LEADER 03065nam 22004933a 450 001 9910557400803321 005 20230124202257.0 024 8 $ahttps://doi.org/10.30819/5337 035 $a(CKB)5400000000041917 035 $a(ScCtBLL)3dfe288a-61e5-4d05-9412-e4756de2e875 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/75070 035 $a(EXLCZ)995400000000041917 100 $a20220504i20212022 uu 101 0 $aeng 135 $auru|||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aStudy of an alternative phase field model for low interfacial energy in elastic solids$fAnke Bo?ttcher 210 $aBerlin$cLogos Verlag Berlin$d2021 210 1$a[s.l.] :$cLogos Verlag Berlin,$d2021. 215 $a1 online resource (152 p.) 311 $a3-8325-5337-1 330 $aIn 2005, the hybrid model was published by Prof. H.-D. Alber and Prof. P. Zhu as an alternative to the Allen-Cahn model for the description of phase field transformations. With low interfacial energy, it is more efficient, since the resolution of the diffuse interface is numerically broader for the same solution accuracy and allows coarser meshing. The solutions of both models are associated with energy minimisation and in this work the error terms introduced in the earlier publications are discussed and documented using one and two dimensional numerical simulations. In the last part of this book, phase field problems, initially not coupled with material equations, are combined with linear elasticity and, after simple introductory examples, a growing martensitic inclusion is simulated and compared with literature data. In addition to the confirmed numerical advantage, another phenomenon not previously described in the literature is found: with the hybrid model, in contrast to the examples calculated with the Allen-Cahn model, an inclusion driven mainly by curvature energy does not disappear completely. The opposite problem prevents inclusions from growing from very small initial configurations, but this fact can be remedied by a very finely chosen diffuse interface width and by analysing and adjusting the terms that generate the modelling errors. The last example shows that the hybrid model can be used with numerical advantages despite the above mentioned peculiarities. 606 $aScience / Chemistry$2bisacsh 606 $aScience / Physics$2bisacsh 606 $aMathematics$2bisacsh 606 $aScience 610 $aphase field modelling 610 $aelasticity 610 $ainterface width 610 $ainterfacial energy 610 $ahybrid Allen-Cahn model 615 7$aScience / Chemistry 615 7$aScience / Physics 615 7$aMathematics 615 0$aScience 700 $aBo?ttcher$b Anke$01227295 801 0$bScCtBLL 801 1$bScCtBLL 906 $aBOOK 912 $a9910557400803321 996 $aStudy of an alternative phase field model for low interfacial energy in elastic solids$92849762 997 $aUNINA