Phase Field: A Methodology to Model Complex Material Behavior

  • José Luiz BoldriniEmail author


This work was done in commemoration of the 50th anniversary of the inauguration of the Institute of Mathematics, Statistics and Scientific Computation of the University of Campinas, Brazil (Instituto de Matemática, Estatística e Computação Científica da Universidade Estadual de Campinas). Our objective is just to give a rather fast introduction to some important modeling aspects of the phase field approach to model complex material behavior; we aim at students of mathematics who have almost no previous background in continuum thermomechanics. Thus, we briefly recall some of its main concepts and explain the main approaches used to derive the governing equations including the phase field variables (diffusification, energetic variational, and entropy approaches); we comment on some of their limitations and relationships, and briefly describe a few simple applications.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Mathematics, Statistics and Scientific ComputingUniversity of CampinasCampinasBrazil

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