caa a22 4500 605515468 CHVBK 20210128100709.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s00205-014-0833-y doi (NATIONALLICENCE)springer-10.1007/s00205-014-0833-y An Analysis of Crystal Cleavage in the Passage from Atomistic Models to Continuum Theory [Elektronische Daten] [Manuel Friedrich, Bernd Schmidt] We study the behavior of brittle atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a particular cleavage law with quadratic response to small boundary displacements followed by a sharp constant cut-off beyond some critical value. Moreover, we show that the minimal energy is attained by homogeneous elastic configurations in the subcritical case and that beyond critical loading cleavage along specific crystallographic hyperplanes is energetically favorable. In particular, our results apply to mass spring models with full nearest and next-to-nearest pair interactions and provide the limiting minimal energy and minimal configurations. Springer-Verlag Berlin Heidelberg, 2014 Friedrich Manuel Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany aut Schmidt Bernd Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/1(2015-07-01), 263-308 0003-9527 217:1<263 2015 217 205 https://doi.org/10.1007/s00205-014-0833-y 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/s00205-014-0833-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Friedrich Manuel Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany aut NATIONALLICENCE 700 1- Schmidt Bernd Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/1(2015-07-01), 263-308 0003-9527 217:1<263 2015 217 205