Continuum approach to computational multiscale modeling of propagating fracture

Abstract

A new approach to two-scale modeling of propagating fracture, based on computational homogenization (FE2), is presented. The specific features of the approach are: a) a continuum setting for representation of the fracture at both scales based on the Continuum Strong Discontinuity Approach (CSDA), and b) the use, for the considered non-smooth (discontinuous) problem, of the same computational homogenization framework than for classical smooth cases. As a key issue, the approach retrieves a characteristic length computed at the lower scale, which is exported to the upper one and used therein as a regularization parameter for a propagating strong discontinuity kinematics. This guarantees the correct transfer of fracture energy between scales and the proper dissipation at the upper scale. Representative simulations show that the resulting formulation provides consistent results, which are objective with respect to, both, size and bias of the upper-scale mesh, and with respect to the size of the lower-scale RVE/failure cell, as well as the capability to model propagating cracks at the upper scale, in combination with crack-path-field and strain injection techniques. The continuum character of the approach confers to the formulation a minimal invasive character, with respect to standard procedures for multi-scale computational homogenization.Peer ReviewedPostprint (published version

Cohesive surface model for fracture based on a two-scale formulation: computational implementation aspects

“…A similar technique for mono-scale analysis has been reported in Manzoli et al [49] and Oliver et al [31].…”

“…Several authors have contributed with new ideas and theoretical or numerical models. To cite only a few of them, we reference the following works: Belytschko et al [25], Belytschko and Song [26], Geers et al [27], Bosco et al [28], Nguyen et al [29], Verhoosel et al [30] Oliver et al [31], Kulkarni et al [32] and references cited therein.…”

Crack Path Field and Strain Injection Techniques in Dynamic Fracture Simulations

“…In both CS-DSM and DDM modes the strain field is partitioned in two terms: ε ε ε = ξ ξ ξ + γ γ γ denoting a compatible (and smooth) strain field ξ ξ ξ and an enhanced strain field γ γ γ which tackles possible singularities in the failure propagation kinematics. The resulting Embedded Finite Element method (E-FEM) has been already presented in [23] and [24] and assessed for the case of quasi-static failure propagation. In the following subsections a brief description of its formulation is given but the reader is referred to the works in [18,23,24] for complete implementation details.…”

“…The domain B inj is, therefore, modeled with finite elements equipped with strain injections, including CS-DSM and DDM modes introduced in [18,24]. Strain injections are included in finite elements through the concept of assumed enhanced strains [34] considering a three-field Petrov-Galerkin mixed formulation by assuming that displacements u and strains ε ε ε in (9) …”

“…[5,6]). The specific formulation developed by Oliver et al [24] and assessed for quasi-static multiscale fracture problems has been adopted and tailored for dynamic fracture propagation problems. One of the main advantages of the present approach is that cracks, represented by strong discontinuities embedded into the finite elements, may propagate through the mesh in arbitrary directions reproducing complex failure patterns and, therefore, significantly coarser meshes can be employed compared to other supra-elemental techniques such as phase-field or gradient models.…”