@Article{duepublico_mods_00083129, author = {Jabs, Lukas and Schneider, Matti}, title = {consistent discretization via the finite radon transform for FFT-based computational micromechanics}, journal = {BeyondRVE: Beyond Representative Volume Elements for Random Heterogeneous Materials}, year = {2024}, month = {Sep}, day = {14}, keywords = {Computational homogenization; FFT-based computational micromechanics; Discretization; Radon transform; Laminates}, abstract = {This work explores connections between FFT-based computational micromechanics and a homogenization approach based on the finite Radon transform introduced by Derraz and co-workers. We revisit periodic homogenization from a Radon point of view and derive the multidimensional Radon series representation of a periodic function from scratch. We introduce a general discretization framework based on trigonometric polynomials which permits to represent both the classical Moulinec-Suquet discretization and the finite Radon approach by Derraz et al. We use this framework to introduce a novel Radon framework which combines the advantages of both the Moulinec-Suquet discretization and the Radon approach, i.e., we construct a discretization which is both convergent under grid refinement and is able to represent certain non-axis aligned laminates exactly. We present our findings in the context of small-strain mechanics, extending the work of Derraz et al. that was restricted to conductivity and report on a number of interesting numerical examples.}, note = {MS acknowledges support from the European Research Council within the Horizon Europe program - project 101040238. Funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -- 516929769 -- is gratefully acknowledged by LJ.}, note = {<p>Jabs, L., Schneider, M. A consistent discretization via the finite radon transform for FFT-based computational micromechanics. <em>Comput Mech</em> (2024). <a href="https://doi.org/10.1007/s00466-024-02542-9">https://doi.org/10.1007/s00466-024-02542-9</a></p> <p>Published 14 September 2024</p>}, note = {Early View. Online Version of Record before inclusion in an issue}, note = {<p>BeyondRVE. Grant agreement ID: 101040238</p> <p>Funded under European Research Council (ERC).</p> <p>Start date 1 July 2022. End date 30 June 2027.</p>}, doi = {10.1007/s00466-024-02542-9}, url = {https://duepublico2.uni-due.de/receive/duepublico_mods_00083129}, url = {https://doi.org/10.1007/s00466-024-02542-9}, file = {:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00082642/Jabs_et_al_2024_consistent_discretization.pdf:PDF}, language = {en} }