caa a22 4500 445812311 CHVBK 20180317145215.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00419-010-0486-8 doi (NATIONALLICENCE)springer-10.1007/s00419-010-0486-8 Unconstrained and Cauchy-Born-constrained atomistic systems: deformational and configurational mechanics [Elektronische Daten] [Paul Steinmann, Sarah Ricker, Elias Aifantis] In this contribution, the deformational and configurational mechanics of (elastic) discrete atomistic systems in relation to their continuum counterparts are considered for the quasi-static case. Thereby, we firstly investigate the basic unconstrained case in the sense of lattice statics as a reference. Based on these results, we consider two Cauchy-Born-type constraints that (locally) describe the change of the position of atoms (between the material and the spatial configuration) in terms of either a linear or a quadratic map, respectively. Insertion of these kinematic constraints into the variation of the total potential energy of the unconstrained case renders eventually Cauchy-Born-type definitions for atomistic stresses and hyperstresses, for both deformational and configurational cases. In the continuum limit, these are the relevant continuum stresses and hyperstresses contributing to the local force balances of first- (classical) and second-order (non-classical) gradient continua (here first- and second-order gradient refers to the highest gradient of the deformation map characterizing the kinematics). It is emphasized that the atomistic and the Cauchy-Born-type configurational quantities represent novel and unexpected contributions. Among other things, they may be useful in assessing the singular or non-singular character of deformation fields at crack tips and comparing numerical estimates resulting from atomistic simulations with analytical predictions resulting from solutions of related boundary value problems for gradient continua. Springer-Verlag, 2010 Cauchy-Born constraint nationallicence Configurational mechanics nationallicence Homogenization nationallicence Gradient continua nationallicence Steinmann Paul Chair of Applied Mechanics, University of Erlangen/Nuremberg, Erlangen, Germany aut Ricker Sarah Chair of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, Germany aut Aifantis Elias Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki, Greece aut Archive of Applied Mechanics Springer-Verlag 81/5(2011-05-01), 669-684 0939-1533 81:5<669 2011 81 419 https://doi.org/10.1007/s00419-010-0486-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0486-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Steinmann Paul Chair of Applied Mechanics, University of Erlangen/Nuremberg, Erlangen, Germany aut NATIONALLICENCE 700 1- Ricker Sarah Chair of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, Germany aut NATIONALLICENCE 700 1- Aifantis Elias Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki, Greece aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/5(2011-05-01), 669-684 0939-1533 81:5<669 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer