Nonlinear piezoelectric effects - towards physics-based computational modelling of micro-cracking, fatigue, and switching

• Piezoelectric ceramics -- as one widely commercialised group of smart materials -- exhibit a great potential for various engineering applications. Their high-frequency capabilities are in particular attractive for actuator and sensor devices, which nowadays are present in daily-life-technologies such as cellular phones, fuel injection systems, and so forth. At high loading levels however, severely nonlinear behaviour of these materials is observed which, from the control point of view, must be further investigated in order to be able to precisely account for such effects within the design of intelligent systems. The reasons for these nonlinearities are manifold and, even investigated within the last decades, not fully understood. Nevertheless, two important sources for these observations are so-called micro-cracking, together with fatigue phenomena, as well as switching or rather phase transformations. Accordingly, the main goal of this contribution is to study these effects by means of developing related constitutive models that can be embedded into iterative algorithmic schemes such as the finite element method. One the one hand, the grain-structure of a piezoceramic specimen will be modelled via the direct incorporation of the grain-boundaries as so-called interface elements. The underlying cohesive-like constitutive law of this layer includes both degrees of freedom of the surrounding bulk material -- or rather the jumps in these fields -- namely displacements and the electric potential. Based on the resulting traction-separation-type relations, micro-cracking is directly accounted for on this micro-level. Moreover, the constitutive law of the interfacial layer is supplemented by additional variables that enable the formulation of fatigue under cyclic loading conditions. On the other hand, phase transformations -- modelled in terms of an energy-based switching criterion -- are discussed and embedded into an iterative finite element context. Symmetry relations of the underlying unit cells are directly included so that the switching model accounts for the micro-mechanical properties of the piezoelectric materials of interest. At this stage, representative numerical simulations of polycrystalline specimens are based on straightforward averaging-techniques, while the combination of the developed micro-cracking model (grain boundaries) with the proposed switching model (bulk) constitutes future research.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering (hsv//eng)

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