{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:46:44Z","timestamp":1792673204662,"version":"4.5.0"},"reference-count":34,"publisher":"Acoustical Society of America (ASA)","issue":"4","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2225215"],"award-info":[{"award-number":["2225215"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:p>Ultrasonic wave propagation in polycrystalline materials is governed by grain scattering, which causes frequency-dependent attenuation and dispersion that are directly linked to the underlying microstructure. Accurate numerical modeling of these phenomena is essential for nondestructive evaluation (NDE) and materials characterization, yet traditional displacement-based finite difference (FD) methods face numerical challenges at grain boundaries due to spatial derivatives of the stiffness tensor. We present a stress-based FD formulation that reformulates the elastodynamic equations in terms of stress components only, eliminating stiffness spatial derivatives and naturally enforcing traction continuity at grain boundaries. The formulation is implemented with GPU acceleration and validated against theoretical predictions based on the Von K\u00e1rm\u00e1n correlation function for aluminum, iron, and lithium polycrystals. The results demonstrate good agreement within the investigated frequency range for both attenuation and phase velocity dispersion, with normalized results revealing material-dependent scattering behavior. The formulation is further extended to coupled fluid-solid systems, demonstrating accurate attenuation predictions in immersion-based NDE configurations. Compared to displacement-based methods, the stress-based approach offers improved numerical stability, a 39% reduction in GPU memory usage, and a unified treatment of fluid-solid coupling through a single primary variable.<\/jats:p>","DOI":"10.1121\/10.0046885","type":"journal-article","created":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:02:34Z","timestamp":1792670554000},"page":"3340-3355","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Computational stress formulation for ultrasonic wave dispersion and attenuation in polycrystalline materials"],"prefix":"10.1121","volume":"160","author":[{"given":"Marzieh","family":"Bahreman","sequence":"first","affiliation":[{"name":"Department of Engineering Science and Mechanics, The Pennsylvania State University 1 , University Park, Pennsylvania 16802,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5868-4244","authenticated-orcid":false,"given":"Ming","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Engineering and Design, University of Sussex 2 , Brighton, BN1 9RH,","place":["United Kingdom"]},{"name":"Department of Mechanical Engineering, Imperial College London 3 , London, SW7 2AZ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Melody","family":"Png","sequence":"additional","affiliation":[{"name":"Advanced Remanufacturing & Technology Centre (ARTC), Agency for Science, Technology and Research (A*STAR) 3 Cleantech Loop 4 , #01\/01 CleanTech Two, Singapore 637143,","place":["Republic of Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Lan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Imperial College London 3 , London, SW7 2AZ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1834-7040","authenticated-orcid":false,"given":"Christopher M.","family":"Kube","sequence":"additional","affiliation":[{"name":"Department of Engineering Science and Mechanics, The Pennsylvania State University 1 , University Park, Pennsylvania 16802,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2026,10,22]]},"reference":[{"key":"2026102208022567200_c1","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1121\/1.1916504","article-title":"Attenuation and scattering of high frequency sound waves in metals and glasses","volume":"19","year":"1947","journal-title":"J. Acoust. Soc. Am."},{"key":"2026102208022567200_c2","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1121\/1.390577","article-title":"A unified theory for elastic wave propagation in polycrystalline materials","volume":"75","year":"1984","journal-title":"J. Acoust. Soc. Am."},{"key":"2026102208022567200_c3","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/0022-5096(90)90021-U","article-title":"Diffusivity of ultrasound in polycrystals","volume":"38","year":"1990","journal-title":"J. Mech. Phys. Solids"},{"key":"2026102208022567200_c4","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1016\/j.ultras.2011.02.002","article-title":"Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials","volume":"51","year":"2011","journal-title":"Ultrasonics"},{"key":"2026102208022567200_c5","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.wavemoti.2015.05.004","article-title":"Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries","volume":"58","year":"2015","journal-title":"Wave Motion"},{"key":"2026102208022567200_c6","doi-asserted-by":"publisher","first-page":"3231","DOI":"10.1007\/s00707-024-03880-8","article-title":"Effects of grain size distributions on scattering attenuation of elastic waves in polycrystalline materials","volume":"235","year":"2024","journal-title":"Acta Mech."},{"key":"2026102208022567200_c7","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/978-1-4615-1987-4_6","article-title":"Single scattering and diffusive limits of the ultrasonic radiative transfer equation","volume-title":"Review of Progress in Quantitative Nondestructive Evaluation","year":"1995"},{"key":"2026102208022567200_c8","doi-asserted-by":"publisher","first-page":"1804","DOI":"10.1121\/1.4978008","article-title":"Iterative solution to bulk wave propagation in polycrystalline materials","volume":"141","year":"2017","journal-title":"J. Acoust. Soc. Am."},{"key":"2026102208022567200_c9","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1190\/1.1440605","article-title":"Synthetic seismograms: A finite-difference approach","volume":"41","year":"1976","journal-title":"Geophysics"},{"key":"2026102208022567200_c10","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1190\/1.1442147","article-title":"P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method","volume":"51","year":"1986","journal-title":"Geophysics"},{"key":"2026102208022567200_c11","doi-asserted-by":"publisher","first-page":"3042","DOI":"10.1785\/0120010167","article-title":"3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities","volume":"92","year":"2002","journal-title":"Bull. Seismol. Soc. Am."},{"key":"2026102208022567200_c12","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1190\/1.1707078","article-title":"Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid","volume":"69","year":"2004","journal-title":"Geophysics"},{"key":"2026102208022567200_c13","doi-asserted-by":"publisher","first-page":"T109","DOI":"10.1190\/1.2213051","article-title":"Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves","volume":"71","year":"2006","journal-title":"Geophysics"},{"key":"2026102208022567200_c14","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1109\/TUFFC.2009.1197","article-title":"Numerical model of longitudinal wave scattering in polycrystals","volume":"56","year":"2009","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"2026102208022567200_c15","doi-asserted-by":"publisher","first-page":"2326","DOI":"10.1121\/1.4931445","article-title":"Finite element modelling of elastic wave scattering within a polycrystalline material in two and three dimensions","volume":"138","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"2026102208022567200_c16","doi-asserted-by":"publisher","first-page":"20160738","DOI":"10.1098\/rspa.2016.0738","article-title":"Finite-element modelling of elastic wave propagation and scattering within heterogeneous media","volume":"473","year":"2017","journal-title":"Proc. R. Soc. A"},{"key":"2026102208022567200_c17","doi-asserted-by":"publisher","first-page":"1890","DOI":"10.1121\/10.0002102","article-title":"Maximizing the accuracy of finite element simulation of elastic wave propagation in polycrystals","volume":"148","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"key":"2026102208022567200_c18","doi-asserted-by":"publisher","first-page":"20210850","DOI":"10.1098\/rspa.2021.0850","article-title":"Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals","volume":"478","year":"2022","journal-title":"Proc. R Soc. A"},{"key":"2026102208022567200_c19","doi-asserted-by":"publisher","first-page":"107517","DOI":"10.1016\/j.ultras.2024.107517","article-title":"Numerical estimation of ultrasonic phase velocity and attenuation for longitudinal and shear waves in polycrystalline materials","volume":"148","year":"2025","journal-title":"Ultrasonics"},{"key":"2026102208022567200_c20","doi-asserted-by":"publisher","first-page":"107642","DOI":"10.1016\/j.ultras.2025.107642","article-title":"Ultrasonic scattering in polycrystalline materials with elongated grains: A comparative 3D and 2D theoretical and numerical analysis","volume":"152","year":"2025","journal-title":"Ultrasonics"},{"key":"2026102208022567200_c21","doi-asserted-by":"publisher","first-page":"9373","DOI":"10.1016\/j.jcp.2010.09.008","article-title":"A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media","volume":"229","year":"2010","journal-title":"J. Comput. Phys."},{"key":"2026102208022567200_c22","doi-asserted-by":"publisher","first-page":"107208","DOI":"10.1016\/j.compstruc.2023.107208","article-title":"A coupled acoustic\/elastic discontinuous Galerkin finite element method: Application to ultrasonic imaging of 3D-printed synthetic materials","volume":"291","year":"2024","journal-title":"Comput. Struct."},{"key":"2026102208022567200_c23","first-page":"375","article-title":"M\u00e9moire sur les lois de l'\u00e9quilibre et du mouvement des corps solides \u00e9lastiques\u201d (\u201cMemoir on the laws of equilibrium and motion of elastic solid bodies\u201d)","volume":"7","year":"1827","journal-title":"M\u00e9m. Acad. R. Sci. Inst. France"},{"key":"2026102208022567200_c24","volume-title":"Le\u00e7ons Sur la Propagation Des Ondes et Les \u00c9quations de L'hydrodynamique (Lectures on the Propagation of Waves and the Equations of Hydrodynamics","year":"1903"},{"key":"2026102208022567200_c25","doi-asserted-by":"publisher","first-page":"3674","DOI":"10.1177\/1081286518757284","article-title":"Ignaczak equation of elastodynamics","volume":"24","year":"2019","journal-title":"Math. Mech. Solids"},{"key":"2026102208022567200_c26","doi-asserted-by":"publisher","first-page":"064001","DOI":"10.1121\/10.0004317","article-title":"Stress formulation of elastic wave motion","volume":"1","year":"2021","journal-title":"JASA Express Lett."},{"key":"2026102208022567200_c27","doi-asserted-by":"publisher","first-page":"103002","DOI":"10.1016\/j.wavemoti.2022.103002","article-title":"Stress formulation of acoustoelasticity","volume":"114","year":"2022","journal-title":"Wave Motion"},{"key":"2026102208022567200_c28","doi-asserted-by":"publisher","first-page":"5069","DOI":"10.1121\/10.0044107","article-title":"A pure stress formulation for modeling elastic waves using central finite differences","volume":"159","year":"2026","journal-title":"J. Acoust. Soc. Am."},{"key":"2026102208022567200_c29","doi-asserted-by":"publisher","first-page":"107369","DOI":"10.1016\/j.compstruc.2024.107369","article-title":"A displacement-based finite element formulation for solving elastic wave problems in coupled fluid-solid media on a GPU","volume":"299","year":"2024","journal-title":"Comput. Struct."},{"key":"2026102208022567200_c30","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1088\/0022-3727\/21\/6\/003","article-title":"Modelling the propagation and scattering of elastic waves in inhomogeneous anisotropic media","volume":"21","year":"1988","journal-title":"J. Phys. D: Appl. Phys."},{"key":"2026102208022567200_c31","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1186\/2193-9772-3-5","article-title":"DREAM.3D: A digital representation environment for the analysis of microstructure in 3D","volume":"3","year":"2014","journal-title":"Integr. Mater. Manuf. Innov."},{"key":"2026102208022567200_c32","doi-asserted-by":"publisher","first-page":"1729","DOI":"10.1016\/j.cma.2011.01.002","article-title":"Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing","volume":"200","year":"2011","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2026102208022567200_c33","doi-asserted-by":"publisher","first-page":"225109","DOI":"10.1063\/5.0091521","article-title":"Von K\u00e1rm\u00e1n spatial correlation function to describe wave propagation in polycrystalline media","volume":"131","year":"2022","journal-title":"J. Appl. Phys."},{"key":"2026102208022567200_c34","volume-title":"Seismic Wave Propagation and Scattering in the Heterogeneous Earth","year":"2012"}],"container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/160\/4\/3340\/21178959\/3340_1_10.0046885.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/160\/4\/3340\/21178959\/3340_1_10.0046885.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:02:36Z","timestamp":1792670556000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/160\/4\/3340\/3407144\/Computational-stress-formulation-for-ultrasonic"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1121\/10.0046885","relation":{},"ISSN":["1520-8524"],"issn-type":[{"value":"1520-8524","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10]]},"published":{"date-parts":[[2026,10,1]]}}}