],"volume":190,"date_updated":"2023-05-31T11:53:38Z","publication":"Computer Methods in Applied Mechanics and Engineering","language":[{"iso":"eng"}],"keyword":["Computer Science Applications","General Physics and Astronomy","Mechanical Engineering","Mechanics of Materials","Computational Mechanics"],"year":"2002","issue":"32-33","quality_controlled":"1","title":"Finite element simulation for rock salt with dilatancy boundary coupled to fluid permeation","date_created":"2023-05-31T11:52:51Z","publisher":"Elsevier BV"},{"type":"journal_article","status":"public","_id":"45417","user_id":"335","department":[{"_id":"9"},{"_id":"154"}],"publication_status":"published","publication_identifier":{"issn":["0178-7675","1432-0924"]},"citation":{"apa":"Döbert, C., Mahnken, R., &#38; Stein, E. 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A unified approach for parameter identification of inelastic material models in the frame of the finite element method. <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>136</i>(3–4), 225–258. <a href=\"https://doi.org/10.1016/0045-7825(96)00991-7\">https://doi.org/10.1016/0045-7825(96)00991-7</a>","bibtex":"@article{Mahnken_Stein_2002, title={A unified approach for parameter identification of inelastic material models in the frame of the finite element method}, volume={136}, DOI={<a href=\"https://doi.org/10.1016/0045-7825(96)00991-7\">10.1016/0045-7825(96)00991-7</a>}, number={3–4}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Mahnken, Rolf and Stein, Erwin}, year={2002}, pages={225–258} }","mla":"Mahnken, Rolf, and Erwin Stein. “A Unified Approach for Parameter Identification of Inelastic Material Models in the Frame of the Finite Element Method.” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 136, no. 3–4, Elsevier BV, 2002, pp. 225–58, doi:<a href=\"https://doi.org/10.1016/0045-7825(96)00991-7\">10.1016/0045-7825(96)00991-7</a>.","short":"R. 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