Table 1:
Maxwell viscoelastic medium.
Model Constitutive equation
(
𝜕
𝑡
/
𝐸
+
1
/
𝜂
)
𝐹
=
(
𝜕
𝑡
)
𝑢
; the differential operator
𝜕
𝑡
≡
𝜕
/
𝜕
𝑡
Viscoelastic Operator Corresponds to the Modulus of Elasticity
𝐸
1
𝐸
→
1
𝐸
𝜕
𝑡
+
1
/
𝜏
𝜕
𝑡
The modified Creep Model
𝑢
(
𝑡
)
ℎ
0
=
𝑏
𝜒
𝐸
𝑃
0
𝐿
0
1
/
(
𝜒
+
1
)
𝑒
−
𝑡
/
𝜏
×
1
𝐹
1
2
+
𝜒
𝑡
1
+
𝜒
;
1
;
𝜏
,
1
𝐹
1
[
2
+
𝜒
/
1
+
𝜒
;
1
;
𝑡
/
𝜏
]
is the confluent
hypergeometric function (called Kummer’s equation) written as:
1
𝐹
1
𝑐
[
𝑐
;
𝑑
;
𝑥
]
=
1
+
𝑑
𝑥
+
𝑐
(
𝑐
+
1
)
𝑥
2
+
𝑑
(
𝑑
+
1
)
2
!
𝑐
(
𝑐
+
1
)
(
𝑐
+
2
)
𝑥
3
𝑑
(
𝑑
+
1
)
(
𝑑
+
2
)
3
!
+
⋯
, or
1
𝐹
1
∑
[
𝑐
;
𝑑
;
𝑥
]
=
∞
𝑛
=
0
(
𝑐
)
𝑛
(
𝑑
)
𝑛
𝑥
𝑛
𝑛
!