{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T22:15:10Z","timestamp":1791411310862,"version":"4.3.3"},"reference-count":78,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:00:00Z","timestamp":1706227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006168","name":"National Nuclear Security Administration","doi-asserted-by":"publisher","award":["89233218CNA000001"],"award-info":[{"award-number":["89233218CNA000001"]}],"id":[{"id":"10.13039\/100006168","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2023,11,16]]},"abstract":"<jats:p>\n                    Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <a:mrow>\n                        <a:msub>\n                          <a:mi>\u03b7<\/a:mi>\n                          <a:mn>0<\/a:mn>\n                        <\/a:msub>\n                        <a:mi>k<\/a:mi>\n                      <\/a:mrow>\n                    <\/a:math>\n                    , the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same\n                    <b:math xmlns:b=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <b:mrow>\n                        <b:msub>\n                          <b:mi>\u03b7<\/b:mi>\n                          <b:mn>0<\/b:mn>\n                        <\/b:msub>\n                        <b:mi>k<\/b:mi>\n                      <\/b:mrow>\n                    <\/b:math>\n                    but different length scales, characterized by the wavelength\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <c:mi>\u03bb<\/c:mi>\n                    <\/c:math>\n                    varying by a factor of 4.9 from 65 to 130 to\n                    <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <d:mrow>\n                        <d:mn>320<\/d:mn>\n                        <d:mspace width=\"0.16em\"\/>\n                        <d:mrow>\n                          <d:mi>\u00b5<\/d:mi>\n                          <d:mi mathvariant=\"normal\">m<\/d:mi>\n                        <\/d:mrow>\n                      <\/d:mrow>\n                    <\/d:math>\n                    . Three such targets with different fixed\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <g:mrow>\n                        <g:msub>\n                          <g:mi>\u03b7<\/g:mi>\n                          <g:mn>0<\/g:mn>\n                        <\/g:msub>\n                        <g:msup>\n                          <g:mi>k<\/g:mi>\n                          <g:mo>\u2032<\/g:mo>\n                        <\/g:msup>\n                        <g:mi mathvariant=\"normal\">s<\/g:mi>\n                      <\/g:mrow>\n                    <\/g:math>\n                    were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <i:mi>\u03bb<\/i:mi>\n                    <\/i:math>\n                    decreased. The different\n                    <j:math xmlns:j=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <j:mrow>\n                        <j:msub>\n                          <j:mi>\u03b7<\/j:mi>\n                          <j:mn>0<\/j:mn>\n                        <\/j:msub>\n                        <j:mi>k<\/j:mi>\n                      <\/j:mrow>\n                    <\/j:math>\n                    targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for\n                    <k:math xmlns:k=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <k:mrow>\n                        <k:mn>320<\/k:mn>\n                        <k:mo>\u2212<\/k:mo>\n                        <k:mn>65<\/k:mn>\n                        <k:mspace width=\"0.16em\"\/>\n                        <k:mrow>\n                          <k:mi>\u00b5<\/k:mi>\n                          <k:mi mathvariant=\"normal\">m<\/k:mi>\n                        <\/k:mrow>\n                      <\/k:mrow>\n                    <\/k:math>\n                    wavelength perturbations, the effective strain rates increased from\n                    <n:math xmlns:n=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <n:mrow>\n                        <n:mn>8.7<\/n:mn>\n                        <n:mo>\u00d7<\/n:mo>\n                        <n:msup>\n                          <n:mrow>\n                            <n:mn>10<\/n:mn>\n                          <\/n:mrow>\n                          <n:mn>6<\/n:mn>\n                        <\/n:msup>\n                      <\/n:mrow>\n                    <\/n:math>\n                    to\n                    <o:math xmlns:o=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <o:mrow>\n                        <o:mn>3.3<\/o:mn>\n                        <o:mo>\u00d7<\/o:mo>\n                        <o:msup>\n                          <o:mrow>\n                            <o:mn>10<\/o:mn>\n                          <\/o:mrow>\n                          <o:mn>7<\/o:mn>\n                        <\/o:msup>\n                        <o:mspace width=\"0.16em\"\/>\n                        <o:msup>\n                          <o:mrow>\n                            <o:mi mathvariant=\"normal\">s<\/o:mi>\n                          <\/o:mrow>\n                          <o:mrow>\n                            <o:mo>\u2212<\/o:mo>\n                            <o:mn>1<\/o:mn>\n                          <\/o:mrow>\n                        <\/o:msup>\n                      <\/o:mrow>\n                    <\/o:math>\n                    , a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates.\n                  <\/jats:p>\n                  <jats:sec>\n                    <jats:title\/>\n                    <jats:supplementary-material>\n                      <jats:permissions>\n                        <jats:copyright-statement>Published by the American Physical Society<\/jats:copyright-statement>\n                        <jats:copyright-year>2024<\/jats:copyright-year>\n                      <\/jats:permissions>\n                    <\/jats:supplementary-material>\n                  <\/jats:sec>","DOI":"10.1103\/physreve.109.015002","type":"journal-article","created":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T10:05:34Z","timestamp":1706263534000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["Multiscale Richtmyer-Meshkov instability experiments to isolate the strain rate dependence of strength"],"prefix":"10.1103","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4098-5620","authenticated-orcid":true,"given":"Michael B.","family":"Prime","sequence":"first","affiliation":[{"name":"Los Alamos National Laboratory (LANL), Los Alamos, New Mexico 87545, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8135-5353","authenticated-orcid":true,"given":"Saryu J.","family":"Fensin","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory (LANL), Los Alamos, New Mexico 87545, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9466-4008","authenticated-orcid":true,"given":"David R.","family":"Jones","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory (LANL), Los Alamos, New Mexico 87545, 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