Different damage models have been proposed to predict the behavior of dynamic fracture of brittle materials using the peridynamic formulation. The prototype micro-brittle material proposed by Silling & Askari (2005), PMB, and its modified version proposed by Du et al. (2018), DTT, concern bond-breakage damage criteria applied to a bond-based constitutive model. These models consider only the direct interaction between material points and have, therefore, a fixed Poisson's ratio. Lipton et al. (2018) propose a state-based peridynamic model, LSJ, which, in addition to the strain state field, also considers a dilatational term and is coupled with a damage criterion that has two unrelated damage factors, one associated with the strain state field and the other one with its dilatational part. In this work, we apply a bond-breakage damage criterion in the two-dimensional ordinary, state-based peridynamic model presented by Le et al. (2014), here called the LPS-T model. We also modify the LSJ model to consider only bond-breakage damage, obtaining the LSJ-T model. In both cases, when the strain state of a bond reaches a critical value, it is continuously damaged until bond breakage occurs. To study the capability of these models in simulating the formation and the propagation of cracks, we have considered the experiment of a thin glass plate with an initial semi-crack under mode I loading. In general, all the models were able to grasp the main features of crack propagation, such as the crack propagation speed and the crack pattern. Both the DTT and the LSJ-T models are the only ones predicting symmetry in the crack paths and no minor branches, which indicate a stable crack propagation path. We have also considered the experiment of a notched cement-mortar plate with a hole under quasi-static mode I loading. This experiment was simulated numerically using the aforementioned damage models together with a dynamic relaxation method. We have obtained solutions of the associated numerical problems, which yield a sequence of graphs force versus displacement that is convergent. It also yields good agreement between numerical and experimental crack patterns. 

References: 
Silling, S. A. & Askari, E., 2005. A meshfree method based on the peridynamic model of solid mechanics. Computers & structures,83:17-18, 1526--1535. 
Du, Q., Tao, Y., & Tian, X., 2018. A peridynamic model of fracture mechanics with bond-breaking. Journal of Elasticity, 132:2, 197--218. 
Le, Q. V., Chan,W. K., & Schwartz, J., 2014. A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. International Journal for Numerical Methods in Engineering, 98:8, 547--561. 
Lipton, R., Said, E., & Jha, P., 2018. Free Damage Propagation with Memory. Journal of Elasticity, 133:2, 129--153.

Acknowledgements. Support of S√£o Paulo Research Foundation (FAPESP), grants # 2019/00428-7 and # 2020/04750-8, is gratefully acknowledged. The first author also acknowledges the support of National Council for Scientific and Technological Development (CNPq), grant # 420099/2018-2.

Brittle Fracture Modeling Using Ordinary State-Based Peridynamics with Continuous Bond-Breakage Damage

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