김경종
481 lines
23 KiB
Markdown
481 lines
23 KiB
Markdown
<!-- source-page: 581 -->
|
||
|
||
Abaqus/Explicit will issue an error message if the initial $p - \alpha$ state lies outside the region of allowed states (see Figure 25.2.1–2). When initial conditions are specified only for p (or for ), Abaqus/Explicit will compute (or p) assuming that the $p - \alpha$ state lies on the primary (monotonic loading) curve.
|
||
|
||
<table><tr><td>Input File Usage:</td><td>Use some or all of the following options, as required:*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY*INITIAL CONDITIONS, TYPE=STRESS*INITIAL CONDITIONS, TYPE=POROSITY</td></tr></table>
|
||
|
||
<table><tr><td>Abaqus/CAE Usage:</td><td>Load module: Create Predefined Field: Step: Initial: choose Mechanical for the Category and Stress for the Types for Selected StepInitial specific energy and initial porosity are not supported in Abaqus/CAE.</td></tr></table>
|
||
|
||
# JWL high explosive equation of state
|
||
|
||
The Jones-Wilkins-Lee (or JWL) equation of state models the pressure generated by the release of chemical energy in an explosive. This model is implemented in a form referred to as a programmed burn, which means that the reaction and initiation of the explosive is not determined by shock in the material. Instead, the initiation time is determined by a geometric construction using the detonation wave speed and the distance of the material point from the detonation points.
|
||
|
||
The JWL equation of state can be written in terms of the internal energy per unit mass, $E _ { m }$ , as
|
||
|
||
$$
|
||
p = A \left(1 - \frac {\omega \rho}{R _ {1} \rho_ {0}}\right) \exp \left(- R _ {1} \frac {\rho_ {0}}{\rho}\right) + B \left(1 - \frac {\omega \rho}{R _ {2} \rho_ {0}}\right) \exp \left(- R _ {2} \frac {\rho_ {0}}{\rho}\right) + \omega \rho E _ {m},
|
||
$$
|
||
|
||
where $A , B , R _ { 1 } , R _ { 2 }$ and $\omega$ are user-defined material constants; $\rho _ { 0 }$ is the user-defined density of the explosive; and $\rho$ is the density of the detonation products.
|
||
<table><tr><td>Input File Usage:</td><td>Use both of the following options:</td></tr><tr><td></td><td>*DENSITY (to specify the density of the explosive $\rho_0$ )</td></tr><tr><td></td><td>*EOS, TYPE=JWL (to specify the material constants $A, B, R_1, R_2$ , and $\omega$ )</td></tr></table>
|
||
|
||
<table><tr><td>Abaqus/CAE Usage:</td><td>Property module: material editor:General→Density (to specify the density of the explosive $\rho_0$ )Mechanical→Eos: Type: JWL (to specify the material constants $A, B, R_1$ , $R_2$ , and $\omega$ )</td></tr></table>
|
||
|
||
# Arrival time of detonation wave
|
||
|
||
Abaqus/Explicit calculates the arrival time of the detonation wave at a material point $( t _ { d } ^ { m p } )$ as the distance from the material point to the nearest detonation point divided by the detonation wave speed:
|
||
|
||
$$
|
||
t _ {d} ^ {m p} = \min \left[ t _ {d} ^ {N} + \sqrt {(\mathbf {x} ^ {m p} - \mathbf {x} _ {d} ^ {N}) \cdot (\mathbf {x} ^ {m p} - \mathbf {x} _ {d} ^ {N})} \bigg / C _ {d} \right],
|
||
$$
|
||
|
||
where $\mathbf { x } ^ { m p }$ is the position of the material point, $\mathbf { x } _ { d } ^ { N }$ is the position of the Nth detonation point, $t _ { d } ^ { N }$ is the detonation delay time of the Nth detonation point, and $C _ { d }$ is the detonation wave speed of the explosive
|
||
|
||
<!-- source-page: 582 -->
|
||
|
||
material. The minimum in the above formula is over the N detonation points that apply to the material point.
|
||
|
||
# Burn fraction
|
||
|
||
To spread the burn wave over several elements, a burn fraction, $F _ { b }$ , is computed as
|
||
|
||
$$
|
||
F _ {b} = \min \left[ 1, \frac {(t - t _ {d} ^ {m p}) C _ {d}}{B _ {s} l _ {e}} \right],
|
||
$$
|
||
|
||
where $B _ { s }$ is a constant that controls the width of the burn wave (set to a value of 2.5) and $l _ { e }$ is the characteristic length of the element. If the time is less than $t _ { d } ^ { m p }$ , the pressure is zero in the explosive; otherwise, the pressure is given by the product of $F _ { b }$ and the pressure determined from the JWL equation above.
|
||
|
||
# Defining detonation points
|
||
|
||
You can define any number of detonation points for the explosive material. Coordinates of the points must be defined along with a detonation delay time. Each material point responds to the first detonation point that it sees. The detonation arrival time at a material point is based upon the time that it takes a detonation wave (traveling at the detonation wave speed $C _ { d } )$ to reach the material point plus the detonation delay time for the detonation point. If there are multiple detonation points, the arrival time is based on the minimum arrival time for all the detonation points. In a body with curved surfaces care should be taken that the detonation arrival times are meaningful. The detonation arrival times are based on the straight line of sight from the material point to the detonation point. In a curved body the line of sight may pass outside of the body.
|
||
|
||
Input File Usage: Use both of the following options to define the detonation points:
|
||
|
||
\*EOS, TYPE=JWL
|
||
|
||
\*DETONATION POINT
|
||
|
||
Abaqus/CAE Usage: Property module: material editor: Mechanical→Eos: Type: JWL: Suboptions→Detonation Point
|
||
|
||
# Initial state
|
||
|
||
Explosive materials generally have some nominal volumetric stiffness before detonation. It may be useful to incorporate this stiffness when elements modeled with a JWL equation of state are subjected to stress before initiation of detonation by the arriving detonation wave. You can define the pre-detonation bulk modulus, $K _ { p d }$ . The pressure will be computed from the volumetric strain and $K _ { p d }$ until detonation, at which time the pressure will be determined by the procedure outlined above. The initial relative density $( \rho / \rho _ { 0 } )$ used in the JWL equation is assumed to be unity. The initial specific energy $E _ { m _ { 0 } }$ is assumed to be equal to the user-defined detonation energy $E _ { 0 }$ .
|
||
|
||
If you specify a nonzero value of $K _ { p d } .$ you can also define an initial stress state for the explosive materials.
|
||
|
||
<!-- source-page: 583 -->
|
||
|
||
Input File Usage: Use the following option to define the initial stress:
|
||
|
||
\*INITIAL CONDITIONS, TYPE=STRESS
|
||
|
||
Optionally, you can also define the initial specific energy directly:
|
||
|
||
\*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY
|
||
|
||
Abaqus/CAE Usage: Load module: Create Predefined Field: Step: Initial: choose Mechanical for the Category and Stress for the Types for Selected Step
|
||
|
||
Initial specific energy is not supported in Abaqus/CAE.
|
||
|
||
# Ignition and growth equation of state
|
||
|
||
The ignition and growth equation of state models shock initiation and detonation wave propagation of solid high explosives. The heterogeneous explosive is modeled as a homogeneous mixture of two phases: the unreacted solid explosive and the reacted gas products. Separate JWL equations of state are prescribed for each phase:
|
||
|
||
$$
|
||
p _ {s} = \tilde {F} _ {1 s} (\rho_ {s}) - \tilde {F} _ {1 s} (\rho_ {0}) + \tilde {F} _ {2 s} (\rho_ {s}) E _ {m s},
|
||
$$
|
||
|
||
$$
|
||
p _ {g} = \tilde {F} _ {1 g} (\rho_ {g}) + \tilde {F} _ {2 g} (\rho_ {g}) \left(E _ {m g} + E _ {d}\right),
|
||
$$
|
||
|
||
where
|
||
|
||
$$
|
||
\tilde {F} _ {1 i} (\rho_ {i}) = A _ {i} \left(1 - \frac {\omega_ {i} \rho_ {i}}{R _ {1 i} \rho_ {0}}\right) \exp \left(- R _ {1 i} \frac {\rho_ {0}}{\rho_ {i}}\right) + B _ {i} \left(1 - \frac {\omega_ {i} \rho_ {i}}{R _ {2 i} \rho_ {0}}\right) \exp \left(- R _ {2 i} \frac {\rho_ {0}}{\rho_ {i}}\right)
|
||
$$
|
||
|
||
and
|
||
|
||
$$
|
||
\tilde {F} _ {2 i} (\rho_ {i}) = \omega_ {i} \rho_ {i}, (i = s, g).
|
||
$$
|
||
|
||
The subscript s refers to the unreacted solid explosive, and g refers to the reacted gas products. $A _ { i } , B _ { i } , R _ { 1 i } , R _ { 2 i }$ and $\omega _ { i }$ are user-defined material constants used in the JWL equations; $E _ { d }$ is the detonation energy; $\rho _ { 0 }$ is the user-defined reference density of the explosive, and $\rho _ { i }$ is the density of the unreacted explosive or the reacted products.
|
||
|
||
Input File Usage: Use both of the following options:
|
||
|
||
\*DENSITY(to specify the density of the explosive $\rho _ { 0 } )$
|
||
\*EOS, TYPE=IGNITION AND GROWTH, DETONATION ENERGY=
|
||
(to specify the material constants $A , B , R _ { 1 } , R _ { 2 }$ and
|
||
of the unreacted solid explosive and the reacted gas product)
|
||
|
||
<!-- source-page: 584 -->
|
||
|
||
Abaqus/CAE Usage: Property module: material editor:
|
||
|
||
General→Density (to specify the density of the explosive )
|
||
|
||
Mechanical→Eos: Type: Ignition and growth: Detonation energy: $E _ { d } ;$
|
||
|
||
Solid Phase tabbed page and Gas Phase tabbed page
|
||
|
||
(to specify the material constants and
|
||
|
||
of the unreacted solid explosive and the reacted gas product)
|
||
|
||
# The mass fraction
|
||
|
||
The mixture of unreacted solid explosive and reacted gas products is defined by the mass fraction
|
||
|
||
$$
|
||
F _ {i} = \frac {m _ {i}}{(m _ {s} + m _ {g})},
|
||
$$
|
||
|
||
where $m _ { s }$ is the mass of the unreacted explosive, and $m _ { g }$ is the mass of the reacted products. It is assumed that the two phases are in thermomechanical equilibrium:
|
||
|
||
$$
|
||
p _ {s} = p _ {g} \quad \mathrm{and} \quad T _ {s} = T _ {g}.
|
||
$$
|
||
|
||
It is also assumed that the volumes are additive:
|
||
|
||
$$
|
||
V = V _ {s} + V _ {g} \quad \mathrm{or} \quad \frac {1}{\rho} = (1 - F) \frac {1}{\rho_ {s}} + F \frac {1}{\rho_ {g}}.
|
||
$$
|
||
|
||
Similarly, the internal energy is assumed to be additive:
|
||
|
||
$$
|
||
\left(m _ {s} + m _ {g}\right) E _ {m} = m _ {s} E _ {m s} + m _ {g} E _ {m g},
|
||
$$
|
||
|
||
where
|
||
|
||
$$
|
||
E _ {m} = E _ {m _ {0}} + \int_ {\theta_ {0} - \theta^ {Z}} ^ {\theta - \theta^ {Z}} c _ {v} (T) d T.
|
||
$$
|
||
|
||
Hence, the specific heat of the mixture is given by
|
||
|
||
$$
|
||
c _ {v} = (1 - F) c _ {v s} + F c _ {v g}.
|
||
$$
|
||
|
||
Input File Usage: Use the following options to define the specific heat of the unreacted solid explosive:
|
||
|
||
\*EOS, TYPE=IGNITION AND GROWTH
|
||
\*SPECIFIC HEAT, DEPENDENCIES=n
|
||
|
||
Use the following options to define the specific heat of the reacted gas product:
|
||
|
||
\*EOS, TYPE=IGNITION AND GROWTH
|
||
|
||
\*GAS SPECIFIC HEAT, DEPENDENCIES=n
|
||
|
||
<!-- source-page: 585 -->
|
||
|
||
Abaqus/CAE Usage: Use the following options to define the specific heat of the unreacted solid explosive:
|
||
|
||
Property module: material editor:
|
||
|
||
Mechanical→Eos: Type: Ignition and GrowthThermal→Specific Heat
|
||
|
||
Use the following options to define the specific heat of the reacted gas product:
|
||
|
||
Property module: material editor:
|
||
|
||
Mechanical→Eos: Type: Ignition and growth:
|
||
|
||
Gas Specific tabbed page: Specific Heat
|
||
|
||
You can toggle on Use temperature-dependent data to define the specific heat as a function of temperature and/or select the Number of field variables to define the specific heat as a function of field variables.
|
||
|
||
# The reaction rate
|
||
|
||
The conversion of unreacted solid explosive to reacted gas products is governed by the reaction rate. The reaction rate equation in the ignition and growth model is a pressure-driven rule, which includes three terms:
|
||
|
||
$$
|
||
\frac {d F}{d t} = \dot {F} _ {i g} + \dot {F} _ {G _ {1}} + \dot {F} _ {G _ {2}}.
|
||
$$
|
||
|
||
These three terms are defined as follows:
|
||
|
||
$$
|
||
\dot {F} _ {i g} = I (1 - F) ^ {b} \left(\frac {\rho_ {s}}{\rho_ {0}} - 1 - a\right) ^ {x},
|
||
$$
|
||
|
||
$$
|
||
\dot {F} _ {G _ {1}} = G _ {1} (1 - F) ^ {c} F ^ {d} p ^ {y},
|
||
$$
|
||
|
||
$$
|
||
\dot {F} _ {G _ {2}} = G _ {2} (1 - F) ^ {e} F ^ {g} p ^ {z},
|
||
$$
|
||
|
||
where $I , G _ { 1 } , G _ { 2 } , a , b , c , d , e , g , x , y ,$ , and z are reaction rate constants.
|
||
|
||
The first term, $\dot { F } _ { i g }$ , describes hot spot ignition by igniting some of the material relatively quickly but limiting it to a small proportion of the total solid $F _ { i g } ^ { m a x }$ . The second term, $\dot { F } _ { G _ { 1 } }$ , represents the growth of reaction from the hot spot sites into the material and describes the inward and outward grain burning phenomena; this term is limited to a proportion of the total solid $F _ { G _ { 1 } } ^ { m a x }$ . The third term, $\dot { F } _ { G _ { 2 } }$ , is used to describe the rapid transition to detonation observed in some energetic materials.
|
||
|
||
$$
|
||
\dot {F} _ {i g} = 0 \text {if} F \geq F _ {i g} ^ {m a x}
|
||
$$
|
||
|
||
$$
|
||
\dot {F} _ {G _ {1}} = 0 \text {if} F \geq F _ {G _ {1}} ^ {m a x}
|
||
$$
|
||
|
||
$$
|
||
\dot {F} _ {G _ {2}} = 0 \mathrm{if} F \leq F _ {G _ {2}} ^ {m i n}
|
||
$$
|
||
|
||
Input File Usage: Use both of the following options to define the reaction rate:
|
||
|
||
\*EOS, TYPE=IGNITION AND GROWTH
|
||
|
||
\*REACTION RATE
|
||
|
||
<!-- source-page: 586 -->
|
||
|
||
Abaqus/CAE Usage: Property module: material editor:
|
||
|
||
Mechanical→Eos: Type: Ignition and growth:
|
||
|
||
Reaction Rate tabbed page
|
||
|
||
# Initial state
|
||
|
||
The initial mass fraction of the unreacted solid explosive is assumed to be one. The initial relative density $( \rho / \rho _ { 0 } )$ used in the ignition and growth equation is assumed to be unity. The initial specific energy can be defined for the unreacted explosive.
|
||
|
||
Input File Usage: Use the following option to define the initial specific energy:
|
||
|
||
\*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY
|
||
|
||
Abaqus/CAE Usage: Initial specific energy is not supported in Abaqus/CAE.
|
||
|
||
# Ideal gas equation of state
|
||
|
||
An ideal gas equation of state can be written in the form of
|
||
|
||
$$
|
||
p + p _ {A} = \rho R \left(\theta - \theta^ {Z}\right),
|
||
$$
|
||
|
||
where $p _ { A }$ is the ambient pressure, R is the gas constant, is the current temperature, and $\theta ^ { Z }$ is the absolute zero on the temperature scale being used. It is an idealization to real gas behavior and can be used to model any gases approximately under appropriate conditions (e.g., low pressure and high temperature).
|
||
|
||
One of the important features of an ideal gas is that its specific energy depends only upon its temperature; therefore, the specific energy can be integrated numerically as
|
||
|
||
$$
|
||
E _ {m} = E _ {m _ {0}} + \int_ {\theta_ {0} - \theta^ {Z}} ^ {\theta - \theta^ {Z}} c _ {v} (T) d T,
|
||
$$
|
||
|
||
where $E _ { m _ { 0 } }$ is the initial specific energy at the initial temperature $\theta _ { 0 }$ and $c _ { v }$ is the specific heat at constant volume (or the constant volume heat capacity), which depends only upon temperature for an ideal gas.
|
||
|
||
Modeling with an ideal gas equation of state is typically performed adiabatically; the temperature increase is calculated directly at the material integration points according to the adiabatic thermal energy increase caused by the work , where v is the specific volume (the volume per unit mass, $v = 1 / \rho )$ . Therefore, unless a fully coupled temperature-displacement analysis is performed, an adiabatic condition is always assumed in Abaqus/Explicit.
|
||
|
||
When performing a fully coupled temperature-displacement analysis, the pressure stress and specific energy are updated based on the evolving temperature field. The energy increase due to the change in state will be accounted for in the heat equation and will be subject to heat conduction.
|
||
|
||
For the ideal gas model in Abaqus/Explicit you define the gas constant, R, and the ambient pressure, $p _ { A }$ . For an ideal gas R can be determined from the universal gas constant, ${ \tilde { R } } ,$ , and the molecular weight, , as follows:
|
||
|
||
<!-- source-page: 587 -->
|
||
|
||
$$
|
||
R = \frac {\tilde {R}}{M W}.
|
||
$$
|
||
|
||
In general, the value R for any gas can be estimated by plotting $p v / ( \theta - \theta ^ { Z } )$ as a function of state (e.g., pressure or temperature). The ideal gas approximation is adequate in any region where this value is constant. You must specify the specific heat at constant volume, $c _ { v }$ . For an ideal gas $c _ { v }$ is related to the specific heat at constant pressure, $c _ { p } ,$ b y
|
||
|
||
$$
|
||
R = c _ {p} - c _ {v}.
|
||
$$
|
||
|
||
Input File Usage: Use both of the following options:
|
||
|
||
\*EOS, TYPE=IDEAL GAS
|
||
|
||
\*SPECIFIC HEAT, DEPENDENCIES=n
|
||
|
||
Abaqus/CAE Usage: Property module: material editor:
|
||
|
||
Mechanical→Eos: Type: Ideal Gas
|
||
|
||
Thermal→Specific Heat
|
||
|
||
# Initial state
|
||
|
||
There are different methods to define the initial state of the gas. You can specify the initial density, $\rho ,$ and either the initial pressure stress, $p _ { 0 }$ , or the initial temperature, $\theta _ { 0 }$ . The initial value of the unspecified field (temperature or pressure) is determined from the equation of state. Alternatively, you can specify both the initial pressure stress and the initial temperature. In this case the user-specified initial density is replaced by that derived from the equation of state in terms of initial pressure and temperature.
|
||
|
||
By default, Abaqus/Explicit automatically computes the initial specific energy, $E _ { m _ { 0 } }$ , from the initial temperature by numerically integrating the equation
|
||
|
||
$$
|
||
E _ {m _ {0}} = \int_ {0} ^ {\theta_ {0} - \theta^ {Z}} c _ {v} (T) d T.
|
||
$$
|
||
|
||
Optionally, you can override this default behavior by defining the initial specific energy for the ideal gas directly.
|
||
|
||
Input File Usage: Use some or all of the following options, as required:
|
||
|
||
\*DENSITY, DEPENDENCIES=n
|
||
|
||
\*INITIAL CONDITIONS, TYPE=STRESS
|
||
|
||
\*INITIAL CONDITIONS, TYPE=TEMPERATURE
|
||
|
||
Use the following option to specify the initial specific energy directly:
|
||
|
||
\*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY
|
||
|
||
Abaqus/CAE Usage: Property module: material editor: General→Density
|
||
|
||
Load module: Create Predefined Field: Step: Initial: choose Other for the Category and Temperature for the Types for Selected Step
|
||
|
||
<!-- source-page: 588 -->
|
||
|
||
Load module: Create Predefined Field: Step: Initial: choose Mechanical for the Category and Stress for the Types for Selected Step
|
||
|
||
Initial specific energy is not supported in Abaqus/CAE.
|
||
|
||
# The value of absolute zero
|
||
|
||
When a non-absolute temperature scale is used, you must specify the value of absolute zero temperature.
|
||
|
||
Input File Usage: \*PHYSICAL CONSTANTS, ABSOLUTE ZERO=
|
||
|
||
Abaqus/CAE Usage: Any module: Model→Edit Attributes→model\_name:
|
||
|
||
Absolute zero temperature
|
||
|
||
# A special case
|
||
|
||
In the case of an adiabatic analysis with constant specific heat (both $c _ { v }$ and $c _ { p }$ are constant), the specific energy is linear in temperature
|
||
|
||
$$
|
||
E _ {m} = c _ {v} \left(\theta - \theta^ {Z}\right).
|
||
$$
|
||
|
||
The pressure stress can, therefore, be recast in the common form of
|
||
|
||
$$
|
||
p + p _ {A} = (\gamma - 1) \rho E _ {m},
|
||
$$
|
||
|
||
where $\gamma = c _ { p } / c _ { v }$ is the ratio of specific heats and can be defined as
|
||
|
||
$$
|
||
\gamma = \frac {n + 2}{n},
|
||
$$
|
||
|
||
where
|
||
|
||
n=3 for a monatomic;
|
||
|
||
n=5 for a diatomic; and
|
||
|
||
n=6 for a polyatomic gas.
|
||
|
||
# Comparison with the hydrostatic fluid model
|
||
|
||
The ideal gas equation of state can be used to model wave propagation effects and the dynamics of a spatially varying state of a gaseous region. For cases in which the inertial effects of the gas are not important and the state of the gas can be assumed to be uniform throughout a region, the hydrostatic fluid model (“Surface-based fluid cavities: overview,” Section 11.5.1) is a simpler, more computationally efficient alternative.
|
||
|
||
# Deviatoric behavior
|
||
|
||
The equation of state defines only the material’s hydrostatic behavior. It can be used by itself, in which case the material has only volumetric strength (the material is assumed to have no shear strength). Alternatively, Abaqus/Explicit allows you to define deviatoric behavior, assuming that the deviatoric
|
||
|
||
<!-- source-page: 589 -->
|
||
|
||
and volumetric responses are uncoupled. Two models are available for the deviatoric response: a linear isotropic elastic model and a viscous model. The material’s volumetric response is governed then by the equation of state model, while its deviatoric response is governed by either the linear isotropic elastic model or the viscous fluid model.
|
||
|
||
# Elastic shear behavior
|
||
|
||
For the elastic shear behavior the deviatoric stress is related to the deviatoric strain as
|
||
|
||
$$
|
||
\mathbf {S} = 2 \mu \mathbf {e} ^ {e l},
|
||
$$
|
||
|
||
where is the deviatoric stress and $\mathbf { e } ^ { e l }$ is the deviatoric elastic strain. See “Defining isotropic shear elasticity for equations of state in Abaqus/Explicit” in “Linear elastic behavior,” Section 22.2.1, for more details.
|
||
|
||
Input File Usage: Use both of the following options to define elastic shear behavior:
|
||
|
||
\*EOS
|
||
|
||
\*ELASTIC, TYPE=SHEAR
|
||
|
||
Abaqus/CAE Usage: Property module: material editor: Mechanical→Elasticity→Elastic; Type: Shear; Shear Modulus
|
||
|
||
# Viscous shear behavior
|
||
|
||
For the viscous shear behavior the deviatoric stress is related to the deviatoric strain rate as
|
||
|
||
$$
|
||
\mathbf {S} = 2 \eta \dot {\mathbf {e}} = \eta \dot {\boldsymbol {\gamma}},
|
||
$$
|
||
|
||
where is the deviatoric stress, is the deviatoric part of the strain rate, is the viscosity, and is the engineering shear strain rate.
|
||
|
||
Abaqus/Explicit provides a wide range of viscosity models to describe both Newtonian and non-Newtonian fluids. These are described in “Viscosity,” Section 26.1.4.
|
||
|
||
Input File Usage: Use both of the following options to define viscous shear behavior:
|
||
|
||
\*EOS
|
||
|
||
\*VISCOSITY
|
||
|
||
Abaqus/CAE Usage: Property module: material editor: Mechanical→Viscosity
|
||
|
||
# Use with the Mises or the Johnson-Cook plasticity models
|
||
|
||
An equation of state model can be used with the Mises (“Classical metal plasticity,” Section 23.2.1) or the Johnson-Cook (“Johnson-Cook plasticity,” Section 23.2.7) plasticity models to model elastic-plastic behavior. In this case you must define the elastic part of the shear behavior. The material’s volumetric response is governed by the equation of state model, while the deviatoric response is governed by the linear elastic shear and the plasticity model.
|
||
|
||
<!-- source-page: 590 -->
|
||
|
||
Input File Usage: Use the following options:
|
||
|
||
\*EOS
|
||
|
||
\*ELASTIC, TYPE=SHEAR
|
||
|
||
\*PLASTIC
|
||
|
||
Abaqus/CAE Usage: Property module: material editor:
|
||
|
||
Mechanical→Elasticity→Elastic; Type: Shear
|
||
|
||
Mechanical→Plasticity→Plastic
|
||
|
||
# Initial conditions
|
||
|
||
You can specify initial conditions for the equivalent plastic strain, $\bar { \varepsilon } ^ { p l }$ (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1).
|
||
|
||
Input File Usage: \*INITIAL CONDITIONS, TYPE=HARDENING
|
||
|
||
Abaqus/CAE Usage: Load module: Create Predefined Field: Step: Initial, choose Mechanical for the Category and Hardening for the Types for Selected Step
|
||
|
||
# Use with the extended Drucker-Prager plasticity models
|
||
|
||
An equation of state model can be used in conjunction with the extended Drucker-Prager (“Extended Drucker-Prager models,” Section 23.3.1) plasticity models to model pressure-dependent plasticity behavior. This approach can be appropriate for modeling the response of ceramics and other brittle materials under high velocity impact conditions. In this case you must define the elastic part of the shear behavior. The material’s deviatoric response is governed by the linear elastic shear and the pressure-dependent plasticity model, while the volumetric response is governed by the equation of state model. In particular, no plastic dilation effects are taken into account (if you specify a dilation angle other than zero, the value is ignored and Abaqus/Explicit issues a warning message).
|
||
|
||
“High-velocity impact of a ceramic target,” Section 2.1.18 of the Abaqus Example Problems Guide illustrates the use of an equation of state model with the extended Drucker-Prager plasticity models.
|
||
|
||
Input File Usage: Use the following options:
|
||
|
||
\*EOS
|
||
|
||
\*ELASTIC, TYPE=SHEAR
|
||
|
||
\*DRUCKER PRAGER
|
||
|
||
\*DRUCKER PRAGER HARDENING
|
||
|
||
Abaqus/CAE Usage: Property module: material editor:
|
||
|
||
Mechanical→Elasticity→Elastic; Type: Shear
|
||
|
||
Mechanical→Plasticity→Drucker Prager: Suboptions→Drucker
|
||
|
||
Prager Hardening
|
||
|
||
# Initial conditions
|
||
|
||
You can specify initial conditions for the equivalent plastic strain, $\bar { \varepsilon } ^ { p l }$ (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1).
|