Peridigm Users Guide

User Manual:

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≥
a
c
h
s
t
∆t
u
v
x x
y y
z z
A
E
F
G
G0C
GI
GIC
GII
GIIC
K
V
δ
ε
γ
ν
ωξ
ρ
σ
τ
ξx x x0
( )C
( )H
( )I
( )II
( )
∆( )
X
X X
X X
X X
X X X
X X
m3
a α R
aαR3
ARn×m
AAijk Aijkl
>
a
A
A
[kg] [g] [t] [slug] [lbf][s]2
[in]
[m] [cm] [mm] [ft] [in]
[s] [s] [s] [s] [s]
[K] [K] [K] [◦R] [◦R]
[m]
[s]
[cm]
[s]
[mm]
[s]
[ft]
[s]
[in]
[s]
[m]
[s]2
[cm]
[s]2
[mm]
[s]2
[ft]
[s]2
[in]
[s]2
[N] [dyn] [N] [lbf] [lbf]
[N] [m] [dyn] [cm] [N] [mm] [lbf] [ft] [lbf] [in]
[Pa] [Ba] [MPa] [lbf] /[ft]2[psi]
[kg]
[m]3
[g]
[cm]3
[t]
[mm]3
[slug]
[ft]3
[lbf][s]2/[in]
[in]3
[J] [erg] [mJ] [ft] [lbf] [in] [lbf]
[J]
[m]2=[N]
[m]
[erg]
[cm]2
[mJ]
[mm]2=[N]
[mm]
ν=(1
4
1
3
K3D=E
3 (1 −2ν)
K2D=
E
2 (1 −ν)
E
2 (1 −ν−2ν2)
K1D=E
G=E
2 (1 + ν)
c=18K
πδ4=30G
πδ4
c=12K
πhδ3=G
πhδ3·(20
24
c=2K
Aδ2
sC=r5G0C
9K3Dδ=r10G0C
πc3Dδ5
sC=rπG0C
3K2Dδ=r4G0C
c2Dhδ4
sC=r3G0C
K1Dδ=r6G0C
c1DAδ3
sC=v
u
u
tG0C
h3G+3
44K−5G
3iδ
sC=sG0C
6
πG+16
9π2(K−2G)δ
sC=
K G
K G
+
+
−
−
∗
/
ˆ
==
>
<
>=
<=
=
||
&&
! =
%
!
x−min x, y
q(x1−x2)2+ (y1−y2)2
(1.0−erf(x))
ex
Γ(x)
px2+y2
log (Γ(x))
log(1 + x)
r·cos(a)a
r·sin(a)a
α=a
β=b
x·sign(y)
x1ˆ
i+y1ˆ
j x2ˆ
i+y2ˆ
j
x1ˆ
i+y1ˆ
j
x
y
z
1.0
→ →
X
X
X
Xx
Xy
Xz
Xx
Xy
Xz
Xx
Xy
Xz
X
X
Xx
Xy
Xz
Xx
Xy
Xz
X
kξkδ
0 0.5 1
0
0.5
1
kξ||
δ
ωξ(ξ)
0 0.5 1
0
0.5
1
kξ||
δ
ωξ(ξ)
0 0.5 1
0
0.5
1
kξ||
δ
ωξ(ξ)
ωξ(ξ) = e−kξk
δ2
ωξ(ξ) = e−kξk
0.4·δ2
≡
K
ε
σ
G
γ
τ
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
K
ε
σ
G
γ
τ
X
X
X
K
1
4
G=3K(1 −2ν)
2·(1 + ν)
K
ε
σ
G
γ
τ
X
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
0.0 0.05
K
ε
σ
G
γ
τ
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
K
ε
σ
G
γ
τ
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
K
ε
σ
G
γ
τ
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
K
ε
σ
G
γ
τ
X
X
X
K G
K
KH= 0
σ
ε
σ
G
GH= 0
τσ
γ
τ
X
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
K
KH= 0
σ
ε
σ
G
GH= 0
τσ
γ
τ
X
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)
K G
0.0 0.05
K
KH
σ
ε
σ
G
GH
τσ
γ
τ
X
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)GH=EH
2·(1 + ν)
K G
K
KH
σ
ε
σ
G
GH
τσ
γ
τ
X
X
X
X
X
X
X
X
K G E ν G
G=E
2·(1 + ν)GH=EH
2·(1 + ν)
K G
0.0 0.05
A
A
X
X
X
X
0.0≤λi≤1.0
sC
G0C
sC=r10G0C
πcδ5=r5G0C
9Kδ
K δ c
sC=v
u
u
tG0C
h3G+3
44K−5G
3iδ
sC
c
s
f
X
>0.0X
δ
X
X
δ
X
>0.0X
δ
X
>0.0X
G0C
X
X
>0.0X
GIC
>0.0
GIC
>0.0
GIIC
X
δ
GI
GIC 2
+GII
GIIC 2
= 1
G0C=GIC +GIIC
X
X
X
t
v a
u
a(t) = ˙v(t) = ¨u(t)
t= 0 t > 0
X
X
X
X
t= 0 t > 0
X
X
X
X
t= 0 t > 0
X
X
X
t
u
t
v
t
a
X
X
X
X
t
t
u
t
v
t
a
t
u
t
v
t
−a
t
t
u
t
v
t
a
X
X
X
FVF V FV=
F/V
X
X
X
X
X0.0
X0
X
X
X
X
X
0.0
0.0
X
X
X
0.0
0.0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
→
→
X
→
→
X
X
γ
β
γ=1
2β=1
4
γ=1
2β=1
6
→
→
X
X
X
F(x) = 0
F:<n→ <n
→
→
X
→
→
X
X
. . .
∆t=s2ρ
∆t
∆t=f∆x, K, δ−4
. . .
. . .
,
. . .
. . .
≥
≥
→ → → →

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