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A novel quasi-brittle damage model implemented under quasistatic loading condition using bond-based peridynamics theory for progressive failure is proposed to better predict damage initiation and propagation in solid materials. Since peridynamics equation of motion was invented in dynamic configuration, this paper applies the adaptive dynamic relaxation equation to achieve steady-state in peridynamics formulation. To accurately characterise the progressive failure process in cohesive materials, we incorporate the dynamic equation with the novel damage model for quasi-brittle materials. Computational examples of 2D compressive and tensile problems using the proposed model are presented. This paper presents advancement by incorporating the adaptive dynamic equation approach into a new damage model for quasi-brittle materials. This amalgamation allows for a more accurate representation of the behavior of damaged materials, particularly in static or quasi-static loading situations, bringing the framework closer to reality. This research paves the way for the peridynamics formulation to be employed for a far broader class of loading condition behaviour than it is now able to.

• A new bond model is proposed and implemented for bond-based peridynamics theory. • The new bond model considers the progressive failure and residual bond strength. • The peridynamics theory is further coupled with standard finite element method. • The new bond model better describes the post-peak responses of structures. In this study, a new bond damage model is proposed in the framework of the bond-based peridynamics theory to better describe the progressive failure process in cohesive brittle materials. The new bond model is able to account for the progressive failure and residual strength of bonds. The peridynamics theory is further coupled with the classical finite element method in order to efficiently describe failure processes at a large scale of structures. Several benchmark tests concerning mode-I and mixed-mode fractures in concrete structures are studied to verify the efficiency of the coupled peridynamics-finite element method. The obtained numerical results are in good agreement with the experimental data for both overall force–displacement responses and crack propagation patterns. It is found that the new bond damage model significantly improves the prediction of progressive failure process in cohesion brittle materials with respect to the classical elastic-brittle bond model. [ABSTRACT FROM AUTHOR]