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A technique based on voxel (3D “volume pixels”) representation of microstructures and corresponding digital solution methods is developed for representative volume element type calculations, which avoids computationally expensive steps involved in usual Finite Element procedures such as topologically conforming meshing, mapping, volume integration, stiffness matrix generation and matrix-based solution methods. The process proceeds by converting the material microstructure into voxels. The problem then becomes “digital” on a regular “voxel-grid”, directly manipulating voxel values, allowing extremely fast methods to be used to construct derivatives and the solve the system. In this paper, we illustrate the process of voxelization, derivative construction and solution, and also supply an analysis of the operation counts. Numerical examples are provided to illustrate the approach.

The objective of this paper is to focus on one of the “building blocks” of additive manufacturing technologies, namely selective laser-processing of particle-functionalized materials. Following a series of work in Zohdi (Int J Numer Methods Eng 53:1511–1532, 2002; Philos Trans R Soc Math Phys Eng Sci 361(1806):1021–1043, 2003; Comput Methods Appl Mech Eng 193(6–8):679–699, 2004; Comput Methods Appl Mech Eng 196:3927–3950, 2007; Int J Numer Methods Eng 76:1250–1279, 2008; Comput Methods Appl Mech Eng 199:79–101, 2010; Arch Comput Methods Eng 1–17. doi: 10.1007/s11831-013-9092-6 , 2013; Comput Mech Eng Sci 98(3):261–277, 2014; Comput Mech 54:171–191, 2014; J Manuf Sci Eng ASME doi: 10.1115/1.4029327 , 2015; CIRP J Manuf Sci Technol 10:77–83, 2015; Comput Mech 56:613–630, 2015; Introduction to computational micromechanics. Springer, Berlin, 2008; Introduction to the modeling and simulation of particulate flows. SIAM (Society for Industrial and Applied Mathematics), Philadelphia, 2007; Electromagnetic properties of multiphase dielectrics: a primer on modeling, theory and computation. Springer, Berlin, 2012), a laser-penetration model, in conjunction with a Finite Difference Time Domain Method using an immersed microstructure method, is developed. Because optical, thermal and mechanical multifield coupling is present, a recursive, staggered, temporally-adaptive scheme is developed to resolve the internal microstructural fields. The time step adaptation allows the numerical scheme to iteratively resolve the changing physical fields by refining the time-steps during phases of the process when the system is undergoing large changes on a relatively small time-scale and can also enlarge the time-steps when the processes are relatively slow. The spatial discretization grids are uniform and dense enough to capture fine-scale changes in the fields. The microstructure is embedded into the spatial discretization and the regular grid allows one to generate a matrix-free iterative formulation which is amenable to rapid computation, with minimal memory requirements, making it ideal for laptop computation. Numerical examples are provided to illustrate the modeling and simulation approach, which by design, is straightforward to computationally implement, in order to be easily utilized by researchers in the field. More advanced conduction models, based on thermal-relaxation, which are a key feature of fast-pulsing laser technologies, are also discussed.

The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of laser processing and subsequent targeted zonal heating of materials composed of packed, discrete, particles. Because of the complex microstructure, containing gaps and interfaces, this type of system is extremely difficult to simulate using continuum-based methods, such as the Finite Difference Time Domain Method or the Finite Element Method. The computationally-amenable model that is developed captures the primary physical events, such as reflection and absorption of optical energy, conversion into heat, thermal conduction through the microstructure and possible phase transformations. Specifically, the features of the computational model are (1) a discretization of a concentrated laser beam into rays, (2) a discrete element representation of the particulate material microstructure and (3) a discrete element transient heat transfer model that accounts for optical (laser) energy propagation (reflection and absorption), its conversion into heat, the subsequent conduction of heat and phase transformations involving possible melting and vaporization. A discrete ray-tracking algorithm is developed, along with an embedded, staggered, iterative solution scheme, which is needed to calculate the optical-to-thermal conversion, particle-to-particle conduction and phase-transformations, implicitly. Numerical examples are given, focusing on concentrated laser beams and the effects of surrounding material conductivity, which draws heat away from the laser contact zone, thus affecting the targeted material state.

This work addresses the modeling and simulation of charged particulate jets in the presence of electromagnetic fields. The presentation is broken into two main parts: (1) the dynamics of charged streams of particles and their interaction with electromagnetic fields and (2) the coupled thermal fields that arise within the jet. An overall model is built by assembling submodels of the various coupled physical events to form a system that is solved iteratively. Specifically, an approach is developed whereby the dynamics of charged particles, accounting for their collisions, inter-particle near-fields, interaction with external electromagnetic fields and coupled thermal effects are all computed implicitly in an iterative, modular, manner. A staggered, temporally-adaptive scheme is developed to resolve the multiple fields involved and the drastic changes in the physical configuration of the stream, for example when impacting a solid wall or strong localized electromagnetic field. Qualitative analytical results are provided to describe the effects of the electromagnetic fields and quantitative numerical results are provided for complex cases.