Matei, Andaluzia; Osiceanu, Madalina Two-field variational formulations for a class of nonlinear mechanical models. (English) Zbl 07619149 Math. Mech. Solids 27, No. 11, 2532-2547 (2022). Summary: A nonlinear boundary value problem arising from continuum mechanics is considered. The nonlinearity of the model arises from the constitutive law which is described by means of the subdifferential of a convex constitutive map. A bipotential \(B\), related to the constitutive map and its Fenchel conjugate, is considered. Exploring the possibility to rewrite the constitutive law as a law governed by the bipotential \(B\), a two-field variational formulation involving a variable convex set is proposed. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed. Cited in 3 Documents MSC: 74-XX Mechanics of deformable solids Keywords:nonlinear constitutive law; bipotential; two-field weak solution; subdifferential inclusion; demicontinuous solution operator Software:OpenCourseWare PDFBibTeX XMLCite \textit{A. Matei} and \textit{M. Osiceanu}, Math. Mech. Solids 27, No. 11, 2532--2547 (2022; Zbl 07619149) Full Text: DOI References: [1] MIT OpenCourseWare. 8.01 Classical Mechanics, Fall 2016. Available at: https://ocw.mit.Edu/courses/physics/8-01sc-classical-mechanics-fall-2016/readings/ (accesed 11 November 2020). [2] Rana NC, Joag PS. Classical Mechanics. New Delhi: Tata McGraw-Hill, 1991. [3] Andreaus U, Chiaia B, Placidi L. Soft-impact dynamics of deformable bodies. Continuum Mech Thermodyn2013; 25: 375-398. · Zbl 1343.74037 [4] Andreaus U, Baragatti P, Placidi L. Experimental and numerical investigations of the responses of a cantilever beam possibly contacting a deformable and dissipative obstacle under harmonic excitation. 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