caa a22 4500 469080833 CHVBK 20180323132949.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01177002 doi (NATIONALLICENCE)springer-10.1007/BF01177002 Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture [Elektronische Daten] [G. Maugin, C. Trimarco] Summary: This work examines critically the various formulations of the balance of linear momentum innonlinear inhomogeneous elasticity. The corresponding variational formulations are presented. From the point of view of the theory of elastic inhomogeneities, the most interesting formulations are those which, being either completely material or mixed-Eulerian, exhibit explicitly the inhomogeneities in the form ofmaterial forces. They correspond to the balance ofpseudomomentum, a material covector which is seldom used but which we show to play a fundamental role in the Hamiltonian canonical formulation of nonlinear elasticity. The flux associated with pseudomomentum is none other than theEshelby material tensor. Applying this formulation to the case of an elastic body containing a crack of finite extent, the notion of suction force acting at the tip of the crack follows while afracture criterion à la Griffith can be deduced from a variational inequality. Possible extensions to higher-grade elastic materials and inelastic materials are indicated as well as the role played by pseudomomentum in the quantization of elastic vibrations. Springer-Verlag, 1992 Maugin G. Laboratoire de Modélisation en Mécanique, Université Pierre-et-Marie Curie, Tour 66, 4 place Jussieu, 75252, Paris Cédex, 05, France aut Trimarco C. Instituto di Matematiche Applicate, Università di Pisa, Via Bonnano 25 B, 56100, Pisa, Italy aut Acta Mechanica Springer-Verlag 94/1-2(1992-03-01), 1-28 0001-5970 94:1-2<1 1992 94 707 https://doi.org/10.1007/BF01177002 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01177002 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Maugin G. Laboratoire de Modélisation en Mécanique, Université Pierre-et-Marie Curie, Tour 66, 4 place Jussieu, 75252, Paris Cédex, 05, France aut NATIONALLICENCE 700 1- Trimarco C. Instituto di Matematiche Applicate, Università di Pisa, Via Bonnano 25 B, 56100, Pisa, Italy aut NATIONALLICENCE 773 0- Acta Mechanica Springer-Verlag 94/1-2(1992-03-01), 1-28 0001-5970 94:1-2<1 1992 94 707 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer