caa a22 4500 605515948 CHVBK 20210128100711.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00205-015-0883-9 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0883-9 Incompatible Sets of Gradients and Metastability [Elektronische Daten] [J. Ball, R. James] We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an L 1 neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiments and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis. Springer-Verlag Berlin Heidelberg, 2015 Ball J. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG, Oxford, UK aut James R. Department of Aerospace Engineering and Mechanics, University of Minnesota, 55455, Minneapolis, MN, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1363-1416 0003-9527 218:3<1363 2015 218 205 https://doi.org/10.1007/s00205-015-0883-9 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/s00205-015-0883-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ball J. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG, Oxford, UK aut NATIONALLICENCE 700 1- James R. Department of Aerospace Engineering and Mechanics, University of Minnesota, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1363-1416 0003-9527 218:3<1363 2015 218 205