{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T00:20:58Z","timestamp":1789690858615,"version":"4.0.1"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:00:00Z","timestamp":1779321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["DMR 2221854"],"award-info":[{"award-number":["DMR 2221854"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["CMMI 2525114"],"award-info":[{"award-number":["CMMI 2525114"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"award":["DMR 2221854"],"award-info":[{"award-number":["DMR 2221854"]}],"id":[{"id":"https:\/\/ror.org\/021nxhr62","id-type":"ROR","asserted-by":"publisher"}]},{"award":["CMMI 2525114"],"award-info":[{"award-number":["CMMI 2525114"]}],"id":[{"id":"https:\/\/ror.org\/021nxhr62","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Mean atomic bond strain (MABS), based on the globally averaged bond length, has recently emerged as a new strain metric that retains clear physical meaning even as severe atomic neighborhood reconstruction occurs. It has been shown to exhibit a nearly perfect linear relationship with global stress throughout the elastic and plastic deformation in single-crystal face-centered cubic (FCC) metals, contradicting conventional expectations based on nonlinear dislocation activity. Whether this near-linear relationship holds in other materials stands out as an important and intriguing question. In this study, we examine the MABS\u2013stress relationship in representative unary, binary, and ternary metallic glasses (MGs), where neither a crystal structure nor dislocations are present. Large-scale molecular dynamics simulations of uniaxial tensile tests and statistical analysis of millions of atomic bonds are performed. Irrespective of their differing compositions, all the MGs exhibit a persistent near-linear relationship between total MABS (all bonds included) and global stress up to fracture, even in the presence of significant local nonaffine displacements (shear transformation zones and shear bands), with the Pearson correlation coefficient consistently exceeding 0.99. Unlike the nonaffine displacements, the spatial distribution of individual atomic bond strain does not localize under the uniaxial loading. In the MGs containing more than one element, MABS computed for a single bond type may not correlate as linearly with global stress as total MABS. The results demonstrate that the persistent near-linear total MABS\u2013stress relationship over the entire deformation process, recently discovered in single-crystal FCC metals, also applies to MGs despite their vastly different atomic structures. This strengthens the candidacy of total MABS as a universal stress descriptor across materials classes and deformation regimes. With further development and implementation in atomistic simulations and constitutive modeling, the MABS concept has the potential to reshape our understanding of materials mechanics and generate new insights into the design of stronger, tougher, and more thermally and chemically stable materials.<\/jats:p>","DOI":"10.3390\/ma19102176","type":"journal-article","created":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T15:02:27Z","timestamp":1779375747000},"page":"2176","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Persistent Near-Linear Relationship Between Global Stress and Mean Atomic Bond Strain in Metallic Glasses Despite Significant Local Nonaffine Displacements"],"prefix":"10.3390","volume":"19","author":[{"given":"Tittaya","family":"Thaiyanurak","sequence":"first","affiliation":[{"name":"Materials Science Program, Oregon State University, Corvallis, OR 97331, USA"},{"name":"School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5018-5603","authenticated-orcid":false,"given":"Donghua","family":"Xu","sequence":"additional","affiliation":[{"name":"Materials Science Program, Oregon State University, Corvallis, OR 97331, USA"},{"name":"School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/0021-9991(92)90048-4","article-title":"The atomic strain tensor","volume":"101","author":"Mott","year":"1992","journal-title":"J. Comput. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7192","DOI":"10.1103\/PhysRevE.57.7192","article-title":"Dynamics of viscoplastic deformation in amorphous solids","volume":"57","author":"Falk","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.2320\/matertrans.MJ200769","article-title":"Theory of shear banding in metallic glasses and molecular dynamics calculations","volume":"48","author":"Shimizu","year":"2007","journal-title":"Mater. Trans."},{"key":"ref_4","unstructured":"Holzapfel, G.A. (2000). Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Wiley."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"205103","DOI":"10.1063\/5.0225095","article-title":"Size-dependent atomic strain localization mechanism in Nb\/amorphous CuNb nanolayered composites","volume":"136","author":"Chen","year":"2024","journal-title":"J. Appl. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"095101","DOI":"10.1063\/1.5085750","article-title":"Structural evolution and dislocation behaviour during nano-rolling process of FCC metals: A molecular dynamics simulation based investigation","volume":"125","author":"Reddy","year":"2019","journal-title":"J. Appl. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"231905","DOI":"10.1063\/1.2821832","article-title":"Assessing the critical sizes for shear band formation in metallic glasses from molecular dynamics simulation","volume":"91","author":"Li","year":"2007","journal-title":"Appl. Phys. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.2320\/matertrans.48.1001","article-title":"Influence of size and number of nanocrystals on shear band formation in amorphous alloys","volume":"48","author":"Park","year":"2007","journal-title":"Mater. Trans."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Xu, D., Gordon, O., Ye, M., Chen, L., Thaiyanurak, T., and Wang, Z. (2024). Non-Equal Contributions of Different Elements and Atomic Bonds to the Strength and Deformability of a Multicomponent Metallic Glass Zr47Cu46Al7. Molecules, 29.","DOI":"10.3390\/molecules29215005"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Thaiyanurak, T., Gordon, O., Ye, M., Wang, Z., and Xu, D. (2025). Compositional Effects on the Tensile Behavior of Atomic Bonds in Multicomponent Cu93\u2212xZrxAl7 (at.%) Metallic Glasses. Molecules, 30.","DOI":"10.3390\/molecules30122602"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Xu, D., Thaiyanurak, T., and Salsabil, N. (2026). Atomic Bond Strain: A New Strain Measure Displaying Nearly Perfect Linear Correlation with Stress Throughout Plastic Deformation of Single-Crystal FCC Metals. Solids, 7.","DOI":"10.3390\/solids7010005"},{"key":"ref_12","unstructured":"Anderson, P.M., Hirth, J.P., and Lothe, J. (2017). Theory of Dislocations, Cambridge University Press."},{"key":"ref_13","unstructured":"Nabarro, F.R.N. (1987). Theory of Crystal Dislocations, Dover Publications."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1557\/S0883769400053252","article-title":"Bulk glass-forming metallic alloys: Science and technology","volume":"24","author":"Johnson","year":"1999","journal-title":"MRS Bull."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.scriptamat.2005.09.051","article-title":"Metallic glasses as structural materials","volume":"54","author":"Ashby","year":"2006","journal-title":"Scr. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1063\/PT.3.1885","article-title":"BULK Metallic Glasses","volume":"66","author":"Schroers","year":"2013","journal-title":"Phys. Today"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/S0966-9795(03)00046-3","article-title":"Bulk metallic glasses","volume":"11","author":"Loffler","year":"2003","journal-title":"Intermetallics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"S2357","DOI":"10.1088\/0953-8984\/15\/31\/311","article-title":"Local structure of Al- and Fe-based metallic glasses","volume":"15","author":"Ahn","year":"2003","journal-title":"J. Phys.-Condens. Matter"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2342","DOI":"10.1063\/1.110520","article-title":"A highly processable metallic glass: Zr41.2Ti13.8Cu12.5Ni10.0Be22.5","volume":"63","author":"Peker","year":"1993","journal-title":"Appl. Phys. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1557\/JMR.2004.0176","article-title":"Fe-based bulk metallic glasses with diameter thickness larger than one centimeter","volume":"19","author":"Ponnambalam","year":"2004","journal-title":"J. Mater. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"011901","DOI":"10.1063\/1.5131645","article-title":"Rare-earth and precious-metal free Cu-based metallic glasses with superior glass-forming ability and processability","volume":"116","author":"Saini","year":"2020","journal-title":"Appl. Phys. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1557\/s43577-022-00370-x","article-title":"Toward damage-tolerant bulk metallic glasses: Fracture behavior and brittle-ductile transition","volume":"47","author":"Ryu","year":"2022","journal-title":"MRS Bull."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3429","DOI":"10.1016\/S1359-6454(03)00164-2","article-title":"Deformation behavior of the Zr41.2Ti13.8CU12.5Ni10Be22.5 bulk metallic glass over a wide range of strain-rates and temperatures","volume":"51","author":"Lu","year":"2003","journal-title":"Acta Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1016\/j.msea.2003.10.032","article-title":"Nanoindentation studies of shear banding in fully amorphous and partially devitrified metallic alloys","volume":"375","author":"Greer","year":"2004","journal-title":"Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Thaiyanurak, T., Soonthornkit, S., Gordon, O., Feng, Z., and Xu, D. (2024). Deformation-Induced Crystal Growth or Redissolution, and Crystal-Induced Strengthening or Ductilization in Metallic Glasses Containing Nanocrystals. Materials, 17.","DOI":"10.3390\/ma17112567"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.intermet.2018.08.012","article-title":"Probing structural changes during ductile fracture in metallic glasses via in situ straining inside a MeV transmission electron microscope","volume":"102","author":"Chang","year":"2018","journal-title":"Intermetallics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"642","DOI":"10.2320\/matertrans.42.642","article-title":"Deformation mechanisms of the Zr40Ti14Ni10Cu12Be24 bulk metallic glass","volume":"42","author":"Wright","year":"2001","journal-title":"Mater. Trans."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"108171","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales","volume":"271","author":"Thompson","year":"2022","journal-title":"Comput. Phys. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jcph.1995.1039","article-title":"Fast Parallel Algorithms For Short-Range Molecular-Dynamics","volume":"117","author":"Plimpton","year":"1995","journal-title":"J. Comput. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"015012","DOI":"10.1088\/0965-0393\/18\/1\/015012","article-title":"Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool","volume":"18","author":"Stukowski","year":"2010","journal-title":"Model. Simul. Mater. Sci. Eng."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/10\/2176\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T04:23:58Z","timestamp":1779769438000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/10\/2176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,21]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["ma19102176"],"URL":"https:\/\/doi.org\/10.3390\/ma19102176","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,21]]}}}