[{"publication":"Archive of Applied Mechanics","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>The micropolar continuum is a special case of a micromorphic material model and has additional degrees of freedom in the form of microrotations compared to the classical continuum. With the micropolar model, size effects can be considered and the boundary value problem can be regularized when localization effects occur. In order to map the microrotations, an additional strain measure and an additional stress are introduced. For simulation of plasticity, it is possible to define one yield function, and thus one plastic multiplier as well as one equivalent plastic strain occur. This approach is known as the single-surface plasticity approach. The macro- and micro-stresses are coupled in a common flow function. On the other hand, there is the so-called double-surface plasticity when one yield function, one plastic multiplier, and one equivalent plastic strain, respectively, are introduced for each of the macro- and micro-variables. The coupling of the macro- and micro-variables is established by a possible coupling of both yield functions. The purpose of this paper is to compare both approaches and to identify similarities and differences.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"issue":"5","quality_controlled":"1","year":"2026","date_created":"2026-04-23T11:55:35Z","publisher":"Springer Science and Business Media LLC","title":"Single-surface and double-surface plasticity for micropolar continuum","type":"journal_article","status":"public","user_id":"85414","department":[{"_id":"9"},{"_id":"952"},{"_id":"321"}],"_id":"65491","article_number":"94","publication_status":"published","publication_identifier":{"issn":["0939-1533","1432-0681"]},"citation":{"short":"A. Börger, R. Mahnken, Archive of Applied Mechanics 96 (2026).","mla":"Börger, Alexander, and Rolf Mahnken. “Single-Surface and Double-Surface Plasticity for Micropolar Continuum.” <i>Archive of Applied Mechanics</i>, vol. 96, no. 5, 94, Springer Science and Business Media LLC, 2026, doi:<a href=\"https://doi.org/10.1007/s00419-026-03049-w\">10.1007/s00419-026-03049-w</a>.","bibtex":"@article{Börger_Mahnken_2026, title={Single-surface and double-surface plasticity for micropolar continuum}, volume={96}, DOI={<a href=\"https://doi.org/10.1007/s00419-026-03049-w\">10.1007/s00419-026-03049-w</a>}, number={594}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Börger, Alexander and Mahnken, Rolf}, year={2026} }","ama":"Börger A, Mahnken R. Single-surface and double-surface plasticity for micropolar continuum. <i>Archive of Applied Mechanics</i>. 2026;96(5). doi:<a href=\"https://doi.org/10.1007/s00419-026-03049-w\">10.1007/s00419-026-03049-w</a>","apa":"Börger, A., &#38; Mahnken, R. (2026). Single-surface and double-surface plasticity for micropolar continuum. <i>Archive of Applied Mechanics</i>, <i>96</i>(5), Article 94. <a href=\"https://doi.org/10.1007/s00419-026-03049-w\">https://doi.org/10.1007/s00419-026-03049-w</a>","ieee":"A. Börger and R. Mahnken, “Single-surface and double-surface plasticity for micropolar continuum,” <i>Archive of Applied Mechanics</i>, vol. 96, no. 5, Art. no. 94, 2026, doi: <a href=\"https://doi.org/10.1007/s00419-026-03049-w\">10.1007/s00419-026-03049-w</a>.","chicago":"Börger, Alexander, and Rolf Mahnken. “Single-Surface and Double-Surface Plasticity for Micropolar Continuum.” <i>Archive of Applied Mechanics</i> 96, no. 5 (2026). <a href=\"https://doi.org/10.1007/s00419-026-03049-w\">https://doi.org/10.1007/s00419-026-03049-w</a>."},"intvolume":"        96","author":[{"first_name":"Alexander","id":"52037","full_name":"Börger, Alexander","last_name":"Börger"},{"full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"}],"volume":96,"date_updated":"2026-04-23T11:56:38Z","doi":"10.1007/s00419-026-03049-w"},{"publication_identifier":{"issn":["0939-1533","1432-0681"]},"publication_status":"published","page":"1221-1242","intvolume":"        94","citation":{"mla":"Hamdoun, Ayoub, and Rolf Mahnken. “A Large Deformation Gradient Theory for Glassy Polymers by Means of Micromorphic Regularization.” <i>Archive of Applied Mechanics</i>, vol. 94, no. 5, Springer Science and Business Media LLC, 2024, pp. 1221–42, doi:<a href=\"https://doi.org/10.1007/s00419-024-02570-0\">10.1007/s00419-024-02570-0</a>.","short":"A. Hamdoun, R. Mahnken, Archive of Applied Mechanics 94 (2024) 1221–1242.","bibtex":"@article{Hamdoun_Mahnken_2024, title={A large deformation gradient theory for glassy polymers by means of micromorphic regularization}, volume={94}, DOI={<a href=\"https://doi.org/10.1007/s00419-024-02570-0\">10.1007/s00419-024-02570-0</a>}, number={5}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Hamdoun, Ayoub and Mahnken, Rolf}, year={2024}, pages={1221–1242} }","apa":"Hamdoun, A., &#38; Mahnken, R. (2024). A large deformation gradient theory for glassy polymers by means of micromorphic regularization. <i>Archive of Applied Mechanics</i>, <i>94</i>(5), 1221–1242. <a href=\"https://doi.org/10.1007/s00419-024-02570-0\">https://doi.org/10.1007/s00419-024-02570-0</a>","ama":"Hamdoun A, Mahnken R. A large deformation gradient theory for glassy polymers by means of micromorphic regularization. <i>Archive of Applied Mechanics</i>. 2024;94(5):1221-1242. doi:<a href=\"https://doi.org/10.1007/s00419-024-02570-0\">10.1007/s00419-024-02570-0</a>","ieee":"A. Hamdoun and R. Mahnken, “A large deformation gradient theory for glassy polymers by means of micromorphic regularization,” <i>Archive of Applied Mechanics</i>, vol. 94, no. 5, pp. 1221–1242, 2024, doi: <a href=\"https://doi.org/10.1007/s00419-024-02570-0\">10.1007/s00419-024-02570-0</a>.","chicago":"Hamdoun, Ayoub, and Rolf Mahnken. “A Large Deformation Gradient Theory for Glassy Polymers by Means of Micromorphic Regularization.” <i>Archive of Applied Mechanics</i> 94, no. 5 (2024): 1221–42. <a href=\"https://doi.org/10.1007/s00419-024-02570-0\">https://doi.org/10.1007/s00419-024-02570-0</a>."},"date_updated":"2024-09-26T11:25:44Z","volume":94,"author":[{"last_name":"Hamdoun","full_name":"Hamdoun, Ayoub","id":"57708","first_name":"Ayoub"},{"full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken","first_name":"Rolf"}],"doi":"10.1007/s00419-024-02570-0","type":"journal_article","status":"public","_id":"54280","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"57708","quality_controlled":"1","issue":"5","year":"2024","publisher":"Springer Science and Business Media LLC","date_created":"2024-05-14T09:05:40Z","title":"A large deformation gradient theory for glassy polymers by means of micromorphic regularization","publication":"Archive of Applied Mechanics","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Cold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}]},{"type":"journal_article","publication":"Archive of Applied Mechanics","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>The open-source parameter identification tool ADAPT (A diversely applicable parameter identification Tool) is integrated with a machine learning-based approach for start value prediction in order to calibrate a Gurson–Tvergaard–Needleman (GTN) and a Lemaitre damage model. As representative example case-hardened steel 16MnCrS5 is elaborated. An artificial neural network (ANN) is initially trained by using load–displacement curves derived from simulations of a boundary value problem—instead of using data generated for homogeneous states of deformation at material point or one-element level—with varying material parameter combinations. The ANN is then employed so as to predict sets of material parameters that already provide close solutions to the experiment. These predicted parameter sets serve as starting values for a subsequent multi-objective parameter identification by using ADAPT. ADAPT allows for the consideration of input data from multiple scales, including integral data such as load–displacement curves, full-field data such as displacement and strain fields, and high-resolution experimental void data at the micro-scale. The influence of each data set on prediction quality is analyzed. Using various types of input data introduces additional information, enhancing prediction accuracy. The validation is carried out with respect to experimental void measurements of forward rod extruded parts. The results demonstrate, by incorporating void measurements in the optimization process, that it is possible to improve the quantitative prediction of ductile damage in the sense of void area fractions by factor 28 in forward rod extrusion.</jats:p>"}],"status":"public","_id":"62770","user_id":"85414","department":[{"_id":"952"},{"_id":"321"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0939-1533","1432-0681"]},"quality_controlled":"1","issue":"8","year":"2024","citation":{"ieee":"J. Gerlach <i>et al.</i>, “Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification,” <i>Archive of Applied Mechanics</i>, vol. 94, no. 8, pp. 2217–2242, 2024, doi: <a href=\"https://doi.org/10.1007/s00419-024-02634-1\">10.1007/s00419-024-02634-1</a>.","chicago":"Gerlach, Jan, Robin Schulte, Alexander Schowtjak, Till Clausmeyer, Richard Ostwald, A. Erman Tekkaya, and Andreas Menzel. “Enhancing Damage Prediction in Bulk Metal Forming through Machine Learning-Assisted Parameter Identification.” <i>Archive of Applied Mechanics</i> 94, no. 8 (2024): 2217–42. <a href=\"https://doi.org/10.1007/s00419-024-02634-1\">https://doi.org/10.1007/s00419-024-02634-1</a>.","ama":"Gerlach J, Schulte R, Schowtjak A, et al. Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification. <i>Archive of Applied Mechanics</i>. 2024;94(8):2217-2242. doi:<a href=\"https://doi.org/10.1007/s00419-024-02634-1\">10.1007/s00419-024-02634-1</a>","apa":"Gerlach, J., Schulte, R., Schowtjak, A., Clausmeyer, T., Ostwald, R., Tekkaya, A. E., &#38; Menzel, A. (2024). Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification. <i>Archive of Applied Mechanics</i>, <i>94</i>(8), 2217–2242. <a href=\"https://doi.org/10.1007/s00419-024-02634-1\">https://doi.org/10.1007/s00419-024-02634-1</a>","bibtex":"@article{Gerlach_Schulte_Schowtjak_Clausmeyer_Ostwald_Tekkaya_Menzel_2024, title={Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification}, volume={94}, DOI={<a href=\"https://doi.org/10.1007/s00419-024-02634-1\">10.1007/s00419-024-02634-1</a>}, number={8}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Gerlach, Jan and Schulte, Robin and Schowtjak, Alexander and Clausmeyer, Till and Ostwald, Richard and Tekkaya, A. Erman and Menzel, Andreas}, year={2024}, pages={2217–2242} }","mla":"Gerlach, Jan, et al. “Enhancing Damage Prediction in Bulk Metal Forming through Machine Learning-Assisted Parameter Identification.” <i>Archive of Applied Mechanics</i>, vol. 94, no. 8, Springer Science and Business Media LLC, 2024, pp. 2217–42, doi:<a href=\"https://doi.org/10.1007/s00419-024-02634-1\">10.1007/s00419-024-02634-1</a>.","short":"J. Gerlach, R. Schulte, A. Schowtjak, T. Clausmeyer, R. Ostwald, A.E. Tekkaya, A. Menzel, Archive of Applied Mechanics 94 (2024) 2217–2242."},"page":"2217-2242","intvolume":"        94","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-03T12:50:41Z","date_created":"2025-12-03T12:46:31Z","author":[{"last_name":"Gerlach","full_name":"Gerlach, Jan","first_name":"Jan"},{"first_name":"Robin","full_name":"Schulte, Robin","last_name":"Schulte"},{"first_name":"Alexander","full_name":"Schowtjak, Alexander","last_name":"Schowtjak"},{"full_name":"Clausmeyer, Till","last_name":"Clausmeyer","first_name":"Till"},{"orcid":"0000-0003-2147-8444","last_name":"Ostwald","full_name":"Ostwald, Richard","id":"106876","first_name":"Richard"},{"last_name":"Tekkaya","full_name":"Tekkaya, A. Erman","first_name":"A. Erman"},{"first_name":"Andreas","last_name":"Menzel","full_name":"Menzel, Andreas"}],"volume":94,"title":"Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification","doi":"10.1007/s00419-024-02634-1"},{"language":[{"iso":"eng"}],"keyword":["Mechanical Engineering"],"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_created":"2022-03-28T13:24:07Z","publisher":"Springer Science and Business Media LLC","title":"Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters","issue":"3","quality_controlled":"1","year":"2022","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","_id":"30656","type":"journal_article","status":"public","volume":92,"author":[{"last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf","first_name":"Rolf"}],"date_updated":"2023-01-24T13:10:27Z","doi":"10.1007/s00419-021-02069-y","publication_identifier":{"issn":["0939-1533","1432-0681"]},"publication_status":"published","page":"713-754","intvolume":"        92","citation":{"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>","short":"R. Mahnken, Archive of Applied Mechanics 92 (2022) 713–754.","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} }","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>.","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>","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>."}},{"volume":92,"author":[{"full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken","first_name":"Rolf"},{"full_name":"Mirzapour, Jamil","last_name":"Mirzapour","first_name":"Jamil"}],"date_created":"2022-11-14T12:51:05Z","date_updated":"2023-04-27T10:07:20Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00419-022-02237-8","title":"A statistically based strain energy function for polymer chains in rubber elasticity","issue":"11","quality_controlled":"1","publication_identifier":{"issn":["0939-1533","1432-0681"]},"publication_status":"published","intvolume":"        92","page":"3295-3323","citation":{"chicago":"Mahnken, Rolf, and Jamil Mirzapour. “A Statistically Based Strain Energy Function for Polymer Chains in Rubber Elasticity.” <i>Archive of Applied Mechanics</i> 92, no. 11 (2022): 3295–3323. <a href=\"https://doi.org/10.1007/s00419-022-02237-8\">https://doi.org/10.1007/s00419-022-02237-8</a>.","ieee":"R. Mahnken and J. Mirzapour, “A statistically based strain energy function for polymer chains in rubber elasticity,” <i>Archive of Applied Mechanics</i>, vol. 92, no. 11, pp. 3295–3323, 2022, doi: <a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>.","ama":"Mahnken R, Mirzapour J. A statistically based strain energy function for polymer chains in rubber elasticity. <i>Archive of Applied Mechanics</i>. 2022;92(11):3295-3323. doi:<a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>","short":"R. Mahnken, J. Mirzapour, Archive of Applied Mechanics 92 (2022) 3295–3323.","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} }","mla":"Mahnken, Rolf, and Jamil Mirzapour. “A Statistically Based Strain Energy Function for Polymer Chains in Rubber Elasticity.” <i>Archive of Applied Mechanics</i>, vol. 92, no. 11, Springer Science and Business Media LLC, 2022, pp. 3295–323, doi:<a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>.","apa":"Mahnken, R., &#38; Mirzapour, J. (2022). A statistically based strain energy function for polymer chains in rubber elasticity. <i>Archive of Applied Mechanics</i>, <i>92</i>(11), 3295–3323. <a href=\"https://doi.org/10.1007/s00419-022-02237-8\">https://doi.org/10.1007/s00419-022-02237-8</a>"},"year":"2022","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","_id":"34074","language":[{"iso":"eng"}],"keyword":["Mechanical Engineering"],"publication":"Archive of Applied Mechanics","type":"journal_article","status":"public"},{"doi":"10.1007/s00419-021-01982-6","title":"A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations","date_created":"2021-12-22T12:28:40Z","author":[{"full_name":"Cheng, C.","last_name":"Cheng","first_name":"C."},{"first_name":"Rolf","id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken"}],"date_updated":"2023-01-24T12:57:22Z","page":"3869-3888","citation":{"ama":"Cheng C, Mahnken R. A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations. <i>Archive of Applied Mechanics</i>. Published online 2021:3869-3888. doi:<a href=\"https://doi.org/10.1007/s00419-021-01982-6\">10.1007/s00419-021-01982-6</a>","ieee":"C. Cheng and R. Mahnken, “A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations,” <i>Archive of Applied Mechanics</i>, pp. 3869–3888, 2021, doi: <a href=\"https://doi.org/10.1007/s00419-021-01982-6\">10.1007/s00419-021-01982-6</a>.","chicago":"Cheng, C., and Rolf Mahnken. “A Modified Zerilli–Armstrong Model as the Asymmetric Visco-Plastic Part of a Multi-Mechanism Model for Cutting Simulations.” <i>Archive of Applied Mechanics</i>, 2021, 3869–88. <a href=\"https://doi.org/10.1007/s00419-021-01982-6\">https://doi.org/10.1007/s00419-021-01982-6</a>.","mla":"Cheng, C., and Rolf Mahnken. “A Modified Zerilli–Armstrong Model as the Asymmetric Visco-Plastic Part of a Multi-Mechanism Model for Cutting Simulations.” <i>Archive of Applied Mechanics</i>, 2021, pp. 3869–88, doi:<a href=\"https://doi.org/10.1007/s00419-021-01982-6\">10.1007/s00419-021-01982-6</a>.","short":"C. Cheng, R. Mahnken, Archive of Applied Mechanics (2021) 3869–3888.","bibtex":"@article{Cheng_Mahnken_2021, title={A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations}, DOI={<a href=\"https://doi.org/10.1007/s00419-021-01982-6\">10.1007/s00419-021-01982-6</a>}, journal={Archive of Applied Mechanics}, author={Cheng, C. and Mahnken, Rolf}, year={2021}, pages={3869–3888} }","apa":"Cheng, C., &#38; Mahnken, R. (2021). A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations. <i>Archive of Applied Mechanics</i>, 3869–3888. <a href=\"https://doi.org/10.1007/s00419-021-01982-6\">https://doi.org/10.1007/s00419-021-01982-6</a>"},"year":"2021","quality_controlled":"1","publication_identifier":{"issn":["0939-1533","1432-0681"]},"publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","_id":"29085","status":"public","publication":"Archive of Applied Mechanics","type":"journal_article"},{"status":"public","type":"journal_article","publication":"Archive of Applied Mechanics","language":[{"iso":"eng"}],"_id":"9933","user_id":"78813","department":[{"_id":"154"}],"year":"2018","citation":{"ama":"Mahnken R, Lenz P, Dammann C. “A least squares approach for effective shear properties in an n-layered sphere model.” <i>Archive of Applied Mechanics</i>. 2018:2081-2099. doi:<a href=\"https://doi.org/10.1007/s00419-018-1431-5\">10.1007/s00419-018-1431-5</a>","chicago":"Mahnken, Rolf, Peter Lenz, and Christian Dammann. “‘A Least Squares Approach for Effective Shear Properties in an n-Layered Sphere Model.’” <i>Archive of Applied Mechanics</i>, 2018, 2081–99. <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">https://doi.org/10.1007/s00419-018-1431-5</a>.","ieee":"R. Mahnken, P. Lenz, and C. Dammann, “‘A least squares approach for effective shear properties in an n-layered sphere model,’” <i>Archive of Applied Mechanics</i>, pp. 2081–2099, 2018.","apa":"Mahnken, R., Lenz, P., &#38; Dammann, C. (2018). “A least squares approach for effective shear properties in an n-layered sphere model.” <i>Archive of Applied Mechanics</i>, 2081–2099. <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">https://doi.org/10.1007/s00419-018-1431-5</a>","short":"R. Mahnken, P. Lenz, C. 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(2018). A least squares approach for effective shear properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -layered sphere model. <i>Archive of Applied Mechanics</i>, 2081–2099. <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">https://doi.org/10.1007/s00419-018-1431-5</a>","short":"R. Mahnken, P. Lenz, C. Dammann, Archive of Applied Mechanics (2018) 2081–2099.","bibtex":"@article{Mahnken_Lenz_Dammann_2018, title={A least squares approach for effective shear properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -layered sphere model}, DOI={<a href=\"https://doi.org/10.1007/s00419-018-1431-5\">10.1007/s00419-018-1431-5</a>}, journal={Archive of Applied Mechanics}, author={Mahnken, Rolf and Lenz, Peter and Dammann, Christian}, year={2018}, pages={2081–2099} }","mla":"Mahnken, Rolf, et al. “A Least Squares Approach for Effective Shear Properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -Layered Sphere Model.” <i>Archive of Applied Mechanics</i>, 2018, pp. 2081–99, doi:<a href=\"https://doi.org/10.1007/s00419-018-1431-5\">10.1007/s00419-018-1431-5</a>.","chicago":"Mahnken, Rolf, Peter Lenz, and Christian Dammann. “A Least Squares Approach for Effective Shear Properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -Layered Sphere Model.” <i>Archive of Applied Mechanics</i>, 2018, 2081–99. <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">https://doi.org/10.1007/s00419-018-1431-5</a>.","ieee":"R. Mahnken, P. Lenz, and C. Dammann, “A least squares approach for effective shear properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -layered sphere model,” <i>Archive of Applied Mechanics</i>, pp. 2081–2099, 2018, doi: <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">10.1007/s00419-018-1431-5</a>.","ama":"Mahnken R, Lenz P, Dammann C. A least squares approach for effective shear properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -layered sphere model. <i>Archive of Applied Mechanics</i>. 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