A consistent characteristic length for smeared cracking models

TLDR

The paper introduces a numerical scheme that models cracks using continuous displacement fields. Cracks are represented as the limiting case of two singular lines with continuous displacements but discontinuous gradients, and an energy‑based analysis yields a characteristic length expression that is mesh‑size independent and applicable in finite element discretizations. Numerical experiments confirm that the derived expressions reliably predict crack behavior.

Abstract

Abstract A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two‐dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.