/MAT/LAW109
Block Format Keyword Elasto-plastic material with isotropic von Mises yield criterion with plastic strain rate and temperature depending nonlinear hardening.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW109/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
ρi | |||||||||
E | ν | ||||||||
Cp | η | Tref | T0 | ||||||
tab_ID_h | tab_ID_t | Xscale_h | Yscale_h | Ismooth | |||||
tab_ID_ η | Xscale_ η |
Definition
Field | Contents | SI Unit Example |
---|---|---|
mat_ID | Material identifier. (Integer, maximum 10 digits) |
|
unit_ID | (Optional) Unit Identifier. (Integer, maximum 10 digits) |
|
mat_title | Material title. (Character, maximum 100 characters) |
|
ρi | Initial density. (Real) |
[kgm3] |
E | Young’s modulus. (Real) |
[Pa] |
ν | Poisson’s ratio. (Real) |
|
Ismooth | Choice of yield function interpolation versus strain rate.
(Integer) |
|
Cp | Specific heat. (Real) |
[Jkg⋅K]
|
Tref | Reference temperature. Default = 293K (Real) |
[K] |
T0 | Initial temperature. Default = Tref (Real) |
[K] |
η | Taylor-Quinney coefficient (fraction of plastic work
converted to heat). Value between 0.0 and
1.0. (Real) |
|
tab_ID_ η | (Optional) Table identifier defining scale factor for
η
depending on strain rate, temperature, and plastic strain.
Value between 0.0 and 1.0. (Integer Id) |
|
tab_ID_h | Table identifier for yield stress depending on effective
plastic strain and strain rate. (Integer) |
|
Xscale_ η | Abscissa scale factor (strain rate) for
tab_ID_
η
. Default = 1.0 (Real) |
[1s] |
Xscale_h | Abscissa scale factor (strain rate) for
tab_ID_h. Default = 1.0 (Real) |
[1s] |
Yscale_h | Scale factor for ordinate (stress) for
tab_ID_h. Default = 1.0 (Real) |
[Pa] |
tab_ID_t | Table identifier for quasi-static yield stress depending on
effective plastic strain and temperature. (Integer Id) |
▸Example (Aluminum)
Comments
- Yield criterion using isotropic von Mises equivalent stress:
(1) ϕ=σVM−σy - Yield stress hardening defined by tabulated input as:
(2) σy=fh(εp,˙εp)ft(εp,T)ft(εp,Tref)Where,- fh(εp,˙εp)
- Function table of yield stresses depending on plastic strain and plastic strain rate.
- ft(εp,T)
- Table ID of quasi-static yield function depending on plastic strain and temperature.
- Tref
- Reference temperature. Corresponds to conditions during experimental tests.
- In adiabatic conditions, the temperature is updated using:
(3) T=T0+η⋅fη(εp,˙εp,T)ρCpWhere, η is the constant Taylor-Quinney coefficient which may be modified by introducing scalar factor defined by function fη(εp,˙εp,T) .
Otherwise, if /HEAT/MAT is present in the model, the temperature is imposed on all elements and cannot be updated using Equation 3.
Function fη(εp,˙εp,T) may be one dimensional, two-dimensional, or three-dimensional, but the first abscissa is always strain rate and the second one may be only the temperature.