Ferroelectric and ferroelastic piezoceramics – modeling of electromechanical hysteresis phenomena

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New finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids (2011, background): “in terms of the fourth order tensor C as the elasticity moduli, the third order tensor h of piezoelectric moduli, and the second order tensor b known as the dielectric moduli which take the form [27,54] given in index notation”
Non-linear constitutive modeling of ferroelectrics (2004, methodology): “Also, a new finite element formulation [*34] has been applied by Haug [35] with the phenomenological constitutive law of McMeeking and Landis [ 27 ] to investigate the fields in actuator layers, near electrode tips, and near crack tips.”
A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics (2002, background): “Comparisons have been made successfully with polarization rotation behavior [ 25 ] and investigations of the effect of stress during hysteresis cycling have been made [26].”
Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions (2012, positive): “A recent study, using a phase-field model of brittle fracture, indicated that the mobility parameter controls the crack velocity, particularly at the initial stages of an unstable crack propagation (Kuhn and Müller, 2010).”