Springback Analysis

It's the high-precision prediction of shape change due to elastic recovery after forming (springback). The accuracy of stress field calculation using implicit methods is key. Composite hardening laws considering the Bauschinger effect (like Yoshida-Uemori) are extremely important.

Expressing this with equations, it looks like this.

Yoshida-Uemori model:

Springback analysis simulation is formulated as a coupled problem of thermodynamics, material mechanics, and fluid dynamics. Since the physical phenomena of manufacturing processes 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, speed, load, etc.) and product quality (dimensional accuracy, defects, mechanical properties).

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

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.).

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

Expressing this with equations, it looks like this.

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

Plastic deformation of metals is described by constitutive laws like Johnson-Cook:

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

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