These tests verify the modeling of element reinforcements in membrane elements. The rebar option is tested in the areas of kinematics, prestressing of the rebar, compatibility with material property definitions, and compatibility with prescribed temperatures and field variables. All membranes that allow rebar are tested and compared to continuum and shell elements. Each input file contains tests for membrane, continuum, and shell elements.
Kinematics are tested by applying a uniaxial displacement with various rebar orientations. In the first test rebar are placed along the x-axis, and a displacement is prescribed in the x-direction. In the second test rebar are oriented at 30° from the x-axis. Again, a prescribed displacement is applied along the x-axis. In the third test rebar are oriented along the y-axis, and a displacement is prescribed in the x-direction. The fourth test includes large geometry changes. The rebar are initially defined at 30° from the x-axis. A large displacement is prescribed in the x-direction and causes the orientation of the rebar to change because of the large shearing strains. The fifth and sixth tests define various rebar orientations. In the seventh test rebar angle output is measured with respect to the second isoparametric direction.
The material test includes five combinations of material definitions for the base element and the rebar. For each combination a single element is loaded with a prescribed uniaxial displacement. Elastic, elastic-plastic, hyperelastic, and hypoelastic material properties are used. The combinations are as follows: elastic base and elastic rebar, elastic base and elastic-plastic rebar, elastic-plastic base and elastic rebar, hyperelastic base and elastic rebar, and elastic base and hypoelastic rebar.
Thermal expansion of the rebar is tested by constraining all the degrees of freedom of the elements and applying a temperature load. The rebar is positioned along the x-axis. The base material is dependent on temperature and the first field variable. The rebar properties are dependent on the second field variable. Step 1 uniformly increases the temperature from 0° to 100°, with both field variables set to 1. Step 2 increases the first field variable from 0 to 1, and Step 3 increases the second field variable from 0 to 1.
Initial stresses are tested in two ways. The tests consist of a single underlying membrane element with isoparametric rebar. In the first test an initial tensile stress is applied to the rebar, and no initial stresses are applied to the underlying membrane element. Thus, the membrane element will compress, and the initial rebar tensile stress will be reduced until equilibrium with the underlying solid is reached. The second test applies an initial tensile stress to the rebar but forces this initial stress to remain constant by means of holding prestress in rebar. The stress in the rebar remains unchanged, whereas the underlying membrane deforms to equilibrate the rebar stress.
Input file em_postoutput.inp tests the postprocessing output procedure and ensures that rebar output quantities are written properly to the restart file.
Input file em_nodalthick.inp tests variable thickness shells and membranes containing rebar. The nodal thickness procedure specifies a linearly varying element thickness.
Results and discussion
The results agree with the analytically obtained values.
SC8R elements; bending with rebar; 0° orientation.
Rebars in axisymmetric membranes
Elements tested
MAX1
MAX2
MGAX1
MGAX2
Problem description
Model:
Length
5.0
Midsurface radius
2.0
Thickness
0.05
Material:
Young's modulus of bulk material
1.0 × 105
Young's modulus of rebar
1.0 × 108
Poisson's ratio of both materials
0.495
Reinforcement for tension and torsion tests
REBAR, 0.005, 0.31416, 0, RBMAT, 50
Results and discussion
If rebars are not axial (rebar angle 0°) or circumferential (rebar angle 90°), element types MGAX1 and MGAX2 predict twist under axial tension (Step 1 in all the input files). The twist angle is determined by the initial rebar angle and the material properties. If the Poisson's ratio of the material is sufficiently different from zero, the twist angle changes sign at some intermediate rebar angle between 0° and 90°. This result is accompanied by a change in sign of the stress in the rebar. This behavior is illustrated in Figure 1(a), where results for the twist angle are shown for element types MGAX1, MGAX2, and CGAX4R (axisymmetric continuum element with twist) when both the rebar and the bulk materials are almost incompressible. Figure 1(b) shows the evolution of this behavior with the Poisson's ratios of the materials. For 0.05 the twist angle does not change sign as the initial rebar angle changes from 0° to 90°.
Rebars with geometry defined by angular spacing and lift equation
Elements tested
SAX2
MAX2
SFMAX2
S4R
M3D4R
SFM3D4R
Problem description
These tests verify reinforcement with spacing that varies as a function of radial position and reinforcement defined by the tire lift equation. Each input file contains two models; one model contains reinforcement with angular spacing and the other model contains reinforcement defined with the lift equation. Aside from the reinforcement geometry, the two models are identical, consisting of an axisymmetric disk with internal radius of 2.0, external radius of 5.0 and thickness of 0.1. The interior edges of the disks are fully constrained and a prescribed displacement of 1.0 × 10-4 is applied to the exterior edges.
One layer of rebar is defined in the model containing rebar with angular spacing. The rebar is oriented along the radial direction. The second model contains 8 layers of rebar, oriented at an angle of 45°, 135°, 225°, 315°, −45°, −135°, −225°, −315° respectively in the uncured configuration.
Material:
Young's modulus of bulk material
1.0 × 103
Young's modulus of rebar
1.0 × 108
Poisson's ratio of both materials
0.3
Results and discussion
The results agree with the analytically obtained values.
