{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:20:04Z","timestamp":1772137204862,"version":"3.50.1"},"reference-count":80,"publisher":"AIP Publishing","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CHE-1944892\/2326678"],"award-info":[{"award-number":["CHE-1944892\/2326678"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["OAC-1827314"],"award-info":[{"award-number":["OAC-1827314"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2138259"],"award-info":[{"award-number":["2138259"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2138286"],"award-info":[{"award-number":["2138286"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2138307"],"award-info":[{"award-number":["2138307"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2137603"],"award-info":[{"award-number":["2137603"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2138296"],"award-info":[{"award-number":["2138296"]}],"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":[[2026,1,14]]},"abstract":"<jats:p>Computational modeling, such as molecular dynamics and Monte Carlo simulations, can be used to estimate the elastic properties of materials through various stress and strain relationships. Here, we demonstrate the effectiveness of the stress\u2013stress fluctuation (SSF) method to estimate the elastic properties of simple van der Waals and molecular materials. The SSF method allows computation of the complete elasticity tensor from a single equilibrium simulation without requiring any type of deformation. While extensively used to characterize the elastic coefficients of crystalline solids and glassy systems, application of the SSF method to fluid systems and biomaterials has been limited. Starting with argon in the solid, liquid, and gas phases, we show that the SSF method gives elastic coefficients and moduli in excellent agreement with values obtained with the explicit deformation and volume fluctuation methods. Comparison of the elastic coefficients and bulk modulus for solid argon with previous computational studies and experimental data provides further validation of our numerical implementation. Beyond argon, we show that the elastic properties of molecular fluids simulated with the coarse-grained MARTINI force-field, which include multi-body interactions such as angle potentials, are also accurately captured by the SSF method. Moreover, the impulsive correction for truncated potentials is essential to obtain accurate values for these fluids and vanishing shear moduli. Our results highlight the broad applicability of the SSF method across a broad range of systems and lay the foundation for its use to characterize the elastic properties of complex molecular systems.<\/jats:p>","DOI":"10.1063\/5.0303843","type":"journal-article","created":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T13:36:02Z","timestamp":1768311362000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Microscopic elasticity from MD. I. Bulk solid and fluid systems"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3718-0930","authenticated-orcid":false,"given":"Andrew L.","family":"Lewis","sequence":"first","affiliation":[{"name":"Department of Physics, The University of Vermont 1 , Burlington, Vermont 05405,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin","family":"Himberg","sequence":"additional","affiliation":[{"name":"Materials Science Graduate Program, The University of Vermont 2 , Burlington, Vermont 05405,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4275-173X","authenticated-orcid":false,"given":"Alejandro","family":"Torres-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"European Molecular Biology Laboratory 3 , Barcelona,","place":["Spain"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1381-1649","authenticated-orcid":false,"given":"Juan M.","family":"Vanegas","sequence":"additional","affiliation":[{"name":"Department of Biochemistry and Biophysics, Oregon State University 4 , Corvallis, Oregon 97331,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,1,13]]},"reference":[{"key":"2026011308355741700_c1","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1016\/0031-8914(69)90031-7","article-title":"Isothermal elastic constants for argon. Theory and Monte Carlo calculations","volume":"42","year":"1969","journal-title":"Physica"},{"key":"2026011308355741700_c2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/physrevb.54.1","article-title":"Fluctuation formula for elastic constants","volume":"54","year":"1996","journal-title":"Phys. Rev. B"},{"key":"2026011308355741700_c3","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1103\/physrevb.33.895","article-title":"Calculation of elastic constants using isothermal molecular dynamics","volume":"33","year":"1986","journal-title":"Phys. Rev. B"},{"key":"2026011308355741700_c4","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1080\/08927022.2017.1313418","article-title":"Computation of elastic constants of solids using molecular simulation: Comparison of constant volume and constant pressure ensemble methods","volume":"43","year":"2017","journal-title":"Mol. Simul."},{"key":"2026011308355741700_c5","doi-asserted-by":"publisher","first-page":"046705","DOI":"10.1103\/physreve.86.046705","article-title":"Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential","volume":"86","year":"2012","journal-title":"Phys. Rev. E"},{"key":"2026011308355741700_c6","doi-asserted-by":"publisher","first-page":"12A533","DOI":"10.1063\/1.4790137","article-title":"Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature, and sampling time","volume":"138","year":"2013","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c7","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/s0022-5193(70)80032-7","article-title":"The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell","volume":"26","year":"1970","journal-title":"J.\u00a0Theor. Biol."},{"key":"2026011308355741700_c8","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1515\/znc-1973-11-1209","article-title":"Elastic properties of lipid bilayers: Theory and possible experiments","volume":"28","year":"1973","journal-title":"Z. Naturforsch. C"},{"key":"2026011308355741700_c9","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1051\/jp2:1993132","article-title":"Bending tensions and the bending rigidity of fluid membranes","volume":"3","year":"1993","journal-title":"J.\u00a0Phys. II Fr."},{"key":"2026011308355741700_c10","doi-asserted-by":"publisher","first-page":"084702","DOI":"10.1063\/1.4990404","article-title":"Novel tilt-curvature coupling in lipid membranes","volume":"147","year":"2017","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c11","doi-asserted-by":"publisher","first-page":"164108","DOI":"10.1063\/1.5119683","article-title":"A consistent quadratic curvature-tilt theory for fluid lipid membranes","volume":"151","year":"2019","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c12","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s101890070003","article-title":"Elastic energy of tilt and bending of fluid membranes","volume":"3","year":"2000","journal-title":"Eur. Phys. J. E"},{"key":"2026011308355741700_c13","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.cis.2014.01.018","article-title":"Helfrich model of membrane bending: From Gibbs theory of liquid interfaces to membranes as thick anisotropic elastic layers","volume":"208","year":"2014","journal-title":"Adv. Colloid Interface Sci."},{"key":"2026011308355741700_c14","doi-asserted-by":"publisher","first-page":"1182","DOI":"10.1103\/physreva.44.1182","article-title":"Shape transformations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models","volume":"44","year":"1991","journal-title":"Phys. Rev. A"},{"key":"2026011308355741700_c15","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1039\/c2sm26891d","article-title":"Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease","volume":"9","year":"2013","journal-title":"Soft Matter"},{"key":"2026011308355741700_c16","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1007\/s10237-013-0528-6","article-title":"Small scale membrane mechanics","volume":"13","year":"2013","journal-title":"Biomech. Model. Mechanobiol."},{"key":"2026011308355741700_c17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12013-008-9024-5","article-title":"Mechanosensitive channels: Insights from continuum-based simulations","volume":"52","year":"2008","journal-title":"Cell Biochem. Biophys."},{"key":"2026011308355741700_c18","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.1016\/j.bpj.2017.01.035","article-title":"Gramicidin A channel formation induces local lipid redistribution II: A 3D continuum elastic model","volume":"112","year":"2017","journal-title":"Biophys. J."},{"key":"2026011308355741700_c19","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.cis.2014.03.003","article-title":"Recent developments in the field of bending rigidity measurements on membranes","volume":"208","year":"2014","journal-title":"Adv. Colloid Interface Sci."},{"key":"2026011308355741700_c20","doi-asserted-by":"publisher","first-page":"214103","DOI":"10.1063\/5.0049448","article-title":"Identifying systematic errors in a power spectral analysis of simulated lipid membranes","volume":"154","year":"2021","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c21","doi-asserted-by":"publisher","first-page":"042413","DOI":"10.1103\/physreve.103.042413","article-title":"Spatial extent of a single lipid\u2019s influence on bilayer mechanics","volume":"103","year":"2021","journal-title":"Phys. Rev. E"},{"key":"2026011308355741700_c22","doi-asserted-by":"publisher","first-page":"1403","DOI":"10.1016\/j.bpj.2012.02.013","article-title":"Determining the Gaussian curvature modulus of lipid membranes in simulations","volume":"102","year":"2012","journal-title":"Biophys. J."},{"key":"2026011308355741700_c23","doi-asserted-by":"publisher","first-page":"6061","DOI":"10.1021\/acs.jpcb.6b02016","article-title":"Determining the lipid tilt modulus by simulating membrane buckles","volume":"120","year":"2016","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026011308355741700_c24","doi-asserted-by":"publisher","first-page":"e2025011118","DOI":"10.1073\/pnas.2025011118","article-title":"A needless but interesting controversy","volume":"118","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026011308355741700_c25","doi-asserted-by":"publisher","first-page":"2258","DOI":"10.1039\/D4SM01312C","article-title":"The effect of cholesterol on the bending modulus of DOPC bilayers: Re-analysis of NSE data","volume":"21","year":"2025","journal-title":"Soft Matter"},{"key":"2026011308355741700_c26","doi-asserted-by":"publisher","first-page":"e2102845118","DOI":"10.1073\/pnas.2102845118","article-title":"Reply to Nagle et\u00a0al.: The universal stiffening effects of cholesterol on lipid membranes","volume":"118","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026011308355741700_c27","doi-asserted-by":"publisher","first-page":"2104","DOI":"10.1016\/j.bpj.2011.03.010","article-title":"Interpretation of fluctuation spectra in lipid bilayer simulations","volume":"100","year":"2011","journal-title":"Biophys. J."},{"key":"2026011308355741700_c28","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.chemphyslip.2014.04.003","article-title":"What are the true values of the bending modulus of simple lipid bilayers?","volume":"185","year":"2015","journal-title":"Chem. Phys. Lipids"},{"key":"2026011308355741700_c29","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.chemphyslip.2017.04.006","article-title":"Experimentally determined tilt and bending moduli of single-component lipid bilayers","volume":"205","year":"2017","journal-title":"Chem. Phys. Lipids"},{"key":"2026011308355741700_c30","doi-asserted-by":"publisher","first-page":"2662","DOI":"10.1063\/1.443248","article-title":"Strain fluctuations and elastic constants","volume":"76","year":"1982","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c31","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1088\/0370-1328\/85\/3\/313","article-title":"Second-order elastic constants of a solid under stress","volume":"85","year":"1965","journal-title":"Proc. Phys. Soc."},{"key":"2026011308355741700_c32","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1007\/bf01127732","article-title":"Statistical mechanics of elastic moduli","volume":"42","year":"1986","journal-title":"J.\u00a0Stat. Phys."},{"key":"2026011308355741700_c33","doi-asserted-by":"publisher","first-page":"1152","DOI":"10.1063\/1.341877","article-title":"Stress and elastic constants in anisotropic solids: Molecular dynamics techniques","volume":"64","year":"1988","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026011308355741700_c34","doi-asserted-by":"publisher","first-page":"2991","DOI":"10.1063\/1.342716","article-title":"Generalized expressions for the calculation of elastic constants by computer simulation","volume":"65","year":"1989","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026011308355741700_c35","doi-asserted-by":"publisher","first-page":"108674","DOI":"10.1016\/j.cpc.2023.108674","article-title":"Computation of the thermal elastic constants for arbitrary manybody potentials in LAMMPS using the stress-fluctuation formalism","volume":"286","year":"2023","journal-title":"Comput. Phys. Commun."},{"key":"2026011308355741700_c36","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.cpc.2011.09.006","article-title":"A deformation\u2013fluctuation hybrid method for fast evaluation of elastic constants with many-body potentials","volume":"183","year":"2012","journal-title":"Comput. Phys. Commun."},{"key":"2026011308355741700_c37","doi-asserted-by":"publisher","first-page":"114107","DOI":"10.1063\/5.0020514","article-title":"Pressure control using stochastic cell rescaling","volume":"153","year":"2020","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c38","volume-title":"Modeling Materials: Continuum, Atomistic, and Multiscale Techniques","year":"2011"},{"key":"2026011308355741700_c39","doi-asserted-by":"publisher","first-page":"184108","DOI":"10.1103\/physrevb.71.184108","article-title":"Statistical calculation of elastic moduli for atomistic models","volume":"71","year":"2005","journal-title":"Phys. Rev. B"},{"key":"2026011308355741700_c40","volume-title":"Dynamical Theory of Crystal Lattices","year":"1954"},{"key":"2026011308355741700_c41","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1098\/rspa.1950.0133","article-title":"On the atomic theory of elasticity","volume":"203","year":"1950","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026011308355741700_c42","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/978-90-481-9778-1_5","article-title":"A unified interpretation of stress in molecular systems","volume":"100","year":"2010","journal-title":"J.\u00a0Elasticity"},{"key":"2026011308355741700_c43","doi-asserted-by":"publisher","first-page":"144506","DOI":"10.1063\/1.2338522","article-title":"Expressions for the stress and elasticity tensors for angle-dependent potentials","volume":"125","year":"2006","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c44","doi-asserted-by":"publisher","first-page":"073603","DOI":"10.1103\/PhysRevMaterials.7.073603","article-title":"Analytic elastic coefficients in molecular calculations: Finite strain, nonaffine displacements, and many-body interatomic potentials","volume":"7","year":"2023","journal-title":"Phys. Rev. Mater."},{"key":"2026011308355741700_c45","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1021\/ct4008926","article-title":"Importance of force decomposition for local stress calculations in biomembrane molecular simulations","volume":"10","year":"2014","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026011308355741700_c46","doi-asserted-by":"publisher","first-page":"258102","DOI":"10.1103\/physrevlett.114.258102","article-title":"Examining the mechanical equilibrium of microscopic stresses in molecular simulations","volume":"114","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"2026011308355741700_c47","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1016\/j.jmps.2016.03.006","article-title":"Geometric derivation of the microscopic stress: A covariant central force decomposition","volume":"93","year":"2016","journal-title":"J.\u00a0Mech. Phys. Solids"},{"key":"2026011308355741700_c48","doi-asserted-by":"publisher","first-page":"061102","DOI":"10.1103\/physreve.71.061102","article-title":"Isothermal stress and elasticity tensors for ions and point dipoles using Ewald summations","volume":"71","year":"2005","journal-title":"Phys. Rev. E"},{"key":"2026011308355741700_c49","doi-asserted-by":"publisher","first-page":"5370","DOI":"10.1103\/physreve.54.5370","article-title":"Elastic properties of randomly cross-linked polymers","volume":"54","year":"1996","journal-title":"Phys. Rev. E"},{"key":"2026011308355741700_c50","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1088\/0965-0393\/7\/3\/307","article-title":"Convergence issues in molecular dynamics simulations of highly entropic materials","volume":"7","year":"1999","journal-title":"Modell. Simul. Mater. Sci. Eng."},{"key":"2026011308355741700_c51","doi-asserted-by":"publisher","first-page":"3841","DOI":"10.1103\/physrevb.54.3841","article-title":"Stability criteria for homogeneously stressed materials and the calculation of elastic constants","volume":"54","year":"1996","journal-title":"Phys. Rev. B"},{"key":"2026011308355741700_c52","doi-asserted-by":"publisher","first-page":"053002","DOI":"10.1103\/physreve.97.053002","article-title":"Stress-stress fluctuation formula for elastic constants in the NPT ensemble","volume":"97","year":"2018","journal-title":"Phys. Rev. E"},{"key":"2026011308355741700_c53","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1038\/s41592-021-01098-3","article-title":"Martini 3: A general purpose force field for coarse-grained molecular dynamics","volume":"18","year":"2021","journal-title":"Nat. Methods"},{"key":"2026011308355741700_c54","doi-asserted-by":"publisher","first-page":"014703","DOI":"10.1063\/5.0303850","article-title":"Microscopic elasticity from MD. II. Liquid interfaces and lipid membranes","volume":"164","year":"2025","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c55","doi-asserted-by":"publisher","first-page":"235","DOI":"10.2307\/2371405","article-title":"Finite deformations of an elastic solid","volume":"59","year":"1937","journal-title":"Am. J. Math."},{"key":"2026011308355741700_c56","doi-asserted-by":"publisher","first-page":"776","DOI":"10.1103\/physrev.162.776","article-title":"Thermoelasticity of stressed materials and comparison of various elastic constants","volume":"162","year":"1967","journal-title":"Phys. Rev."},{"key":"2026011308355741700_c57","volume-title":"Thermodynamics of Crystals","year":"1972"},{"key":"2026011308355741700_c58","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1103\/physrev.71.809","article-title":"Finite elastic strain of cubic crystals","volume":"71","year":"1947","journal-title":"Phys. Rev."},{"key":"2026011308355741700_c59","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1023\/a:1007675928019","article-title":"An area modulus of elasticity: Definition and properties","volume":"58","year":"2000","journal-title":"J.\u00a0Elasticity"},{"key":"2026011308355741700_c60","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.softx.2015.06.001","article-title":"GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers","volume":"1\u20132","year":"2015","journal-title":"SoftwareX"},{"key":"2026011308355741700_c61","unstructured":"J. M. Vanegas , B.Himberg, A.Lewis, and A.Torres-S\u00e1nchez (2025). \u201cGROMACS-LS and MDStress library: Tools for local stress and elasticity calculations,\u201d Zenodo.https:\/\/zenodo.org\/records\/17179200"},{"key":"2026011308355741700_c62","doi-asserted-by":"publisher","first-page":"816","DOI":"10.1088\/0370-1328\/82\/6\/302","article-title":"On the statistical mechanics of the ideal inert gas solids","volume":"82","year":"1963","journal-title":"Proc. Phys. Soc."},{"key":"2026011308355741700_c63","doi-asserted-by":"publisher","first-page":"014101","DOI":"10.1063\/1.2408420","article-title":"Canonical sampling through velocity rescaling","volume":"126","year":"2007","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026011308355741700_c64","doi-asserted-by":"publisher","first-page":"8919","DOI":"10.1021\/acs.jctc.3c00777","article-title":"Neighbor list artifacts in molecular dynamics simulations","volume":"19","year":"2023","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026011308355741700_c65","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","year":"2020","journal-title":"Nature"},{"key":"2026011308355741700_c66","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental algorithms for scientific computing in Python","volume":"17","year":"2020","journal-title":"Nat. Methods"},{"key":"2026011308355741700_c67","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/mcse.2007.55","article-title":"Matplotlib: A 2D graphics environment","volume":"9","year":"2007","journal-title":"Comput. Sci. Eng."},{"key":"2026011308355741700_c68","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0375-9601(71)90321-5","article-title":"Temperature dependence of the hypersonic velocity in a single crystal of argon","volume":"37","year":"1971","journal-title":"Phys. Lett. A"},{"key":"2026011308355741700_c69","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/0375-9601(72)90680-9","article-title":"The elastic constants of solid argon determined by stimulated Brillouin scattering","volume":"40","year":"1972","journal-title":"Phys. Lett. A"},{"key":"2026011308355741700_c70","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1103\/physrev.150.703","article-title":"Measurements of X-ray lattice constant, thermal expansivity, and isothermal compressibility of argon crystals","volume":"150","year":"1966","journal-title":"Phys. Rev."},{"key":"2026011308355741700_c71","doi-asserted-by":"publisher","first-page":"1587","DOI":"10.3103\/s0025654423601301","article-title":"Comparison of isothermal and adiabatic elasticity characteristics of the single crystal nickel-based superalloy CMSX-4 in the temperature range between room temperature and 1300\u00b0C","volume":"58","year":"2023","journal-title":"Mech. Solids"},{"key":"2026011308355741700_c72","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/0031-8914(69)90217-1","article-title":"Adiabatic elastic constants for argon. Theory and Monte Carlo calculations","volume":"44","year":"1969","journal-title":"Physica"},{"key":"2026011308355741700_c73","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/BF01325676","article-title":"On three body forces in solid argon","volume":"192","year":"1966","journal-title":"Z. Phys. A Hadron Nucl."},{"key":"2026011308355741700_c74","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1038\/nmat3134","article-title":"Poisson\u2019s ratio and modern materials","volume":"10","year":"2011","journal-title":"Nat. Mater."},{"key":"2026011308355741700_c75","doi-asserted-by":"publisher","first-page":"8209","DOI":"10.1021\/acs.jpcb.5b03611","article-title":"MARTINI coarse-grained models of polyethylene and polypropylene","volume":"119","year":"2015","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026011308355741700_c76","doi-asserted-by":"publisher","first-page":"14353","DOI":"10.1021\/jp3095165","article-title":"A coarse-grained MARTINI model of polyethylene glycol and of polyoxyethylene alkyl ether surfactants","volume":"116","year":"2012","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026011308355741700_c77","doi-asserted-by":"publisher","first-page":"7112","DOI":"10.1021\/acs.jctc.3c00733","article-title":"Pragmatic coarse-graining of proteins: Models and applications","volume":"19","year":"2023","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026011308355741700_c78","doi-asserted-by":"publisher","first-page":"7812","DOI":"10.1021\/jp071097f","article-title":"The MARTINI force field: Coarse grained model for biomolecular simulations","volume":"111","year":"2007","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026011308355741700_c79","doi-asserted-by":"publisher","first-page":"1934","DOI":"10.1039\/b818713d","article-title":"On using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models","volume":"11","year":"2009","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026011308355741700_c80","volume-title":"An Introduction to Fourier Analysis and Generalised Functions","year":"1958"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0303843\/20868862\/024110_1_5.0303843.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0303843\/20868862\/024110_1_5.0303843.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T13:36:04Z","timestamp":1768311364000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/164\/2\/024110\/3376267\/Microscopic-elasticity-from-MD-I-Bulk-solid-and"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,13]]},"references-count":80,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,1,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0303843","relation":{"has-preprint":[{"id-type":"doi","id":"10.26434\/chemrxiv-2025-j17x4-v2","asserted-by":"object"}]},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,1,14]]},"published":{"date-parts":[[2026,1,13]]},"article-number":"024110"}}