36. VISCOPLASTIC_MODEL Namelist

36.1. Overview

The VISCOPLASTIC_MODEL namelist defines the viscoplastic model to be used for a particular solid material phase in material stress-strain calculations. Two viscoplastic models are available: a mechanical threshold stress (MTS) model and a power law model. When no model is given for a solid material phase, it is modeled as a purely elastic material. The models specify a relation for the effective plastic strain rate Μ‡as a function of temperature \(T\) and von Mises stress \(\sigma\). For more details on the models see the Truchas Physics and Algorithms manual. Briefly:

Power Law Model. In the simple power law model, the strain rate relation is

(36.1.1)\[\dot{\epsilon} = A*exp(-Q/R(T - T_0))*\sigma^n\]

where A, n, Q, and R are parameters given by this namelist.

MTS Model. The MTS model uses the strain rate relation

(36.1.2)\[\dot{\epsilon} = \dot{\epsilon_{0i}} exp[-\frac{\mu b^3 g_{0i}}{kT}(1-(\frac{\mu_0}{\mu\sigma_i}(\sigma - \sigma_a))^{p_i})^{q_i}], \mu = \mu_0 - \frac{D}{exp(T_0/T) - 1}\]

where \(\dot{\epsilon_{0i}}\), \(\dot{g_{0i}}\), b, k, D, \(\mu_0\), \(T_0\), \(\sigma_i\), \(\sigma_a\), \(p_i\), and \(q_i\) are parameters given by this namelist. When \(\sigma \lt \sigma_a\) we instead use \(\dot{\epsilon} = K\sigma^5\), where K is chosen to give continuity with the previous relation at \(\sigma = \sigma_a\). And when \(\sigma - \sigma_a \gt \mu\sigma_i/\mu_0\) we take \(\dot{\epsilon} = \dot{\epsilon_{0i}}\).

36.2. VISCOPLASTIC_MODEL Namelist Features

Required/Optional : Optional; only relevant when Solid_Mechanics is true.
Single/Multiple Instances: Multiple; at most one per solid material phase.

36.3. Components

Phase

Description : The name of the material PHASE to which this viscoplastic model applies.
Type : case-sensitive string
Default : none

Model

Description : The type of viscoplastic strain rate model.
Type : case-insensitive string
Default : none
Valid Values: β€œMTS”, β€œpower law”, β€œelastic”
Notes : The effect of the β€œelastic” option is equivalent to not specifying a viscoplastic model at all; it is provided as a convenience.

MTS_b

Description : Burgers vector length \(b\) in Eq.36.1.2
Physical Dimension: \(L\)
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_d

Description : Constant \(D\) used in Eq.36.1.2
Physical Dimension: \(F/L^2\)
Type : real
Default : none

MTS_edot_0i

Description : Reference strain rate \(\dot{\epsilon_{0i}}\) used in Eq.36.1.2
Physical Dimension: \(T^{-1}\)
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_g_0i

Description : Material constant \(g_{0i}\) used in Eq.36.1.2
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_k

Description : Boltzmanns constant \(k\) used in Eq.36.1.2
Physical Dimension: \(E/\Theta\)
Type : real
Default : none
Valid Values: \(\gt 0\)
Note : Temperature should be expressed in Kelvin, or other temperature scale where 0 corresponds to absolute zero. If SI units are being used, \(k\) should be \(1.38Γ—10^{βˆ’23}\). Use a value appropriate to the units used in Eq.36.1.2

MTS_mu_0

Description : Reference value \(\mu_0\) for the temperature dependent shear modulus used in Eq.36.1.2
Physical Dimension: \(F/L^2\)
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_p_i

Description : Exponent term \(p_i\) used in Eq.36.1.2
Physical Dimension: \(F/L^2\)
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_q_i

Description : Exponent term \(q_i\) used in Eq.36.1.2
Physical Dimension: \(F/L^2\)
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_sig_a

Description : The athermal stress term \(\sigma_a\) used in Eq.36.1.2
Physical Dimension: \(F/L^2\)
Type : real
Default : none
Valid Values: \(\geq 0\)

MTS_sig_i

Description : A stress term \(\sigma_i\) related to obstacles to dislocation motion in Eq.36.1.2
Physical Dimension: \(F/L^2\)
Type : real
Default : none
Valid Values: \(\gt 0\)

MTS_temp_0

Description : Constant \(T_0\) used in the temperature dependent shear modulus in Eq.36.1.2
Physical Dimension: \(\Theta\)
Type : real
Default : none
Valid Values: \(\gt 0\)

Pwr_Law_A

Description : Constant term \(A\) in Eq.36.1.1
Physical Dimension: \(F/L^2\)
Type : real
Default : none
Valid Values: \(\geq 0\)

Pwr_Law_N

Description : Stress exponent term \(n\) in Eq.36.1.1
Type : real
Default : none
Valid Values: \(\gt 0\)

Pwr_Law_Q

Description : Activation energy \(Q\) in Eq.36.1.1
Physical Dimension: \(E/mol\)
Type : real
Default : none
Valid Values: \(\geq 0\)

Pwr_Law_R

Description : Gas constant \(R\) in Eq.36.1.1
Physical Dimension: \(E/(\Theta mol)\)
Type : real
Default : none
Valid Values: \(\gt 0\)
Note : Temperature should be expressed in Kelvin, or other temperature scale where \(0\) corresponds to absolute zero. Use the value for \(R\) appropriate to the units used in Eq.36.1.1

Pwr_Law_Tref

Description : Reference temperature \(T_0\)
Physical Dimension: \(E\)
Type : real
Default : 0
Note : Used to offset temperature units from an absolute scale like Kelvin to non-absolute units like Celsius.