1.10.2 Line spring elements

Product: ABAQUS/Standard

I. LS3S with constant-depth notch under far-field bending

Problem description

*ELEMENT, TYPE=LS3S, ELSET=ALL
1, 2, 5, 1
*SURFACE FLAW, SIDE=POSITIVE
1, .05
5, .05
2, .05
*SHELL SECTION, MAT=M1, ELSET=ALL
.1,

Material:

Linear elastic, Young's modulus = 1.0, Poisson's ratio = 0.0.

Boundary conditions:

0 at nodes 1, 2, and 5.

Loading:

M –1.0 at nodes 1 and 2. M –4.0 at node 5.

Results and discussion

Element	Pt.	J	K	J_elastic
1	1	4.43 × 10⁶	2105.0	4.43 × 10⁶
1	2	4.43 × 10⁶	2105.0	4.43 × 10⁶
1	3	4.43 × 10⁶	2105.0	4.43 × 10⁶

Input file

exls3bx2.inp

Single-edge constant-depth notch strip under far-field bending.

II. LS3S with variable depth notch under far-field bending

Problem description

*ELEMENT, TYPE=LS3S, ELSET=ALL
1, 2, 5, 1
*SURFACE FLAW, SIDE=POSITIVE
1, .07
5, .05
2, .04
*SHELL SECTION, MAT=M1, ELSET=ALL, NODAL THICKNESS
99,
*NODAL THICKNESS
1, 0.7
5, 0.5
2, 0.4
3, 0.1
4, 0.1
6, 0.1
7, 0.1
8, 0.1

Material:

Linear elastic, Young's modulus = 1.0, Poisson's ratio = 0.0.

Boundary conditions:

0 at nodes 1, 2, and 5.

Loading:

M –1.0 at nodes 1 and 2. M –4.0 at node 5.

Results and discussion

Element	Pt.	J	K	J_elastic
1	1	6891.0	83.012	6891.0
1	2	3528.5	59.401	3528.5
1	3	1286.2	35.864	1286.2

Input file

exls3vx2.inp

Single-edge variable-depth notch strip under far-field bending.

III. LS6 under far-field bending

Problem description

*ELEMENT, TYPE=LS6, ELSET=ALL
1, 2, 5, 1, 12, 15, 11
*SURFACE FLAW, SIDE=POSITIVE
1, .05
5, .05
2, .05
*SHELL SECTION, MAT=M1, ELSET=ALL
.1,

Material:

Linear elastic, Young's modulus = 1.0, Poisson's ratio = 0.0.

Boundary conditions:

Node 17 is fully constrained. 0 for all nodes. Nodes 1, 2, and 5 are constrained to move together. Nodes 11, 12, and 15 are constrained to move together.

Loading:

M –6.0 at node 5. M 6.0 at node 15.

Results and discussion

Element	Pt.	J	J_elastic	K_I
1	1	4.43 × 10⁶	4.43 × 10⁶	2105.0
1	2	4.43 × 10⁶	4.43 × 10⁶	2105.0
1	3	4.43 × 10⁶	4.43 × 10⁶	2105.0

Input file

exls6bx2.inp

Single-edge notch strip under far-field bending about an axis (along the crack-tip line).

IV. LS3S under far-field tension

Problem description

*ELEMENT, TYPE=LS3S, ELSET=ALL
1, 2, 5, 1
*SURFACE FLAW, SIDE=POSITIVE
1, .05
5, .05
2, .05
*SHELL SECTION, MAT=M1, ELSET=ALL
.1,

Material:

Linear elastic, Young's modulus = 1.0, Poisson's ratio = 0.0.

Boundary conditions:

0 at nodes 1, 2, and 5.

Loading:

F 1.0 at nodes 3 and 4. F 4.0 at node 7.

Results and discussion

Element	Pt.	J	K	J_elastic
1	1	4518.0	67.22	4518.0
1	2	4518.0	67.22	4518.0
1	3	4518.0	67.22	4518.0

Input file

exls3tx2.inp

Single-edge notch strip under far-field tension.

V. LS6 under Mode I, II, and III loading

Problem description

*ELEMENT, TYPE=LS6, ELSET=ALL
1, 2, 5, 1, 12, 15, 11
*SURFACE FLAW, SIDE=POSITIVE
1, .05
5, .05
2, .05
*SHELL SECTION, MAT=M1, ELSET=ALL
.1,

Material:

Linear elastic, Young's modulus = 1.0, Poisson's ratio = 0.0.

Boundary conditions:

Node 17 is fully constrained. 0 for all nodes. Nodes 1, 2, and 5 are constrained to move together. Nodes 11, 12, and 15 are constrained to move together.

Loading:

1.0 at node 5. –1.0 at node 15.

Results and discussion

Element	Pt.	J	J_elastic	K_I	K_II	K_III
1	1	170.10	170.10	11.20	4.962	–4.472
1	2	170.10	170.10	11.20	4.962	–4.472
1	3	170.10	170.10	11.20	4.962	–4.472

Input file

exls6sx2.inp

Single-edge notch strip under far-field tension (Mode I), in-plane shear (Mode II), and uniform out-of-plane shear (Mode III).