caa a22 4500 605514968 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00205-014-0806-1 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0806-1 Differential Complexes in Continuum Mechanics [Elektronische Daten] [Arzhang Angoshtari, Arash Yavari] We study some differential complexes in continuum mechanics that involve both symmetric and non-symmetric second-order tensors. In particular, we show that the tensorial analogue of the standard grad-curl-div complex can simultaneously describe the kinematics and the kinetics of motion of a continuum. The relation between this complex and the de Rham complex allows one to readily derive the necessary and sufficient conditions for the compatibility of displacement gradient and the existence of stress functions on non-contractible bodies.We also derive the local compatibility equations in terms of the Green deformation tensor for motions of 2D and 3D bodies, and shells in curved ambient spaces with constant curvatures. Springer-Verlag Berlin Heidelberg, 2014 Angoshtari Arzhang School of Civil and Environmental Engineering, Georgia Institute of Technology, 30332, Atlanta, GA, USA aut Yavari Arash School of Civil and Environmental Engineering, The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, GA, 30332, Atlanta, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 193-220 0003-9527 216:1<193 2015 216 205 https://doi.org/10.1007/s00205-014-0806-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0806-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Angoshtari Arzhang School of Civil and Environmental Engineering, Georgia Institute of Technology, 30332, Atlanta, GA, USA aut NATIONALLICENCE 700 1- Yavari Arash School of Civil and Environmental Engineering, The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, GA, 30332, Atlanta, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 193-220 0003-9527 216:1<193 2015 216 205