Element: SED3H2SDFHYH2SNeoHooke

Solid Static - 3D continuum - Hexahedron with 20 nodes - Standard displacement - Hyperelastic

Standard 3D serendipity 20 node element, isoparametric, displacement based (H2S). Strain driven hyperelastic.

AceGen input	SED3H2SDFHYH2SNeoHooke.nb
AceFEM source file	SED3H2SDFHYH2SNeoHookeC.c
AceFEM-MDriver source file	SED3H2SDFHYH2SNeoHookeM.m
FEAP source file	SED3H2SDFHYH2SNeoHookeF.f
ABAQUS source file	SED3H2SDFHYH2SNeoHookeA.for

Input data keywords (default values):
E -elastic modulus (21000.) n -Poisson ratio (0.3)
Postprocessing keywords:
(1) DeformedMeshX (2) DeformedMeshY (3) DeformedMeshZ (4) u (5) v
(6) w (7) Sxx (8) Sxy (9) Sxz (10) Syx
(11) Syy (12) Syz (13) Szx (14) Szy (15) Szz
(16) Exx (17) Exy (18) Exz (19) Eyx (20) Eyy
(21) Eyz (22) Ezx (23) Ezy (24) Ezz (25) Mises stress
(26) Specific strain energy (27) Integration weight

Max. sensitivity order : second order

Shape sensitivity : available

SEssential BC sensitivity : available
General sensitivity parameters:
(1) X -spatial coordinate (2) Y -spatial coordinate (3) Z -spatial coordinate (4) E -elastic modulus (5) n -Poisson ratio

Postprocessing:
• Sij - small stress tensor
• Eij - small strain tensor
Character type element tags:
"Volume and sensitivity" → task that returns total mesh volume with its sensitivity
"Integrated stress and sensitivity (P, 3D)" → task that returns integral of stresses over domain with its sensitivity
"Integrated strain energy and sensitivity (3D)" → task that returns integral of strain energy over domain with its sensitivity
"Reset sensitivity data" → task that deletes nodal data sp and st and sensitivity related part of element data hp and ht.
Author: J. Korelc
Documentation:
Standard displacement formulation , Hexahedron , Standard numerical integration , NeoHooke ,

Topology	H2S
Standard acronym	H2S
Default integration code	8
No. of nodes	20
No. of spatial dimensions	3
No. of global d.o.f	60
No. of internal d.o.f.	0
Efficiency treshold:	50.3472
Convergence test fulfilled :	Inconclusive
Volumetric locking free:	False
Objective:	False
Patch test fulfilled:	True

Benchmark tests

Generic one element test

Group data :

E -elastic modulus	3000
\[Nu] -Poisson ratio	0.2

Results for first d.o.f. in node 2 :

Time	Load	a_2,1	da_2,1/dp_i
1.	1.	-0.03671	{0.00001921, 0.06255, -0.0749}

Detailed results for time : 1.
Main diagonals of the global tangent matrix and residual:

K_i,i	-0.002584	-23.57	58.82	1526.	1396.	1689.	1679.	1441.	1837.	1610.	1693.	1365.	1390.	1420.	1545.	1434.	1609.	1335.	1965.	1738.	2051.	2116.	2138.	2844.	4798.	2640.	3137.	2468.	3009.	2715.	3736.	2369.	2635.	2395.	3257.	2317.	2631.	2477.	4279.	2053.	2114.	3259.	1803.	1503.	2226.	2401.	2425.	4077.	3108.	2106.	2003.	1904.	2294.	1856.	2034.	1787.	2355.	2655.	3729.	3219.
K_i,NDOF-i+1	-105.9	-649.6	-51.3	-30.08	231.8	-45.	143.4	-630.9	108.3	156.6	66.53	142.1	159.5	-451.4	217.6	-64.16	-313.2	-77.38	-150.6	-351.3	-133.6	346.7	-615.9	372.5	2.388	-77.31	-106.3	-15.55	283.4	-113.7	-113.7	283.4	-15.55	-106.3	-77.31	2.388	372.5	-615.9	346.7	-133.6	-351.3	-150.6	-77.38	-313.2	-64.16	217.6	-451.4	159.5	142.1	66.53	156.6	108.3	-630.9	143.4	-45.	231.8	-30.08	-2.436	29.8	6.581 10^-17
R_i	-7.752	-42.4	-8.419	-5.951 10^-14	-45.33	-13.08	6.546	-27.5	-9.78	-15.11	105.	55.	18.95	14.34	-1.19	-6.728	-8.882 10^-15	-3.255	-12.21	25.96	28.76	16.3	-30.07	-48.03	2.59 10^-13	-1.581 10^-13	-1.343 10^-13	1.465 10^-13	1.599 10^-13	-2.105 10^-13	2.198 10^-13	1.283 10^-13	-1.548 10^-13	-1.06 10^-13	2.032 10^-14	-2.254 10^-14	-2.082 10^-13	-2.124 10^-13	1.448 10^-13	1.692 10^-13	-3.73 10^-14	3.135 10^-13	-7.994 10^-15	-4.974 10^-14	1.066 10^-13	-5.906 10^-14	-9.992 10^-15	1.47 10^-13	2.331 10^-13	-4.796 10^-14	2.323 10^-13	-1.954 10^-14	-3.553 10^-15	6.75 10^-14	1.519 10^-13	2.132 10^-14	8.615 10^-14	-7.55 10^-14	-1.052 10^-13	1.128 10^-13

Solution for all d.o.f.:

0.015

-0.12

0.1

-0.03671

0.01

0.02

0.03

0.021

0.3732

0.3881

0.1

0.03

0.09587

0.02

0.11

0.1

0.03

0.02

0.03

0.003805

0.06016

0.08232

-0.003835

0.06581

0.06172

0.0002584

0.1274

0.1494

-0.02374

0.1057

0.14

0.04241

0.06181

0.1037

0.01637

0.05046

0.01207

0.02116

0.1048

0.07395

0.05636

0.07009

0.1469

0.05792

0.04943

0.03797

0.0375

0.07432

0.06297

0.03208

0.08099

0.08321

0.05766

0.07854

0.0851

Error norms (NR):

Finite difference verification of sensitivity analysis (da_2,1/dp_i)

p_i\Time	1.
p₁=E -elastic modulus	0.00001921
p₂=\[Nu] -Poisson ratio	0.06255
p₃=Shape sensitivity	-0.0749

Convergence test: Inconclusive

N_elem	12	40	144	840	3600
a_A	2.0147	2.1889	2.2383	2.2517	2.2573

Corresponding flux element: SES3S2DFFLS2Uniform

Test of the eigenvalues of the global tangent matrix

Geometry: undistorted Material: incompressible Load factor: 1. f_c: 0. f_b: 0.

u_T

-0.00010584

v_T

-0.00036395

u_Tref

-0.00010584

v_Tref

-0.00036395

0.012506

0.031198

0.0427

98.605

98.632

125.92

125.93

125.97

178.14

201.57

201.69

201.83

280.26

280.33

424.7

424.74

424.79

444.37

548.63

548.69

548.74

587.91

588.04

588.19

601.7

601.71

1459.4

1460.1

1460.2

1518.6

1518.7

1518.8

1585.4

1585.8

2236.7

2237.

2237.2

2400.5

2400.6

21934.

21940.

21948.

22495.

22499.

22504.

43387.

111820.

333650.

695940.

695950.

696010.

1.1702 10⁶

1.1703 10⁶

1.1704 10⁶

1.553 10⁶

Geometry: distorted Material: incompressible Load factor: 1. f_c: 0. f_b: 0.

u_T

0.00033023

v_T

-0.00013246

u_Tref

0.00033023

v_Tref

-0.00013246

0.014941

0.034907

0.044774

88.213

140.39

172.21

192.84

221.34

237.88

273.45

287.67

319.6

372.44

400.8

457.

515.05

550.41

555.99

651.39

710.31

812.65

961.99

1132.9

1226.1

1344.

1374.1

1711.3

1745.2

1831.9

1977.1

2228.3

2327.3

3479.7

3664.3

4587.5

5157.7

8774.8

11065.

11716.

22765.

24632.

35466.

38961.

51954.

65325.

83162.

106270.

188790.

209810.

465310.

788610.

859120.

1.0289 10⁶

1.18 10⁶

1.3142 10⁶

1.8029 10⁶

2.1742 10⁶

Geometry: undistorted Material: generic Load factor: 1. f_c: 0. f_b: 0.

u_T

0.000013159

v_T

-0.00024698

u_Tref

0.000013159

v_Tref

-0.00024698

0.0056147

0.017963

0.022599

110.17

110.18

123.16

123.17

147.01

147.02

155.46

155.47

222.24

283.45

283.47

283.49

413.49

433.72

433.76

440.1

440.12

440.17

516.63

685.43

685.45

685.48

751.8

751.85

1027.5

1081.9

1250.

1250.2

1642.1

1945.

1945.1

1981.1

1981.3

2592.5

2592.6

2592.7

3364.4

3364.6

4965.4

4965.7

7168.6

7758.4

7758.6

Geometry: undistorted Material: generic Load factor: 1. f_c: 1.16355 f_b: 0.

u_T

0.00023199

v_T

-0.000085742

u_Tref

0.000013159

v_Tref

-0.00024698

0.0056147

0.017963

0.022599

110.17

110.18

123.16

123.17

147.01

147.02

155.46

155.47

222.24

283.45

283.47

283.49

413.49

433.72

433.76

440.1

440.12

440.17

516.63

685.43

685.45

685.48

751.8

751.85

1027.5

1081.9

1250.

1250.2

1642.1

1945.

1945.1

1981.1

1981.3

2592.5

2592.6

2592.7

3364.4

3364.6

4965.4

4965.7

7168.6

7758.4

7758.6

Geometry: undistorted Material: generic Load factor: 1. f_c: 0. f_b: 0.141372

u_T

-0.14085

v_T

-0.010225

u_Tref

0.000017875

v_Tref

-0.0002539

0.0057982

0.01778

0.022609

110.17

110.18

123.16

123.17

147.01

147.02

155.46

155.47

222.24

283.45

283.47

283.49

413.49

433.72

433.76

440.1

440.12

440.17

516.63

685.43

685.45

685.48

751.8

751.85

1027.5

1081.9

1250.

1250.2

1642.1

1945.

1945.1

1981.1

1981.3

2592.5

2592.6

2592.7

3364.4

3364.6

4965.4

4965.7

7168.6

7758.4

7758.6

Geometry: undistorted Material: generic Load factor: 1. f_c: 4.08407 f_b: 0.0959931

u_T

0.052384

v_T

0.08036

u_Tref

0.000017875

v_Tref

-0.0002539

0.0057982

0.01778

0.022609

110.17

110.18

123.16

123.17

147.01

147.02

155.46

155.47

222.24

283.45

283.47

283.49

413.49

433.72

433.76

440.1

440.12

440.17

516.63

685.43

685.45

685.48

751.8

751.85

1027.5

1081.9

1250.

1250.2

1642.1

1945.

1945.1

1981.1

1981.3

2592.5

2592.6

2592.7

3364.4

3364.6

4965.4

4965.7

7168.6

7758.4

7758.6

Geometry: distorted Material: generic Load factor: 1. f_c: 0. f_b: 0.

u_T

0.00014025

v_T

-0.00018073

u_Tref

0.00014025

v_Tref

-0.00018073

0.0067027

0.014371

0.018547

71.602

95.908

115.29

124.09

143.99

157.31

160.99

172.62

185.48

195.66

213.89

264.45

297.87

315.66

343.71

383.56

406.12

466.59

480.49

520.95

596.33

683.34

721.65

838.14

928.03

1056.7

1112.1

1171.

1193.4

1262.4

1439.3

1532.

1634.5

1660.9

1809.9

1917.

2044.9

2273.3

2491.4

2669.5

2818.2

3360.5

3434.2

3692.8

4179.5

4873.8

4975.8

5900.3

6811.3

7635.9

7966.4

8501.4

10765.

12778.

Geometry: distorted Material: generic Load factor: 1. f_c: 1.16355 f_b: 0.

u_T

0.0002215

v_T

0.000057198

u_Tref

0.00014025

v_Tref

-0.00018073

0.0067027

0.014371

0.018547

71.602

95.908

115.29

124.09

143.99

157.31

160.99

172.62

185.48

195.66

213.89

264.45

297.87

315.66

343.71

383.56

406.12

466.59

480.49

520.95

596.33

683.34

721.65

838.14

928.03

1056.7

1112.1

1171.

1193.4

1262.4

1439.3

1532.

1634.5

1660.9

1809.9

1917.

2044.9

2273.3

2491.4

2669.5

2818.2

3360.5

3434.2

3692.8

4179.5

4873.8

4975.8

5900.3

6811.3

7635.9

7966.4

8501.4

10765.

12778.

Geometry: distorted Material: generic Load factor: 1. f_c: 0. f_b: 0.141372

u_T

-0.14073

v_T

-0.010139

u_Tref

0.00014288

v_Tref

-0.00018451

0.0068629

0.014245

0.018595

71.602

95.909

115.29

124.09

143.99

157.31

160.99

172.62

185.48

195.66

213.89

264.45

297.87

315.66

343.71

383.56

406.12

466.59

480.49

520.95

596.33

683.34

721.65

838.14

928.03

1056.7

1112.1

1171.

1193.4

1262.4

1439.3

1532.

1634.5

1660.9

1809.9

1917.

2044.9

2273.3

2491.4

2669.5

2818.2

3360.5

3434.2

3692.8

4179.5

4873.8

4975.8

5900.3

6811.3

7635.8

7966.4

8501.4

10765.

12778.

Geometry: distorted Material: generic Load factor: 1. f_c: 4.08407 f_b: 0.0959931

u_T

0.052381

v_T

0.080217

u_Tref

0.00014288

v_Tref

-0.00018451

0.0068629

0.014245

0.018595

71.602

95.909

115.29

124.09

143.99

157.31

160.99

172.62

185.48

195.66

213.89

264.45

297.87

315.66

343.71

383.56

406.12

466.59

480.49

520.95

596.33

683.34

721.65

838.14

928.03

1056.7

1112.1

1171.

1193.4

1262.4

1439.3

1532.

1634.5

1660.9

1809.9

1917.

2044.9

2273.3

2491.4

2669.5

2818.2

3360.5

3434.2

3692.8

4179.5

4873.8

4975.8

5900.3

6811.3

7635.8

7966.4

8501.4

10765.

12778.

Patch test : OK

Efficiency test

Floating point operations per element tangent and residual: 883490.
Assembly time (s): 0.203
Linear solution time (s): 0.504
Treshold: 50.347

On-line FEM Library 2 May 2016