A widespread use of lasers in additive manufacturing is to induce a given temperature and a phase transformation in materials deposited onto a substrate. For a laser to induce a phase transformation in the material, the power intensity must be sufficiently high to induce melting and, in all cases, stay below a vaporization or burn-off temperature of the target material. Oftentimes, there is variability in the laser input to the target zone. For a process designer, a central question is to determine the uncertainty of the resulting target state, i.e., temperature and state (solid or melted), due to uncertainty in the energy (laser) input. This motivates the present work, which integrates relatively fundamental heat transfer models that describe the thermal effects due to (a) laser irradiation, (b) heat conduction into the surface of deposition, (c) infrared radiation outwards into the surroundings, (d) convection due to an exhaust apparatus to control the cooling of the system, and (e) phase transformations, for a dry Nylon 6 powder as a sample material. One key advantage of this framework is that it is amenable to a sensitivity and uncertainty analysis with respect to any of its parameter inputs. Accordingly, uncertainty quantification studies are also undertaken to ascertain the relationship between variation in laser input to variation in the processed material state. Examples will be presented to illustrate the thermal behavior of the numerical model. Due to its simplicity, this framework is designed to be computationally implemented in a straightforward fashion. The model allows for rapid computation and sensitivity analyses, which are provided as numerical examples. Extensions are also given to include mass transport (losses) due to ablation of the target material.

Due to increasing demands for faster and faster manufacturing of new complex materials, such as casting of particulate composites, the determination of pumping pressures needed for particle-laden fluids through channels is critical. In particular, the increase in viscosity as a function of the particle volume fraction can lead to system malfunction, due to an inability to deliver necessary pressures to pump the more viscous fluid through the system. This paper studies the pressure gradient needed to maintain a given flow rate, explicitly as a function of the volume fraction of particles present in the fluid. It is also crucial to control voids in the casted products, which can be traced to air-entrainment, spurious internal reactions, dewetting, etc., which can be traced to high Reynolds numbers. Accordingly, an expression for the resulting Reynolds number as a function of the particle volume fraction and flow rate is also developed. Numerical examples are provided to illustrate the practical use of the derived relations to characterize the necessary pumping pressures for process-driven, particle-laden fluid flows.

This paper develops a statistically based computational method to rapidly determine stresses in flexible substrates during particle printing processes. Specifically, substrate stresses due to multiple surface particle contact sites are statistically computed by superposing point load solutions for different random particle realizations (sets of random loading sites) within a fixed feature boundary. The approach allows an analyst to rapidly determine the number of particles in a surface feature needed to produce repeatable substrate stresses, thus minimizing the deviation from feature to feature and ensuring consistent production. Three-dimensional examples are provided to illustrate the technique. The utility of the approach is that an analyst can efficiently ascertain the number of particles needed within a feature, without resorting to computationally intensive numerical procedures, such as the finite element method.

In many small-scale devices, the materials employed are functionalized (doped) with microscale and/or nanoscale particles, in order to deliver desired overall dielectric properties. In this work, we develop a reduced-order lumped-mass model to characterize the dynamic response of a material possessing a microstructure that is comprised of an electromagnetically-neutral binder with embedded electromagnetically-sensitive (charged) particles. In certain industrial applications, such materials may encounter external electrical loading that can be highly oscillatory. Therefore, it is possible for the forcing frequencies to activate the inherent resonant frequencies of these micro- and nanostructures. In order to extract qualitative information, this paper first analytically investigates the mechanical and electromagnetic (cyclotronic) contributions to the dynamic response for a single particle, and then quantitatively investigates the response of a model problem consisting of a coupled multiparticle periodic array, via numerical simulation, using an implicit temporally-adaptive trapezoidal time-stepping scheme. For the model problem, numerical studies are conducted to observe the cyclotronically-dominated resonant frequency and associated beat phenomena, which arises due to the presence of mechanical and electromagnetic harmonics in the material system.