An elastoplastic phase field model for fracture in concrete based on a generalized continuum formulation

Concrete's complex heterogeneous internal structure leads to an involved quasi-brittle response where a progressive loss of material integrity is observed.Additionally, in real-life applications, concrete structures are under loading conditions resulting in complex mixed-mode fracture patterns.Hence, prediction of crack behavior in concrete structures is a challenging task.Owing to the high costs of experimental testing, computational modeling has emerged as a viable alternative for studying concrete fracture.The phase field approach has proven to be a well-established formulation for simulating different fracture phenomena, where crack propagation is tracked implicitly using an additional independent field that diffuses the damage.Previously we introduced a phase field model investigating various crack driving forces considering only the elastic response of concrete.Following a thermodynamically consistent approach, we extend that model to an elastoplastic formulation which can accurately capture the quasi-brittle response of concrete, including the pressure dependency of strength.We formulate the equations within a generalized continuum framework, which accounts for the microstructure of the solid, naturally captures the size effect of materials, and addresses stability issues arising from complex plastic formulations.We demonstrate that employing this framework captures the internal microstructure of concrete by incorporating an internal length scale, which characterizes the microstructural fracture response and represents the finite size of the fracture process zone ahead of the crack tip.A comparison with experimental results confirms the good performance of the model in capturing mixed-mode I-II or I-III failures of concrete.