*MAT_240 (COHESIVE_MIXED_MODE_ELASTOPLASTIC_RATE)

LS-DYNA Input Interface KeywordDefines a perfectly plastic cohesive material with state dependency, normal and shear damage, and normal and shear failure.

Format


(1)	(2)	(3)	(4)	(5)	(6)	(7)
MAT_240 or MAT_COHESIVE_MIXED_MODE_ELASTOPLASTIC_RATE
`mat_ID`	$ρ_{i}$			`En`	`Gs`	`Thick`
`En_0`	`En_1`	`En_rate`	$σ$ `n_0`	$σ$ `n_1`	`N_rate`	`Form_n`
`Es_0`	`Es_1`	`Es_rate`	$σ$ `s_0`	$σ$ `s_1`	`S_rate`	`Form_s`

Definition


Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`En`	Young’s modulus in the normal direction. (Real)	$[\frac{N}{m}]$
`Gs`	Shear modulus in the shear plane. (Real)	$[\frac{N}{m}]$
`Thick`	Reference cohesive thickness. (Real)	$[m]$
`En_0`	Energy for damage and failure in the normal direction. > 0 Energy value (no rate dependency). < 0 Lower energy value. (Real)	$[J]$
`En_1`	Upper energy value for damage and failure in the normal direction (used only if `En_0` < 0). (Real)	$[J]$
`En_rate`	Plastic strain rate factor for damage and failure in the normal direction (used only if `En_0` < 0). (Real)
$σ$ `n_0`	Yield stress in normal direction. > 0 Yield value (no rate dependency). < 0 Yield value for rate dependency. (Real)	$[Pa]$
$σ$ `n_1`	Yield stress factor in the normal direction (used only if < 0). (Real)	$[Pa]$
`N_rate`	Plastic strain rate factor for yield stress in the normal direction (used only if < 0). (Real)
`Form_n`	Tri-linear shape formulation in the normal direction. > 0 Ratio of fracture energy. < 0 Ratio of fracture displacement. (Real)
`Es_0`	Energy for damage and failure in the shear plane. > 0 Energy value (no rate dependency). < 0 Lower energy value. (Real)	$[J]$
`Es_1`	Upper energy value for damage and failure in shear plane (used only if `Es_0` < 0). (Real)	$[J]$
`Es_rate`	Plastic strain rate factor for damage and failure in shear plane (used only if `Es_0` < 0). (Real)
$σ$ `s_0`	Yield stress in the shear plane. > 0 Yield value (no rate dependency). < 0 Yield value for rate dependency. (Real)	$[Pa]$
$σ$ `s_1`	Yield stress factor in the shear plane (used only if < 0). (Real)	$[Pa]$
`S_rate`	Plastic strain rate factor for yield stress in the shear plane (used only if < 0). (Real)
`Form_s`	Tri-linear shape formulation in the shear plane. > 0 Ratio of fracture energy. < 0 Ratio of fracture displacement. (Real)

Comments

This keyword maps to /MAT/LAW116 and /PROP/TYPE43 (CONNECT).
Yield stress when rate dependency is defined with:
- If $σ n_1$ > 0: $σ n = |σ n_0| + |σ n_1| * \max {(0, \ln (\frac{\dot{ε}}{N_r a t e}))}^{2}$
- If $σ n_1$ < 0: $σ n = |σ n_0| + |σ n_1| * \max (0, \ln (\frac{\dot{ε}}{N_r a t e}))$
- If $σ s_1$ > 0: $σ s = |σ s_0| + |σ s_1| * \max {(0, \ln (\frac{\dot{ε}}{S_r a t e}))}^{2}$
- If $σ s_1$ < 0: $σ s = |σ s_0| + |σ s_1| * \max (0, \ln (\frac{\dot{ε}}{S_r a t e}))$
Energy for damage and failure dependency is defined with:
- $E n = |E n_0| + (E n_1 - E n_0) * \exp (\frac{- E n_r a t e}{\dot{ε}})$
- $E s = |E s_0| + (E s_1 - E s_0) * \exp (\frac{- E s_r a t e}{\dot{ε}})$
The tri-linear fracture model is defined with:
Figure 1.
- If Form > 0,
  - $|F o r m_n| = \frac{E p_n}{E t_n}$ with $E t_n$ = total energy, $E P_n$ = perfect plastic energy in normal direction
  - $|F o r m_s| = \frac{E p_s}{E t_s}$ with $E t_s$ = total energy, $E P_s$ = perfect plastic energy in shear plane
- If Form < 0,
  - $|F o r m_n| = \frac{(δ n 2 - δ n 1)}{(δ n f - δ n 1)}$ with $δ n i$ = displacement in normal direction
  - $|F o r m_s| = \frac{(δ s 2 - δ s 1)}{(δ s f - δ s 1)}$ with $δ n i$ = displacement in shear plane
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