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Efficient modelling of complex multi-phase fluid-flows is one of the most common engineering challenges nowadays. The majority of the commonly used CFD solvers are based on Eulerian approaches (grid-based). These methods are, in general, efficient with some drawbacks, e.g. it is necessary to handle additionally the location of the interface or free-surface within computational cells. Very promising alternatives to the Eulerian methods are Lagrangian approaches which, roughly speaking, discretize fluid instead of the domain. One of the most common methods of this kind is the Smoothed Particle Hydrodynamics (SPH) method, a fully Lagrangian, particle-based approach for fluid-flow simulations. One of its main advantages, over the Eulerian techniques, is no need for a numerical grid. Consequently, there is no necessity to handle the interface shape because it is directly obtained from the set of computational particles.

The virtual optimisation of tooling equipment is nowadays one of the common challenges in mechanical serial production. Even some numerical Eulerian approaches (grid-based) exist for modelling solid materials under dynamic loading, most of them are not very successful. Especially the solids undergoing large deformation and the subsequent material separation and propagating cracks demonstrate the limitations: variables become discontinuous across the crack surface, and the computational domain loses its continuum nature. Grid-based methods are not naturally equipped to deal with such situations due to the mesh distortion, mesh entanglement and requirement of mesh refinement. Very promising alternatives to the Eulerian methods are meshfree Lagrangian methods. Among them, smoothed particle hydrodynamics (SPH) is entirely meshfree and naturally equipped to handle large material deformation. In SPH the computational domain is discretised by a set of particles.

Large material distortion, plastic deformation and forging make the numerical modelling of metal forming a difficult task. Grid-based methods such as the Finite Element Method (FEM) are incapable of simulating this process as these schemes suffer from mesh distortion and mesh entanglement. The mesh-based numerical frameworks with discontinuous enrichment can model finite deformation problems with limited success. Moreover, the presence of flaws, multiple crack surfaces and their interaction make the simulation even more numerically and computationally intensive. In this regard, Lagrangian particle-based meshfree methods are more relevant. There exist several mesh-free methods and among these Smoothed Particle Hydrodynamics (SPH) is a truly meshfree method. In SPH the computational domain is discretised by a set of particles. A given particle interacts only with its neighbouring particles through a kernel function with a constant radius.