Phase-field modeling for polarization evolution in ferroelectric materials via an isogeometric collocation method

• Published in: Computer methods in applied mechanics and engineering Vol. 351; pp. 789 - 807
• Main Authors: Fedeli, P., Frangi, A., Auricchio, F., Reali, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-07-2019; Elsevier BV
• Subjects: Collocation; Collocation methods; Computer simulation; Evolution; Ferroelectric domains; Ferroelectric materials; Ferroelectricity; Finite element method; Ginzburg–Landau equation; Isogeometric analysis; Mathematical models; Mechanical analysis; Phase-field modeling; Polarization; Staggered explicit coupling; Vectorial order parameter; Isogeometric analysis; Vectorial order parameter; Ginzburg–Landau equation; Collocation; Phase-field modeling; Staggered explicit coupling
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.04.001

We herein use a (vectorial) phase-field model description of the evolution of ferroelectric domains to be coupled with the equations of electroelasticity, with the aim of building a simulation framework for electromechanically active materials. The governing equations of the coupled model are discretized in strong form by means of isogeometric collocation and numerically solved by a staggered explicit approach. This is the first time that isogeometric collocation is used for such a complex problem, comprising a vectorial phase-field model for polarization coupled with the equations describing the electrical and the mechanical response of the system. Several numerical experiments are carried out to test the behavior of the adopted simulation framework. The obtained results are excellent and propose isogeometric collocation as an inexpensive but very accurate alternative to standard finite element discretizations also for complex coupled problems.