In previous work [1, 2], Lee et al. introduced a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility. A first order system of hyperbolic equations was presented expressed in terms of the linear momentum and the minors of the deformation, namely the deformation gradient, its co-factor and its Jacobian. Taking advantage of this representation, the suppression of numerical deficiencies (e.g. spurious pressure, long term instability and/or consistency issues) was addressed through well-established stabilisation procedures. In Reference [1], the adaptation of the very efficient Jameson-Schmidt-Turkel algorithm was presented. Reference [2] introduced an adapted variationally consistent Streamline Upwind Petrov Galerkin methodology. In this paper, we now introduce a third alternative stabilisation strategy, extremely competitive, and which does not require the selection of any user-defined artificial stabilisation parameter. Specifically, a characteristic-based Riemann solver in conjunction with a linear reconstruction procedure is used, with the aim to guarantee both consistency and conservation of the overall algorithm. We show that the proposed SPH formulation is very similar in nature to that of the upwind vertex centred Finite Volume Method presented in [3]. In order to extend the application range towards the incompressibility limit, an artificial compressibility algorithm is also developed. Finally, an extensive set of challenging numerical examples is analysed. The new SPH algorithm shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding second order of convergence for velocities, deviatoric and volumetric components of the stress.

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This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of deformation measures (also known as minors of the deformation gradient tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity [1-3]. To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation.

Background. Glass ceramic materials have multiple applications in various prosthetic fields. Despite the many advantages of these materials, they still have limitations such as fragility and surface machining and ease of repairing. Crack propagation has been a typical concern in fullceramic crowns, for which many successful numerical simulations have been carried out using the extended finite element method (XFEM). However, XFEM cannot correctly predict a primary crack growth direction under dynamic loading on the implant crown. Methods. In this work, the dental implant crown and abutment were modeled in CATIA V5R19 software using a CT-scan technique based on the human first molar. The crown was approximated with 39514 spherical particles to reach a reasonable convergence in the results. In the present work, glass ceramic was considered the crown material on a titanium abutment. The simulation was performed for an impactor with an initial velocity of 25 m/s in the implant-abutment axis direction. We took advantage of smooth particle hydrodynamics (SPH) such that the burden of defining a primary crack growth direction was suppressed. Results. The simulation results demonstrated that the micro-crack onset due to the impact wave in the ceramic crown first began from the crown incisal edge and then extended to the margin due to increased stress concentration near the contact region. At 23.36 µs, the crack growth was observed in two different directions based on the crown geometry, and at the end of the simulation, some micro-cracks were also initiated from the crown margin. Moreover, the results showed that the SPH algorithm could be considered an alternative robust tool to predict crack propagation in brittle materials, particularly for the implant crown under dynamic loading. Conclusion. The main achievement of the present study was that the SPH algorithm is a helpful tool to predict the crack growth pattern in brittle materials, especially for ceramic crowns under dynamic loading. The predicted crack direction showed that the initial crack was divided into two branches after its impact, leading to the crown fracture. The micro-crack initiated from the crown incisal edge and then extended to the crown margin due to the stress concentration near the contact area.