# Analysis of transition variables in a continuous-discontinuous model to describe the crack process in concrete structures

## Palavras-chave:

Continuous-discontinuous model, Fracture representation, Transition variable, Damage, Phase-field## Resumo

The complete characterization of fracture in quasi-brittle materials such as concrete remains a chal-

lenge in computational modeling because of the complexity of this phenomenon and the material constitution.

Continuous-discontinuous approaches have been developed to fill this gap, embracing the continuous degradation

process related to smeared cracks and the discontinuity representation when discrete cracks emerge. Besides the

efforts, there is no consensus about the transition procedure between continuous and discontinuous. The literature

indicates that many parameters can be monitored to annunciate the transition, such as energy, historical variables,

crack length, crack opening, etc. But the most frequently used variable is damage. More recently, the phase-field

models have shown an ability to connect Continuum Damage Mechanics and Fracture Mechanics, acting as a crack

enunciator and tracker. Considering the context, an analysis of the transition variable and the value it assumes dur-

ing the evolution of smeared degradation to an explicit crack is proposed. A combined strategy that associates

nonlocal damage models with a mesh redefinition model based on nodal duplication is adopted. Two parameters

are compared in the transition function: the damage variable and the phase-field variable. Some numerical simula-

tions were performed, admitting different limit values. The results are analyzed to establish the optimal value that

characterizes crack nucleation and which parameter works better as a transition variable.