Strain softening and hysteresis arising from 3D multicellular dynamics during long-term large deformation

Abstract

Living tissues exhibit complex mechanical properties, including viscoelastic and elastoplastic responses, that are crucial for regulating cell behaviors and tissue deformations. Despite their significance, the intricate properties of three-dimensional (3D) multicellular tissues are not well understood and are inadequately implemented in biomaterial engineering. To address this gap, we developed a numerical method to analyze the dynamic properties of multicellular tissues using a 3D vertex model framework. By focusing on 3D tissues composed of confluent homogeneous cells, we characterized their properties in response to various deformation magnitudes and time scales. Stress relaxation tests revealed that large deformations initially induced relaxation in the shapes of individual cells. This process is amplified by subsequent transient cell rearrangements, homogenizing cell shapes and leading to tissue fluidization. Additionally, dynamic viscoelastic analyses showed that tissues exhibited strain softening and hysteresis during large deformations. Interestingly, this strain softening originates from multicellular structures independent of cell rearrangement, while hysteresis arises from cell rearrangement. Moreover, tissues exhibit elastoplastic responses over the long term, which are well represented by the Ramberg-Osgood model. These findings highlight the characteristic properties of multicellular tissues emerging from their structures and rearrangements, especially during long-term large deformations. The developed method offers a new approach to uncover the dynamic nature of 3D tissue mechanics and could serve as a technical foundation for exploring tissue mechanics and advancing biomaterial engineering.