[{"citation":{"chicago":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Goal‐oriented Adaptivity Based on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Elasto‐plasticity.” <i>PAMM</i> 22, no. 1 (2023). <a href=\"https://doi.org/10.1002/pamm.202200053\">https://doi.org/10.1002/pamm.202200053</a>.","ieee":"A. Tchomgue Simeu and R. Mahnken, “Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity,” <i>PAMM</i>, vol. 22, no. 1, 2023, doi: <a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>.","ama":"Tchomgue Simeu A, Mahnken R. Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity. <i>PAMM</i>. 2023;22(1). doi:<a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>","apa":"Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity. <i>PAMM</i>, <i>22</i>(1). <a href=\"https://doi.org/10.1002/pamm.202200053\">https://doi.org/10.1002/pamm.202200053</a>","mla":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Goal‐oriented Adaptivity Based on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Elasto‐plasticity.” <i>PAMM</i>, vol. 22, no. 1, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>.","bibtex":"@article{Tchomgue Simeu_Mahnken_2023, title={Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity}, volume={22}, DOI={<a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>}, number={1}, journal={PAMM}, publisher={Wiley}, author={Tchomgue Simeu, Arnold and Mahnken, Rolf}, year={2023} }","short":"A. Tchomgue Simeu, R. Mahnken, PAMM 22 (2023)."},"intvolume":"        22","year":"2023","issue":"1","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["1617-7061","1617-7061"]},"doi":"10.1002/pamm.202200053","title":"Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity","date_created":"2023-05-16T12:18:15Z","author":[{"id":"83075","full_name":"Tchomgue Simeu, Arnold","last_name":"Tchomgue Simeu","first_name":"Arnold"},{"id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"}],"volume":22,"publisher":"Wiley","date_updated":"2023-05-25T10:02:34Z","status":"public","type":"journal_article","publication":"PAMM","language":[{"iso":"eng"}],"keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics"],"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"44890"},{"year":"2023","citation":{"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>.","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>","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>"},"publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0178-7675","1432-0924"]},"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":"10.1007/s00466-023-02347-2","date_updated":"2023-06-23T06:48:42Z","publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Rolf","full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken"}],"date_created":"2023-06-23T06:47:36Z","abstract":[{"lang":"eng","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>"}],"status":"public","type":"journal_article","publication":"Computational Mechanics","keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"language":[{"iso":"eng"}],"_id":"45757","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}]},{"quality_controlled":"1","publication_status":"published","citation":{"ama":"Tchomgue Simeu A, Mahnken R. Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations. In: <i>XI International Conference on Adaptive Modeling and Simulation</i>. CIMNE; 2023. doi:<a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>","chicago":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Mesh- and Model Adaptivity for Elasto-Plastic Mean-Field and Full-Field Homogenization Based on Downwind  and Upwind Approximations.” In <i>XI International Conference on Adaptive Modeling and Simulation</i>. CIMNE, 2023. <a href=\"https://doi.org/10.23967/admos.2023.054\">https://doi.org/10.23967/admos.2023.054</a>.","ieee":"A. Tchomgue Simeu and R. Mahnken, “Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations,” 2023, doi: <a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>.","bibtex":"@inproceedings{Tchomgue Simeu_Mahnken_2023, title={Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations}, DOI={<a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>}, booktitle={XI International Conference on Adaptive Modeling and Simulation}, publisher={CIMNE}, author={Tchomgue Simeu, Arnold and Mahnken, Rolf}, year={2023} }","mla":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Mesh- and Model Adaptivity for Elasto-Plastic Mean-Field and Full-Field Homogenization Based on Downwind  and Upwind Approximations.” <i>XI International Conference on Adaptive Modeling and Simulation</i>, CIMNE, 2023, doi:<a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>.","short":"A. Tchomgue Simeu, R. Mahnken, in: XI International Conference on Adaptive Modeling and Simulation, CIMNE, 2023.","apa":"Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations. <i>XI International Conference on Adaptive Modeling and Simulation</i>. <a href=\"https://doi.org/10.23967/admos.2023.054\">https://doi.org/10.23967/admos.2023.054</a>"},"year":"2023","author":[{"id":"83075","full_name":"Tchomgue Simeu, Arnold","last_name":"Tchomgue Simeu","first_name":"Arnold"},{"first_name":"Rolf","last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf"}],"date_created":"2023-09-01T07:52:20Z","publisher":"CIMNE","date_updated":"2023-09-01T07:54:31Z","doi":"10.23967/admos.2023.054","title":"Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations","publication":"XI International Conference on Adaptive Modeling and Simulation","type":"conference","status":"public","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","_id":"46762","language":[{"iso":"eng"}]},{"date_created":"2022-05-10T11:18:45Z","author":[{"last_name":"Ju","full_name":"Ju, Xiaozhe","first_name":"Xiaozhe"},{"first_name":"Rolf","id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken"},{"first_name":"Yangjian","last_name":"Xu","full_name":"Xu, Yangjian"},{"first_name":"Lihua","last_name":"Liang","full_name":"Liang, Lihua"},{"first_name":"Chun","full_name":"Cheng, Chun","last_name":"Cheng"},{"first_name":"Wangmin","last_name":"Zhou","full_name":"Zhou, Wangmin"}],"publisher":"Elsevier BV","date_updated":"2023-01-24T13:11:40Z","doi":"10.1016/j.compstruct.2022.115699","title":"Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0263-8223"]},"citation":{"chicago":"Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, Lihua Liang, Chun Cheng, and Wangmin Zhou. “Multiscale Analysis of Composite Structures with Goal-Oriented Mesh Adaptivity and Reduced Order Homogenization.” <i>Composite Structures</i>, 2022. <a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">https://doi.org/10.1016/j.compstruct.2022.115699</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, and W. Zhou, “Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization,” <i>Composite Structures</i>, Art. no. 115699, 2022, doi: <a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>.","ama":"Ju X, Mahnken R, Xu Y, Liang L, Cheng C, Zhou W. Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization. <i>Composite Structures</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>","apa":"Ju, X., Mahnken, R., Xu, Y., Liang, L., Cheng, C., &#38; Zhou, W. (2022). Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization. <i>Composite Structures</i>, Article 115699. <a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">https://doi.org/10.1016/j.compstruct.2022.115699</a>","short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, W. Zhou, Composite Structures (2022).","mla":"Ju, Xiaozhe, et al. “Multiscale Analysis of Composite Structures with Goal-Oriented Mesh Adaptivity and Reduced Order Homogenization.” <i>Composite Structures</i>, 115699, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>.","bibtex":"@article{Ju_Mahnken_Xu_Liang_Cheng_Zhou_2022, title={Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization}, DOI={<a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>}, number={115699}, journal={Composite Structures}, publisher={Elsevier BV}, author={Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua and Cheng, Chun and Zhou, Wangmin}, year={2022} }"},"year":"2022","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"31185","language":[{"iso":"eng"}],"article_number":"115699","keyword":["Civil and Structural Engineering","Ceramics and Composites"],"type":"journal_article","publication":"Composite Structures","status":"public"},{"publisher":"Springer Science and Business Media LLC","date_created":"2022-03-28T13:24:07Z","title":"Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters","quality_controlled":"1","issue":"3","year":"2022","keyword":["Mechanical Engineering"],"language":[{"iso":"eng"}],"publication":"Archive of Applied Mechanics","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Optimized material parameters obtained from parameter identification for verification wrt a certain loading scenario are amenable to two deficiencies: Firstly, they may lack a general validity for different loading scenarios. Secondly, they may be prone to instability, such that a small perturbation of experimental data may ensue a large perturbation for the material parameters. This paper presents a framework for extension of hyperelastic models for rubber-like materials accounting for both deficiencies. To this end, an additive decomposition of the strain energy function is assumed into a sum of weighted strain mode related quantities. We propose a practical guide for model development accounting for the criteria of verification, validation and stability by means of the strain mode-dependent weighting functions and techniques of model reduction. The approach is successfully applied for 13 hyperelastic models with regard to the classical experimental data on vulcanized rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting capabilties and stable material parameters.</jats:p>","lang":"eng"}],"date_updated":"2023-01-24T13:10:27Z","author":[{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"volume":92,"doi":"10.1007/s00419-021-02069-y","publication_status":"published","publication_identifier":{"issn":["0939-1533","1432-0681"]},"citation":{"ieee":"R. Mahnken, “Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters,” <i>Archive of Applied Mechanics</i>, vol. 92, no. 3, pp. 713–754, 2022, doi: <a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>.","chicago":"Mahnken, Rolf. “Strain Mode-Dependent Weighting Functions in Hyperelasticity Accounting for Verification, Validation, and Stability of Material Parameters.” <i>Archive of Applied Mechanics</i> 92, no. 3 (2022): 713–54. <a href=\"https://doi.org/10.1007/s00419-021-02069-y\">https://doi.org/10.1007/s00419-021-02069-y</a>.","ama":"Mahnken R. Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters. <i>Archive of Applied Mechanics</i>. 2022;92(3):713-754. doi:<a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>","apa":"Mahnken, R. (2022). Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters. <i>Archive of Applied Mechanics</i>, <i>92</i>(3), 713–754. <a href=\"https://doi.org/10.1007/s00419-021-02069-y\">https://doi.org/10.1007/s00419-021-02069-y</a>","bibtex":"@article{Mahnken_2022, title={Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters}, volume={92}, DOI={<a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>}, number={3}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf}, year={2022}, pages={713–754} }","short":"R. Mahnken, Archive of Applied Mechanics 92 (2022) 713–754.","mla":"Mahnken, Rolf. “Strain Mode-Dependent Weighting Functions in Hyperelasticity Accounting for Verification, Validation, and Stability of Material Parameters.” <i>Archive of Applied Mechanics</i>, vol. 92, no. 3, Springer Science and Business Media LLC, 2022, pp. 713–54, doi:<a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>."},"intvolume":"        92","page":"713-754","_id":"30656","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"type":"journal_article","status":"public"},{"year":"2022","citation":{"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>.","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.","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>","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>","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>.","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>."},"intvolume":"        69","page":"847-863","publication_status":"published","publication_identifier":{"issn":["0178-7675","1432-0924"]},"quality_controlled":"1","issue":"3","title":"Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua","doi":"10.1007/s00466-021-02117-y","publisher":"Springer Science and Business Media LLC","date_updated":"2023-01-24T13:10:56Z","date_created":"2022-03-28T13:23:17Z","author":[{"last_name":"Ju","full_name":"Ju, Xiaozhe","first_name":"Xiaozhe"},{"id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"},{"full_name":"Xu, Yangjian","last_name":"Xu","first_name":"Yangjian"},{"full_name":"Liang, Lihua","last_name":"Liang","first_name":"Lihua"}],"volume":69,"status":"public","type":"journal_article","publication":"Computational Mechanics","keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"language":[{"iso":"eng"}],"_id":"30655","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}]},{"type":"journal_article","publication":"Computer Methods in Applied Mechanics and Engineering","status":"public","_id":"30657","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"article_number":"114790","keyword":["Computer Science Applications","General Physics and Astronomy","Mechanical Engineering","Mechanics of Materials","Computational Mechanics"],"language":[{"iso":"eng"}],"publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0045-7825"]},"year":"2022","citation":{"short":"A. Henkes, H. Wessels, R. Mahnken, Computer Methods in Applied Mechanics and Engineering 393 (2022).","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} }","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>.","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>","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>","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>.","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>."},"intvolume":"       393","date_updated":"2023-01-24T13:09:40Z","publisher":"Elsevier BV","author":[{"last_name":"Henkes","full_name":"Henkes, Alexander","first_name":"Alexander"},{"first_name":"Henning","last_name":"Wessels","full_name":"Wessels, Henning"},{"first_name":"Rolf","last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf"}],"date_created":"2022-03-28T13:24:32Z","volume":393,"title":"Physics informed neural networks for continuum micromechanics","doi":"10.1016/j.cma.2022.114790"},{"type":"journal_article","publication":"Archive of Applied Mechanics","status":"public","_id":"34074","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"keyword":["Mechanical Engineering"],"language":[{"iso":"eng"}],"publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0939-1533","1432-0681"]},"issue":"11","year":"2022","citation":{"bibtex":"@article{Mahnken_Mirzapour_2022, title={A statistically based strain energy function for polymer chains in rubber elasticity}, volume={92}, DOI={<a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>}, number={11}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf and Mirzapour, Jamil}, year={2022}, pages={3295–3323} }","short":"R. 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