Bustamante, R.; Sfyris, D. Direct determination of stresses from the stress equations of motion and wave propagation for a new class of elastic bodies. (English) Zbl 1327.74080 Math. Mech. Solids 20, No. 1, 80-91 (2015); corrigendum ibid. 25, No. 3, 866-868 (2020). Summary: For a new class of elastic bodies, where the linearized strain tensor is given as a function of the Cauchy stress tensor, the problem of considering unsteady motions is studied. A system of partial differential equations that only depends on the stress tensor is found from the equation of motion, which is a system of six partial differential equations for the six components of the stress tensor. A simple boundary value problem is solved for a 1D bar using exact and numerical methods. Cited in 1 ReviewCited in 15 Documents MSC: 74J10 Bulk waves in solid mechanics 74B99 Elastic materials 74A10 Stress Keywords:equation of motion; unsteady motions; strain limiting behaviour; finite element method PDFBibTeX XMLCite \textit{R. Bustamante} and \textit{D. Sfyris}, Math. Mech. Solids 20, No. 1, 80--91 (2015; Zbl 1327.74080) Full Text: DOI References: [1] DOI: 10.1023/A:1026062615145 · Zbl 1099.74009 [2] Rajagopal KR, Z Angew Math Phys 58 pp 309– (2007) · Zbl 1113.74006 [3] DOI: 10.1177/1081286510387856 · Zbl 1269.74014 [4] Rajagopal KR, Proc Roy Soc Lond A 463 pp 357– (2007) · Zbl 1129.74010 [5] Rajagopal KR, Proc Roy Soc Lond A 465 pp 493– (2009) · Zbl 1186.74009 [6] Rajagopal KR, Math Computat Appl 15 pp 506– (2010) [7] Bustamante R, Math Mech Solids 15 pp 229– (2010) · Zbl 1257.74022 [8] Bustamante R, Proc Roy Soc Lond A 465 pp 1377– (2009) · Zbl 1186.74016 [9] DOI: 10.1007/978-3-662-10388-3 [10] Rajagopal KR, Math Mech Solids 16 pp 122– (2011) · Zbl 1269.74026 [11] Bustamante R, Int J Nonlinear Mech 46 pp 376– (2011) [12] Ortiz A, Acta Mech 223 (9) pp 1971– (2012) · Zbl 1356.74122 [13] Rajagopal KR, Int J Fracture 169 pp 39– (2011) · Zbl 1283.74074 [14] Bustamante R, Math Mech Solids 17 pp 762– (2012) [15] Saito T, Science 300 pp 464– (2003) [16] Withey E, Mater Sci Eng A 493 pp 26– (2008) [17] Zhang SQ, Scripta Mater 60 pp 733– (2009) [18] Johnson PA, Nonlinear Proc Geoph 3 pp 77– (1996) [19] DOI: 10.1063/1.882648 [20] DOI: 10.1029/94JB01941 [21] Lu Z, Geophys Res Lett 32 pp L14302– (2005) [22] Ostrovsky LA, J Acoust Soc Am 90 pp 3332– (1991) [23] Ten Cate JA, Geophys Res Lett 23 pp 3019– (1996) [24] Guyer RA, Nonlinear mesoscopic elasticity (2009) [25] Rajagopal KR, Acta Mech 255 (6) pp 1545– (2014) · Zbl 1401.74045 [26] Popovics S, Cement Concrete Res 20 pp 259– (1990) [27] Iacovache M, Buletin Ştiinţific, Seria 2 pp 700– (1950) [28] Vâlcovici V, Comunicările Academiei Republicii Populare Române 4 pp 337– (1951) [29] Ignaczak J, Arch Mech 15 pp 225– (1963) [30] Ignaczak J, Arch Mech 11 pp 671– (1959) [31] Chadwick P, Continuum mechanics: Concise theory and problems (1999) [32] Truesdell CA, Handbuch der Physik pp 226– (1960) [33] Rajagopal KR, Int J Nonlinear Mech 46 pp 1167– (2011) [34] Sfyris D, Q J Mech Appl Math 66 pp 157– (2013) · Zbl 1291.74016 [35] Gurtin ME, Mechanics of solids pp 1– (1984) [36] Polyanin AD, Handbook of exact solutions for ordinary differential equations (2003) [37] Ortiz-Bernardin A, Int J Sol Struct 51 (3) pp 875– (2014) [38] Comsol Multiphysics Version 3.4, Comsol Inc. Palo Alto, CA, 2007. [39] Kannan K, Wave Motion 51 (5) pp 833– (2014) [40] Saada AS, Elasticity: Theory and application (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.