Speaker
Description
Additive manufacturing of piezoceramics enables the acquisition of high resolution lead-free piezoelectric architected microgeometries that are difficult to realize with conventional processing. To exploit these design freedoms, predictive multiphysics models must capture the electromechanical coupling together with the non linear, history dependent response typical of ferroelectric materials.
We present a user element (UEL) implementation in Abaqus for fully coupled electromechanical simulations of piezoelectric solids, accounting for both direct and inverse effects. The element uses a hexahedral 8 node formulation with 4-DOF per node. At each integration point, the constitutive update is driven by the local mechanical and electric fields and is handled through a Jiles–Atherton type phenomenological model adapted to ferroelectric behavior.
In the proposed framework, the polarization is split into irreversible and reversible parts, $P={P}^{\mathrm{irr}}+{P}^{\mathrm{rev}}$ with the reversible contribution defined as ${P}^{\mathrm{rev}}=c{P}^{\mathrm{an}}-{P}^{\mathrm{irr}}$, where c is the reversibility coefficient and $P^{\mathrm{an}}$ is the anhysteretic polarization. This contribution is modeled through a Langevin relation that is driven by an effective electric field $E_{\mathrm{eff}}$, which combines the applied electrical field with internal electromechanical interactions. The irreversible evolution law drives ${P}^{\mathrm{irr}}$ toward ${P}^{\mathrm{an}}$ in a history dependent manner, capturing memory and minor loop behavior. The updated polarization is coupled to strain through electrostrictive terms, yielding a nonlinear, path dependent electromechanical response.
The set of internal variables evolves with the load history and enforces the nonlinear relationship between the electric field, polarization, and strain. In representative cyclic electrical and combined electromechanical loading cases, the model reproduces the characteristic hysteresis and strain “butterfly” loops observed in ferroelectric ceramics.
The proposed framework targets efficient simulation of components with complex microarchitectures produced by 3D printing, providing a route to virtual prototyping and parameter exploration prior to fabrication. Ongoing work focuses on validation across a set of loading paths and applying the model to lattice-like and porous geometries.