DED (Directed Energy Deposition) Simulation

Category: Analysis | Consolidated Edition 2026-04-06
CAE visualization for ded simulation theory - technical simulation diagram
DED (Directed Energy Deposition) Simulation

Theory and Physics

Overview

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Professor! Today's topic is DED (Directed Energy Deposition) simulation, right? What is it?


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DED (Directed Energy Deposition) is a technology that deposits layers by melting metal powder or wire with a laser/electron beam. It simulates the thermal history of multi-layer deposition and the material deposition process.



Governing Equations


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Expressing this in a mathematical formula, it looks like this.


$$\rho c_p \frac{\partial T}{\partial t} = \nabla\cdot(k\nabla T) + \dot{Q} - \rho L_f \frac{\partial f_s}{\partial t}$$

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Hmm, just the formula doesn't really click... What does it represent?


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Element activation for material deposition:



$$V_{deposit} = \frac{\dot{m}}{\rho} \cdot \eta_{capture}$$

Theoretical Foundation

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I've heard of "theoretical foundation," but I might not fully understand it...


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DED (Directed Energy Deposition) simulation is formulated as a coupled problem of thermodynamics, material mechanics, and fluid dynamics. Since the physical phenomena of the manufacturing process span multiple time and spatial scales, an appropriate combination of macro-scale continuum models and meso/micro-scale material models is required. The goal is to quantitatively predict the causal relationship between process parameters (temperature, velocity, load, etc.) and product quality (dimensional accuracy, defects, mechanical properties).


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Wait, wait, directed energy deposition... so, can it also be used in cases like this?


Governing Equations for Manufacturing Processes

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I'm not good with formulas... Could you explain the "meaning" of the DED (Directed Energy Deposition) simulation equation?


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Manufacturing process simulation is formulated as a coupled problem of thermodynamics, fluid dynamics, and solid mechanics.



Heat Conduction Equation (Energy Conservation)

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What exactly does the heat conduction equation mean?



$$ \rho c_p \frac{\partial T}{\partial t} + \rho c_p \mathbf{v} \cdot \nabla T = \nabla \cdot (k \nabla T) + Q $$


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Here, $T$ is temperature, $\mathbf{v}$ is the material velocity field, $k$ is thermal conductivity, and $Q$ is internal heat generation (Joule heating, latent heat, frictional heat, etc.).


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Now I understand what my senior meant when they said, "At least do manufacturing process simulation properly."



Solidification and Phase Change

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Please tell me about "solidification and phase change"!


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During the solidification process, the release/absorption of latent heat significantly affects the temperature field. Formulation using the enthalpy method:



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Expressing this in a mathematical formula, it looks like this.


$$ H(T) = \int_0^T \rho c_p(T') \, dT' + \rho L f_l(T) $$

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Hmm, just the formula doesn't really click... What does it represent?


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Here, $L$ is the latent heat, and $f_l(T)$ is the liquid fraction (takes a value between 0 and 1 in the solid-liquid coexistence region).




Constitutive Law for Plastic Deformation

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What exactly does the constitutive law for plastic deformation mean?


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Plastic deformation of metals is described by constitutive laws such as the Johnson-Cook model:



$$ \sigma_y = (A + B\varepsilon_p^n)(1 + C \ln \dot{\varepsilon}^*)(1 - T^{*m}) $$


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$A$: Initial yield stress, $B$: Hardening coefficient, $n$: Hardening exponent, $C$: Strain rate sensitivity, $m$: Thermal softening exponent.


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After hearing all this, I finally understand why manufacturing process simulation is so important!




Flow Analysis (Filling/Casting)

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Next is flow analysis. What's it about?


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The flow of molten metal or resin follows the Navier-Stokes equations, but high viscosity and non-Newtonian fluid characteristics must be considered. For injection molding, the Cross-WLF model is standard:



$$ \eta(\dot{\gamma}, T, p) = \frac{\eta_0(T, p)}{1 + (\eta_0 \dot{\gamma} / \tau^*)^{1-n}} $$
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I see... Manufacturing process simulation seems simple at first glance, but it's actually very profound.


Assumptions and Applicability Limits

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Isn't this formula universal? When can't it be used?


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