An elasto-viscoplastic interface model for investigating the constitutive behavior of nacre

In order to better understand the strengthening mechanism observed in nacre, we have developed an interface computational model to simulate the behavior of the organic present at the interface between aragonite tablets. In the model, the single polymer-chain behavior is characterized by the worm-like-chain (WLC) model, which is in turn incorporated into the eight-chain cell model developed by Arruda and Boyce [Arruda, E.M., Boyce, M.C., 1993a. A three-dimensional constitutive model for the large stretches, with application to polymeric glasses. Int. J. Solids Struct. 40, 389-412] to achieve a continuum interface constitutive description. The interface model is formulated within a finite-deformation framework. A fully implicit time-integration algorithm is used for solving the discretized governing equations. Finite element simulations were performed on a representative volume element (RVE) to investigate the tensile response of nacre. The staggered arrangement of tablets and interface waviness obtained experimentally by Barthelat et al. [Barthelat, F., Tang, H., Zavattieri, P.D., Li, C.-M., Espinosa, H.D., 2007. On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J. Mech. Phys. Solids 55 (2), 306-337] was included in the RVE simulations. The simulations showed that both the rate-dependence of the tensile response and hysteresis loops during loading, unloading and reloading cycles were captured by the model. Through a parametric study, the effect of the polymer constitutive response during tablet-climbing and its relation to interface hardening was investigated. It is shown that stiffening of the organic material is not required to achieve the experimentally observed strain hardening of nacre during tension. In fact, when ratios of contour length/persistent length experimentally identified are employed in the simulations, the predicted stress-strain behavior exhibits a deformation hardening consistent with the one measured experimentally and also captured by the phenomenological cohesive model used in the study carried out by Barthelat et al. [Barthelat, F., Tang, H., Zavattieri, P.D., Li, C.-M., Espinosa, H.D., 2007. On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J. Mech. Phys. Solids 55 (2), 306-337]. The simulation results also reveal that the bulk modulus of the polymer controls the rate of hardening, feature not captured by more simple cohesive laws.