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Additive Manufacturing (AM) has enabled the fabrication of metallic cellular materials that are of interest in the design of lightweight impact resistant structures. However, there is a need to understand the interactions between: (i) the material architecture, (ii) the AM process parameters, and (iii) the as-built geometry, microstructure and energy absorbing properties. In this work, we investigate the quasi-static and dynamic behaviour of cellular materials manufactured from 316L stainless steel using laser powder bed fusion (LPBF). Four cellular architectures are considered (octet lattice, lattice-walled square honeycomb, origami and square honeycomb), as well as three sets of AM process parameters, characterised by laser powers of 50, 125 and 200 W. The exposure time is adjusted to deliver the same total heat input. The 125 W case leads to material with the highest strength and ductility. The cellular materials with this process variant match their nominal densities most closely, and have the highest strength and energy absorption. Either reducing (50 W) or increasing (200 W) the power leads to a significant increase in porosity, reducing strength and energy absorption. However, we find that changes due to process-induced porosity have a smaller influence than those resulting from the choice of cellular architecture., Comment: 25 pages, 21 figures, Supplementary data availabel at https://doi.org/10.1016/j.matdes.2022.111398

We present a phase field-based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalised phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker-Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearised system is solved using a robust monolithic scheme, based on quasi-Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress-strain hysteresis and temperature. Namely, we compute $\Delta \varepsilon-N$ curves, quantify Paris law parameters and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large-scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, {\epsilon}^\star_AB, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of \epsilon^\star_AB, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multicritical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime., Comment: 29 pagres, 9 figures

The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour of recurrent epidemics, and the former the superimposed noise of observed incidence patterns. Recently, a stochastic theory based on a mechanism of resonance with internal noise has shifted the role of stochasticity closer to the center stage, by showing that the major dynamic patterns found in the incidence data can be explained as resonant fluctuations, whose behaviour is largely independent of the amplitude of seasonal forcing, and by contrast very sensitive to the basic epidemiological parameters. Here we elaborate on that approach, by adding an ingredient which is missing in standard epidemic models, the 'mixing network' through which infection may propagate. We find that spatial correlations have a major effect in the enhancement of the amplitude and the coherence of the resonant stochastic fluctuations, providing the ordered patterns of recurrent epidemics, whose period may differ significantly from that of the small oscillations around the deterministic equilibrium. We also show that the inclusion of a more realistic, time correlated, recovery profile instead of exponentially distributed infectious periods may, even in the random-mixing limit, contribute to the same effect., Comment: 29 pages, 8 figures

The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds \Gamma\backslash{\Bbb H}^d and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds., Comment: AMSTeX file, 20 pages