A full‐discontinuous Galerkin formulation of nonlinear Kirchhoff–Love shells: elasto‐plastic finite deformations, parallel computation, and fracture applications

Abstract

SUMMARYDue to its ability to take into account discontinuities, the discontinuous Galerkin (DG) method presents some advantages for modeling crack initiations and propagations. This concept has been recently applied to 3D simulations and to elastic thin bodies. In this last case, the assumption of small elastic deformations before crack initiations or propagations reduces drastically the applicability of the framework to a reduced number of materials. To remove this limitation, a full-DG formulation of non-linear Kirchhoff-Love shells is presented and is used in combination with an elasto-plastic finite deformations model. The results obtained by this new formulation are in agreement with other continuum elasto-plastic shell formulations. Then this full-DG formulation of Kirchhoff-Love shells is coupled with the cohesive zone model to perform thin body fracture simulations. As this method allows considering elasto-plastic constitutive laws in combination with the cohesive model, accurate results compared to the experiments are found. In particular, the crack path and propagation rate of a blasted cylinder are shown to match experimental results. One of the main advantages of this framework is its ability to run in parallel with a high speed-up factor, allowing the simulation of ultra fine meshes.

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

“…In the 1D-setting, the total localization energy, Φ loc , of the damage law is depicted However, contrarily to the case for which the CZM substitutes the CDM at strain softening onset, the surface separation u DT cannot be directly calculated from Eq. (27). Indeed, the strain in the bar is not homogeneous anymore as the parts of the bar beside the discontinuous surface are in the localizing damage zone and are thus subjected to a higher damage, see Fig.…”

“…We need to mention that in the case of snap-back, the jump of displacement can still be computed through Eq. (27).…”

“…• The problem can thus be stated as finding, during the damage evolution D(x 0 ) from 0 to 1, the relation between the stress σ and the equivalent displacement jump u at x 0 , which derives from (27):…”

“…Nevertheless the computational efficiency of the extrinsic approach is still challenging for 3D parallel applications as it requires mesh topology modifications on the fly. An energetically rigorous and computationally efficient way to introduce a CZM is to combine the extrinsic cohesive law with a discontinuous Galerkin (DG) approach [22,23,24,25,26,27]. With this hybrid DG/ECL method, interface elements are inserted between bulk elements at the beginning of the simulation, but the consistency and continuity during the pre-fracture stage are ensured by having recourse to the DG interface terms, contrarily to a classical intrinsic CZM.…”

Phase-field modeling of fracture in linear thin shells

“…Furthermore, many of the approaches are applied to simple geometries such as plates, or spherical and cylindrical geometries [18,19,12,20]. Towards a general, flexible and robust methodology to deal with fracture in Kirchhoff-Love shells, we propose here treating fracture with a phasefield model and discretizing the coupled thin-shell/phase-field equations with a recently proposed meshfree method for partial differential equations on manifolds of complex geometry and topology [21,22].…”