Glass transition temperature. Only present in amorphous materials.
Set of simplifying assumptions of each model component. They can be of three kinds: geometric, physical and statistical.
Boundary conditions are required for the solution of partial differential equations. There is one boundary condition required per degree of the equation for each dimension.
Is a model element that gives information about the variable of interest on certain regions of the design space. A model requires one boundary condition per degree of the partial derivative on each dimension. Boundary conditions are required for the solution of partial differential equations.
Density of fully-dense material. It is usually assumed as a function of temperature.
Radiative properties of a material: absorptivity, emissivity, and transmissivity. They depend on temperature and wavelength.
Thermal conductivity of bulk material. It is often modeled as a function of temperature.
A cellular automaton (CA) is a discrete model that describes interactions between different cells in a grid, each of them in one of a finite number of states.
Equations that describe consolidation in which the loose material is heated above the melting point to become fully-dense. Melting is only possible for crystalline or semi-crystalline materials, as amorphous polymers degrade at high temperatures.
Equation that describe consolidation in which the loose material is heated below the melting point. In these cases, the driving force for sintering is often given by viscosity-controlled reduction of surface tension.
Initial condition for consolidation model. It may be described as the initial distribution of porosity (or density) in the powder bed before the process.
They describe thermally-activated consolidation processes. In this case two different kinds of consolidation models are included: sintering and melting models.
Internal variables used by consolidation models.
Mathematical form of the equation describing a physical relationship between a set of variables that does not change with time.
Latent heat of phase transformation. Only present in crystalline materials.
Reference temperatures for melting in crystalline materials. They can be assumed at a constant temperature for metals (and Stefan problems), or in a range for alloys.
Definition of the different terms in the equation chosen to describe the physical process. Inclusion or neglection of physical phenomena.
Elastic modulus for solid mechanics equations.
Values of this type of parameter are approximated with experiments
Distribution of enthalpy in the powder bed.
Equilibrium partition coefficient for phase field or cellular automaton model.
Transport equation for momentum in a viscous flow. The solution is given by the distribution of velocity in the liquid region.
Boundary conditions for fluid mechanics model, often given by the velocity or its gradient on a given surface.
Initial condition for fluid mechanics model, given by the initial distribution of velocity in powder bed.
A set of differential equations used to simulate fluid mechanics. They include conservation equations for momentum and mass. Equations for conservation of momenutm are given by parabolic PDE for transient simulations and an elliptic one for steady-state simulations.
Internal variables used by fluid mechanics models.
Thermal conductivity of fully sintered material, if assumed not equal to bulk material. This is reserved for cases in which fully sintered material is not fully-dense.
Modeling assumptions that describe the geometry of the physical problem to be solved: number of dimensions (1-D, 2-D, 3-D), computational domian, location of the coordinate system, possible axes of symmetry.
Determination of the computational domain.
Irradiation model is a representation of the irradiation produced by the heat source --> IrradiationModel = HeatSourceModel
A heat source model describes the distribution of a given heat source on an irradiated surface.
Heat Transfer Equation is also designated in the literature as Energy Conservation Equation Heat Transfer Equation is a type of Transport Equation
A heat transfer equation describes the flow of thermal energy (heat) due to gradients in temperature, external sources, and generation and dissipation of heat. Mathematically, it is expressed with a partial differential equation for temperature or enthalpy.
Equation that describes the transport of energy due to differences in temperature, external sources, and heat generation/dissipation. Equations for conservation of energy (enthalpy) are given by parabolic PDE for transient simulations and an elliptic one for steady-state simulations. The output is given by the distribution of temperature.
In the case of transient models, initial conditions are required as starting points for the propagation of the solution of the equation.
Initial value of porosity in the powder bed. Often close to 50%.
A physics-based model to describe how irradiation penetrates and heats up a porous medium. This often involves a study of the radiative and optical properties of randomly-packed particles.
Latent heat of fusion: energy barrier to overcome to transform from solid to liquid phase.
Latent heat of vaporization: energy barrier to overcome to transform from liquid to gas phase.
Assumed length scale for the physical processes included in the model component: micro-, meso-, or macro-scale.
The group of the identified limitations for each model component.
Mass diffusion coefficient for liquid phase, for phase field model.
Emissivity of liquid on top of powder bed.
Slope of the liquidus curve on a Temperature vs. Concentratrion curve.
Temperature in which mushy zone and liquid phases coexist.
It describes the transport of different species in a mixture, due to differences in chemical potential. Mass transport is controlled by diffusion coefficients.
Assumptions for material properties: constant, dependent on other variables, etc.
Temperature in which solid and liquid coexist.
Initial condition of microstructural evolution model. Given by initial distribution of phase field (in phase field methods) or the state in each cell (for a cellular automaton).
A set of equations that describe thermally-activated phase transformations in a metal or alloy.
Internal variables used by microstructural models.
A model component represents a certain physical process at given length- and time- scales.
This entity defines different types of models
Simplifying assumption used to reduce the physical process to a solvable mathematical form.
Input parameters as required by each component of the model.
Output parameters as required by each component of the model.
Constraints in the applicability of the model, as identified by the developers and users.
Physical properties as published in tables.
A representation of a possibly multi-physics multi-scale process. A model entity can be defined as a composition of several model components.
The set of input parameters required to simulate a physics-based model.
The set of output parameters required to simulate a physics-based model.
Internal variables used in model components.
An equation that describes the transport of momentum in a viscous fluid flow. The solution is given by the distribution of velocity in the liquid region.
Dimensionality of the physics-based model: one-dimensional, two-dimensional, three-dimensional.
A phase field model is a mathematical model for solving interfacial problem, e.g. diffusion-co ntrolled solidification dynamics.
Group of physical parameters that determine phase transformation, depending on the physical nature of the material: amorphous, semi-crystalline, or crystalline.
Simplifying assumptions of physical processes. They may include neglection of certain physical domains, adoption of physical laws, assumption of steady-state solutions, etc.
A set of mathematical expressions that describe a physical process.
Coefficient of contraction on transverse directions due to axial strain.
Distribution of porosity in the powder bed.
Emissivity of powder on top of powder bed.
Mathematical form of the equation describing a physical phenomenon which evolves in time.
Equations that describe the physical phenomenon of energy transfer in the form of electromagnetic radiation, which depends on the absorption, emission and scattering processes in the medium.
Activation energy for an Arrhenius-type sintering equation.
Distribution of sintering potential in the powder bed.
Distribution of solid fraction in the powder bed (in the case of melting with a mushy zone)
Mass diffusion coefficient for solid phase, for phase field model.
A continuum mechanics model that models the response of a solid material under elastic and plastic loads.
Emissivity of fully-dense solid on top of powder bed.
Equations that describe phase transformations for a metal or alloy starting from a liquid phase. The solution depends on the temperature history of the material.
Temperature in which mushy zone and solid phases coexist.
Chemical composition of solute in binary alloys.
Methods used to solve the systems of equations in each model component.
Chemical composition of solvent in binary alloys.
Specific heat of the material. It can be assumed as temperature dependent and it can be made discontinuous in the mushy zone to artificially model latent heat of fusion.
In the case of a stochastic model, assumptions regarding the probability of different events.
Boundary condition for solid mechanics model, as defined by mechanical constraints (no displacement, no rotation, etc).
Initial condition for a solid mechanics model, defined as the initial distribution of stresses and strains.
A model that describes the behavior of a certain material under the action of forces, temperature changes, phase changes, and other agents.
Internal variables used by structural models.
Thermal conductivity of the material used for the substrate.
Convection coefficient on top surface of powder bed.
Emissivity for radiation on top of the powder bed. Value depends on whether material is liquid, fully-dense solid, or powder.
Surface tension is the elastic tendency of liquid which makes them acquire the least surface area possible.
Boundary condition for heat transfer model, as given by a specific temperature or heat flux on a certain surface.
Thermal conductivity of the gas in the pores of the powder bed.
Coefficient of thermal expansion caused by a change in temperature.
Initial condition for thermal model, defined by the initial distribution of temperature or enthalpy in ""the powder bed"".
A model that describes the flow of thermal energy in a given system.
Internal variables used by thermal models.
Time-dependent or steady-state solution, and if time-dependent, time scale for the physical phenomenon.
Boundary condition for the heat transfer problem atop a surface or a bulk material.
Activation energy in case of an Arrhenius-type model for viscosity as a function of temperature.