Computation of brittle fracture propagation in strain gradient materials by the FEniCS library

Abstract

Strain gradient continuum damage modelling has been applied to quasistatic brittle fracture within an approach based on a maximum energy-release rate principle. The model was implemented numerically, making use of the FEniCS open-source library. The considered model introduces non-locality by taking into account the strain gradient in the deformation energy. This allows for stable computations of crack propagation in differently notched samples. The model can take wedges into account, so that fracture onset can occur at wedges. Owing to the absence of a damage gradient term in the dissipated energy, the normal part of the damage gradient is not constrained on boundaries. Thus, non-orthogonal and non-parallel intersections between cracks and boundaries can be observed.

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

“…We have implemented a transient, fully coupled solution strategy by using open-source packages from the FEniCS Project [163]. We refer to [164,165,166] for implementations in FEniCS by means of a staggered scheme. Herein, the implementation is using a monolithic approach, where displacement and phase fields are solved at once.…”

Verification of strain gradient elasticity computation by analytical solutions

“…Motivation for introducing higher order gradient of strains in the stored energy arises from various aspects, we refer to [1,7,11,31,36,63,86]. First, an investigation of highly localized phenomena, such as crack formation and propagation, may be realized by involving higher order gradients in order to regularize the solution of cracks by penalizing the displacements, which are localized above a given threshold [17,68,71,73,78,93]. Second, an accurate modeling of metamaterials is achieved in the framework of strain gradient theory [16,26,28,35,38,40,45,89].…”

“…, and(17), the so-called tractions 𝑡 𝑖 , double tractions 𝑟 𝑖 and wedge forces 𝑓 𝑘 are expressed as 𝑡 𝑖 = 𝑛 𝑗 (𝜎 𝑖𝑗 − 𝜏 𝑖𝑗𝑘,𝑘 ) + 𝑛 𝑘 𝑛 𝑗 𝜏 𝑖𝑗𝑘 (𝐷 𝑝 𝑛 𝑝 ) − 𝐷 𝑗 (𝑛 𝑘 𝜏 𝑖𝑗𝑘 ), 𝑟 𝑖 = 𝑛 𝑗 𝑛 𝑘 𝜏 𝑖𝑗𝑘 , 𝑓 𝑖 = Δ𝜈 𝑗 𝑛 𝑘 𝜏 𝑖𝑗𝑘 .…”

A block-based variational elasto-damage model for masonry analysis inspired from granular micromechanics: Preliminary study

“…These approaches can be roughly divided into continuous and discrete [3,4] ones. The former have been developed to find a remedy to the high computational cost of discrete approaches [5][6][7][8] and proved to be a promising and versatile predictive tool [9,10]. Indeed, those continuous models can successfully deal with size effects.…”