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Contrary to what often seems to be accepted, 100% Tit-for-Tat is not an ESS, even in the three-pure-strategy game Tit-for-Tat-Always Cooperate-Always Defect, for which 100% Always Defect finally remains the only attractor for the composition of “asexual” populations. The present paper firstly investigates the dynamics of the Tit-for-Tat-Always Cooperate-Always Defect game for asexual populations, with the more realistic assumption that Tit-for-Tat sometimes fails to apply its algorithm. Surprisingly, this perturbation of the original game leads to different attractor patterns, in relation to the numerical values of the expected number of meetings and of Tit-for-Tat’s failure rate. These patterns generally include one punctual attractor for which most dyads at least partially cooperate. Nevertheless, the attractor alternative to 100% Always Defect in each pattern may become unstable when certain mixed strategies (cooperating and defecting at random) are introduced into the game, and the whole flow of strategy frequencies may then converge towards 100% Always Defect. Beyond the reiterated Prisoner’s Dilemma, the present analysis illustrates how self-organizing processes at infra-populational levels, like that occurring in dyads including at least one fallible Tit-for-Tat, can influence the evolution of populations.

We present an extended radial point interpolation method (XRPIM) for modeling cracks and material interfaces in two-dimensional elasto-static problems. Therefore, partition of unity enrichment is incorporated into RPIM. We employ both step enrichment and crack tip enrichment for cracks. The studies are restricted to stationary cracks though the method can be extended easily to moving boundaries. We compare the results to the extended finite element method to show the superiority of our method. We show for two selected problems that the error is of magnitudes lower compared to XFEM simulations.

We present a Smoothed Finite Element Methods (SFEM) for thermo-mechanical impact problems. The smoothing is applied to the strains and the standard finite element approach is used for the temperature field. The SFEM allows for highly accurate results and large deformations. No isoparametric mapping is needed; the shape functions are computed in the physical domain. Moreover, no derivatives of the shape functions must be computed. We implemented a visco-plastic constitutive model and validate the method by comparing numerical results to experimental data.

This paper presents a multi-scale model that can predict the ballistic impact behavior of multi-layer plain-woven fabrics using the finite element method (FEM). Multi-layer fabrics of 30.5 × 30.5 cm, woven by high performance yarns Kevlar^® 29 3000 denier, are impacted by a 0.3 fragment simulating projectile (FSP). Using a multi-scale approach, behavior of multi-layer fabrics subjected to different impact velocities is numerically analyzed. Ballistic limit of the fabric can also be predicted. The multi-scale model shows an effective gain of computation time in comparison with current mesoscopic ones. Computational results show a good agreement with experimental data.

We present impact simulations with the Smoothed Finite Element Method (SFEM). Therefore, we develop the SFEM in the context of explicit dynamic applications based on diagonalized mass matrix. Since SFEM is not based on the isoparametric concept and is based on line integration rather than domain integration, it is very promising for events involving large deformations and severe element distortion as they occur in high dynamic events such as impacts. For some benchmark problems, we show that SFEM is superior to standard FEM for impact events. To our best knowledge, this is the first time SFEM is applied in the context of impact analysis based on explicit time integration.