Electromechanical response of Hyperelastic-Piezoelectric composites using Direct FE2 multiscale modeling

• Efficient multiscale Direct FE2 models hyperelastic composites with BaTiO3 inclusions. • Fiber inclusions at 90° maximize electric potential over circular or misaligned fibers. • “Magic fiber angles” 54.74° and 9.74° yield responses similar to random inclusions. • Nonlinear electromechanical behavior dominates tension/compression; shear has minimal effect. • Soft gripper models demonstrate performance sensitivity to electrical boundary conditions. Piezoelectric soft materials generating electrical signals in response to mechanical deformation have been of great interest over the past decade, owing to their potential applications in human activity sensing and energy harvesting. In this study, a multiscale Direct FE 2 method is introduced to investigate the electromechanical behavior of hyperelastic composites reinforced with piezoelectric BaTiO 3 inclusions—a scenario not readily addressed by sequential multiscale modeling due to the simultaneous presence of hyperelasticity and piezoelectricity. The study explores variations in inclusion volume fractions, geometries, and alignment orientations for stretchable sensor applications. A two-dimensional square material domain and a soft gripper structure are analyzed, concurrently in the macroscale and microscale representative volume element of the composite. The results for circular inclusions demonstrate that this highly efficient multiscale approach yields accurate predictions that align closely with analytical solutions. Under uniaxial loading conditions, the electromechanical properties exhibit nonlinear behavior as the inclusion volume fraction and shape aspect ratio change, while shear deformation has a negligible effect. The rectangular fiber-like piezoelectric inclusions significantly enhance electric potential, with the highest values observed at a 90° alignment, outperforming other less asymmetrical aspect ratios, including circular inclusions. Additionally, aligning inclusions along the electrical poling direction is not always optimal, depending on the applied loading mode—tension, compression, or shear. Notably, at a fiber orientation of 54.74° relative to the principal stress direction, the composite’s mechanical and electrical responses become indistinguishable from those of randomly oriented inclusions. These findings provide valuable insights into the ferroelectric behavior of soft hybridized solids, contributing to the advancement of materials for applications in robotic systems and flexible electromechanical devices.