Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [Prog. Theor. Phys. 92 (1994), 939] boundary integrals. The analysis has been carried out by studying the convergence of the first- and second-order differential operators as the smoothing length (that is, the characteristic length on which relies the SPH interpolation) decreases. These differential operators are of fundamental importance for the computation of the viscous drag and the viscous/diffusive terms in the momentum and energy equations. It has been proved that close to the boundaries some of the mirroring techniques leads to intrinsic inaccuracies in the convergence of the differential operators. A consistent formulation has been derived starting from Takeda et al. boundary integrals (see the above reference). This original formulation allows implementing no-slip boundary conditions consistently in many practical applications as viscous flows and diffusion problems.

On the non-slip boundary condition enforcement in SPH methods.

The implementation of boundary conditions is one of the points where the SPH methodology still has some work to do. The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [1] boundary integrals. A Pouseuille flow has been used as a example to gradually evaluate the accuracy of the different implementations. Our goal is to test the behavior of the second-order differential operator with the proposed boundary extensions when the smoothing length h and other dicretization parameters as dx/h tend simultaneously to zero. First, using a smoothed continuous approximation of the unidirectional Pouseuille problem, the evolution of the velocity profile has been studied focusing on the values of the velocity and the viscous shear at the boundaries, where the exact solution should be approximated as h decreases. Second, to evaluate the impact of the discretization of the problem, an Eulerian SPH discrete version of the former problem has been implemented and similar results have been monitored. Finally, for the sake of completeness, a 2D Lagrangian SPH implementation of the problem has been also studied to compare the consequences of the particle movement

Study of bond stress-slip relationship and radial dilation in prestressed concrete

This paper presents two test procedures for evaluating the bond stress–slip and the slip–radial dilation relationships when the prestressing force is transmitted by releasing the steel (wire or strand) in precast prestressed elements. The bond stress–slip relationship is obtained with short length specimens, to guarantee uniform bond stress, for three depths of the wire indentation (shallow, medium and deep). An analytical model for bond stress–slip relationship is proposed and compared with the experimental results. The model is also compared with the experimental results of other researchers. Since numerical models for studying bond-splitting problems in prestressed concrete require experimental data about dilatancy angle (radial dilation), a test procedure is proposed to evaluate these parameters. The obtained values of the radial dilation are compared with the prior estimated by numerical modelling and good agreement is reached

Analysis of crystallographic slip and grain boundary sliding in a Ti-45Al-2Nb-2Mn (at%)-0.8 vol%TiB2 alloy by high temperature in situ mechanical testing

This work aims to contribute to a further understanding of the fundamentals of crystallographic slip and grain boundary sliding in the γ-TiAl Ti–45Al–2Nb–2Mn (at%)–0.8 vol%TiB2 intermetallic alloy, by means of in situ high-temperature tensile testing combined with electron backscatter diffraction (EBSD). Several microstructures, containing different fractions and sizes of lamellar colonies and equiaxed γ-grains, were fabricated by either centrifugal casting or powder metallurgy, followed by heat treatment at 1300 °C and furnace cooling. in situ tensile and tensile-creep experiments were performed in a scanning electron microscope (SEM) at temperatures ranging from 580 °C to 700 °C. EBSD was carried out in selected regions before and after straining. Our results suggest that, during constant strain rate tests, true twin γ/γ interfaces are the weakest barriers to dislocations and, thus, that the relevant length scale might be influenced by the distance between non-true twin boundaries. Under creep conditions both grain/colony boundary sliding (G/CBS) and crystallographic slip are observed to contribute to deformation. The incidence of boundary sliding is particularly high in γ grains of duplex microstructures. The slip activity during creep deformation in different microstructures was evaluated by trace analysis. Special emphasis was placed in distinguishing the compliance of different slip events with the Schmid law with respect to the applied stress.