A novel explicit three-sub-step time integration method for wave propagation problems

A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

Simulation of crack propagation based on eigenerosion in brittle and ductile materials subject to finite strains

In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. 10.1002/nme.4352) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented.