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

DED (Directed Energy Deposition): Theoretical Foundations

Overview

πŸ§‘πŸŽ“

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.


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

πŸ§‘πŸŽ“

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).


πŸ§‘πŸŽ“

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


Governing Equations for Manufacturing Processes

πŸ§‘πŸŽ“

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.).


πŸ§‘πŸŽ“

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



Solidification and Phase Change

πŸ§‘πŸŽ“

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:



πŸŽ“

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


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

πŸ§‘πŸŽ“

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.


πŸ§‘πŸŽ“

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:



$$ \eta(\dot{\gamma}, T, p) = \frac{\eta_0(T, p)}{1 + (\eta_0 \dot{\gamma} / \tau^*)^{1-n}} $$
πŸ§‘πŸŽ“

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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