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The effective granular stress is decomposed into viscoplastic structural and suspension-stress contributions. The former is obtained from a hypoplastic model combined with a Herschel\u2013Bulkley rheology, whereas the latter encompasses the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mu (I_m)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03bc<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>I<\/mml:mi>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    rheology and the Wyart\u2013Cates frictional-contact transition, and shows stress-dependent jamming state. Benchmark calculations show that the proposed formulation captures the transition between shear-thinning and shear-thickening behaviour. A depth-averaged long-wave analysis further shows that non-monotonicity induced by discontinuous shear thickening may persist to promote instability in the macro-viscous flow regime.\n                  <\/jats:p>","DOI":"10.1007\/s11440-026-03242-9","type":"journal-article","created":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T19:30:24Z","timestamp":1788204624000},"page":"5341-5362","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A simple constitutive framework for thinning\u2013thickening transitions in dense granular\u2013fluid mixtures"],"prefix":"10.1007","volume":"21","author":[{"given":"Yadong","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-0720","authenticated-orcid":false,"given":"Wei","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaogang","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongcheng","family":"Jiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"3242_CR1","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmps.2021.104388","volume":"151","author":"E Alaei","year":"2021","unstructured":"Alaei E, Marks B, Einav I (2021) A hydrodynamic-plastic formulation for modelling sand using a minimal set of parameters. 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