Structural size effect: experimental, theoretical and accurate computational assessment

Abstract

In this paper, experimental evidence, theoretical predictions and the finite element modelling of the structural size effect in cracking problems of quasi-brittle materials are discussed and assessed against each other. The fracture process is modelled through the crack band approach, using an isotropic damage constitutive law. The correct dissipation of the fracture energy, essential for modelling the phenomenon with precision, is introduced. An enhanced accuracy mixed finite element formulation is used to ensure mesh bias independent results. Several experimental campaigns where size effect is investigated are numerically reproduced in 2D and in 3D to assess the feasibility and the performance of the method. For this, mode I and mixed mode I and II fracture situations are considered in notched and unnotched beams. The correlation of the experimental results with the numerical simulations shows the capacity of the mixed FE formulation to reproduce crack paths, force-displacement curves and collapse mechanisms with precision for a wide range of structural sizes. The enhanced accuracy FE formulation eliminates the spurious mesh dependency that is characteristic of standard FE simulations. In addition, the model is able to follow Bazant’s size effect law with precision. Results confirm that the energy release rate in the progressing fracture is the fundamental cause of size effect in quasi-brittle materials. This is additionally verified in a study of the relative influence of statistical and energetic size effect. Computations show that the essential requirements to suitably simulate the phenomenon are (1) a fracture model ensuring the correct energy dissipation at the crack and (2) a method guaranteeing mesh objective results.