Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

Abstract

In this work we propose and compare the two models for crack propagation in dynamics. Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms. The first one is based on discrete lattice approach, where the domain is discretized with Voronoi cells held together prior to crack occurrence by cohesive links represented in terms of Timoshenko beams. The second one is based on constant strain triangular solid element. In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities. The latter remain localized inside the element, regulated by the localized traction separation behavior defined through exponential softening law. Thus, the both models provide the result that remain mesh-independent, with fracture energy as the model parameter. We show that implementation in dynamics framework can be obtained by adding inertial effects without modifying the existing quasi-statics models. In order to provide reliable results, classical implicit Newmark algorithm can be used for time integration. The two presented models are subjected to dynamic crack propagation benchmarks, where detailed analysis on strain, kinetic, plastic free and dissipated energy during simulation is verified by comparison to the amount of total work which is introduced into the system. The main strength of the proposed approach is that cracks initiation, propagation, their coalescence, merging and branching are automatically obtained without any tracking algorithms. In addition, since the discontinuities remain localized inside elements, accurate results can be obtained even with coarser grids, leading to efficient methodology capable of capturing complex crack patterns in dynamics.

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“…The UPM solves the coupled transport equations one after another and transfers the field states among different physical/chemical fields back and forth, avoiding strong coupled description of the multi-fields such as [53][54][55][56][57]. Moreover, the simulations of crack initiation and propagation are not considered, avoiding complex models presented in such as [58][59][60][61][62][63][64][65][66]. The UPM transforms 3D complicated fractures and porous medium into 1D artificial connected pipes in domain space and it uses the equivalent pipe networks to simulate the mass/energy transport processes within a 3D fractured porous medium.…”

Simulating the Filtration Effects of Cement-Grout in Fractured Porous Media with the 3D Unified Pipe-Network Method

“…The unified pipe-network method (UPM) is one of these simplified methods; it uses equivalent pipe networks to simulate the mass/energy transport processes within a porous/fractured medium. With the UPM, 2D and 3D mass/energy transport problems can be transformed into equivalent 1D problems, similar to the lattice element method (LEM) [50][51][52]. The fractures and porous medium can then be discretized using the same pipe-network system [53,54], which represents a significant advantage that provides a higher computing efficiency and greater numerical stability than other methods.…”

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“…The UPM solves the coupled transport equations one after another and transfers the field states among different physical/chemical fields back and forth, avoiding strong coupled description of the multi-fields such as [53][54][55][56][57]. Moreover, the simulations of crack initiation and propagation are not considered, avoiding complex models presented in such as [58][59][60][61][62][63][64][65][66]. The UPM transforms 3D complicated fractures and porous medium into 1D artificial connected pipes in domain space and it uses the equivalent pipe networks to simulate the mass/energy transport processes within a 3D fractured porous medium.The properties of pipes are obtained according to the geometrical, hydraulic and transport properties of the corresponding fractures and rock matrices.…”