# Thermal Stress — Welcome to LS-DYNA Examples

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This problem demonstrates using LS-DYNA to solve for the unconstrained expansion of a block due to heating. The model consists of one 8 node brick element at an initial temperature of 10. The brick material is given a volumetric thermal generation rate. Explicit time integration is used for the structural calculations and implicit time integration is used for the thermal calculations. Implicit time integration is unconditionally stable and, therefore, a larger thermal time step can be taken.

## Keywords

```*CONTROL_SOLUTION
*CONTROL_TERMINATION
*CONTROL_THERMAL_SOLVER
*CONTROL_THERMAL_TIMESTEP
*CONTROL_TIMESTEP
*DATABASE_BINARY_D3PLOT
*DATABASE_GLSTAT
*ELEMENT_SOLID
*END
*INITIAL_TEMPERATURE_NODE
*KEYWORD
*MAT_ELASTIC_PLASTIC_THERMAL
*MAT_THERMAL_ISOTROPIC
*NODE
*PART
*SECTION_SOLID
*TITLE```

## Reduced Input

```  \$ Thermal Expansion of a Block
\$
*KEYWORD
\$
\$=============================CONTROL DEFINITIONS ==============================
\$
*TITLE
thermal expansion of a block
*CONTROL_SOLUTION
2
*CONTROL_THERMAL_SOLVER
1         0         1
*CONTROL_TIMESTEP
.01
*CONTROL_THERMAL_TIMESTEP
0       1.         .1
*CONTROL_TERMINATION
3.
*DATABASE_BINARY_D3PLOT
.01
*database_glstat
.03
\$
\$============================== PART DEFINITIONS ===============================
\$
*PART
\$      PID     SECID       MID                                              TMID
slab
1         1         1                                                 1
\$
\$============================= SECTION PROPERTIES ==============================
\$
*SECTION_SOLID
\$    SECID    ELFORM
1         1
\$
\$====================== MECHANICAL MATERIAL PROPERTIES =========================
\$
*MAT_ELASTIC_PLASTIC_THERMAL
1        1.
0.       10.       20.       30.       40.       50.
1.e+10    1.e+10    1.e+10    1.e+10    1.e+10    1.e+10
.3        .3        .3        .3        .3        .3
0.e-06   20.e-07   40.e-07   60.e-07   80.e-07  100.e-07
1.e+20    1.e+20    1.e+20    1.e+20    1.e+20    1.e+20
0.        0.        0.        0.        0.        0.
\$
\$======================== THERMAL MATERIAL PROPERTIES ==========================
\$
*MAT_THERMAL_ISOTROPIC
1        1.         0       10.
1.        1.
\$
\$============================= NODE DEFINTIONS =================================
\$
*NODE
1              0.              0.              0.       7
2              1.              0.              0.       5
3              1.              1.              0.       3
4              0.              1.              0.       6
5              0.              0.              1.       4
6              1.              0.              1.       2
7              1.              1.              1.       0
8              0.              1.              1.       1
\$
\$============================ ELEMENT DEFINITIONS ==============================
\$
*ELEMENT_SOLID
1       1       1       2       3       4       5       6       7       8
\$
\$============================ ELEMENT DEFINITIONS ==============================
\$
*INITIAL_TEMPERATURE_NODE
1       10.
2       10.
3       10.
4       10.
5       10.
6       10.
7       10.
8       10.
*END```