Brittle cracking constitutive model

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/Explicit

Elements tested

CAX4R

C3D8R

CPS4R

CPE4R

B21

Features tested

Brittle cracking model response under loading/unloading/reloading conditions. Different combinations of active cracks are tested.

Problem description

This problem contains 21 single-element verification problems that are all run in one input file. The problem exercises the brittle cracking material model under loading/unloading/reloading conditions; all possible crack states are exercised for single and multiple crack cases.

Figure 1 shows the 21 elements used in the analysis in their original and deformed shapes. The dashed lines illustrate the original shapes. The bottom row contains CAX4R and C3D8R elements only since they are the only elements for which it is not possible to create three simultaneous cracks. The next row up contains all but B21 elements since they are the only elements for which it is not possible to create two simultaneous cracks. The top three rows contain all five element types since they refer to loading cases resulting in a single crack. The three rows are used to test the three different ways available for input of the tension softening data.

The original length of each side of the elements is L0=​ 1. The elements are loaded using an amplitude function that subjects them to tension, followed by unloading and loading into compression, followed by reloading in tension. This loading program is applied in one direction (rows (c), (d), and (e) in Figure 1), two directions (row (b)) or three directions (row (a)). This creates one, two, or three simultaneous cracks, respectively.

The material properties used are those of a typical medium strength concrete: the elastic properties are E=​ 30 × 109 Pa, ν=​ 0.2; the cracking failure stress is 3 × 106 Pa; and the mass density is 2400 kg/m3.

Results and discussion

Figure 2 shows stress-strain in all three cracking directions for elements CAX4R and C3D8R (row (a) in Figure 1). For CAX4R the radial and axial loading is applied equally. For C3D8R directions 1 and 3 are loaded at the same rate, whereas direction 2 is loaded at three-quarters of that rate. The results for the two kinds of elements are identical.

Figure 3 shows stress-strain in two cracking directions for elements CAX4R, C3D8R, CPS4R, and CPE4R (row (b) in Figure 1). For all but the axisymmetric case, direction 2 is loaded at three-quarters of the loading rate in direction 1. In the axisymmetric case the radial and axial directions are loaded at the same rate. The results for all elements are in agreement.

Figure 4 shows stress-strain in the only cracking direction (direction 2) for elements CAX4R, C3D8R, CPS4R, CPE4R, and B21 (row (c) in Figure 1). The tension softening data are defined by specifying the postfailure stress-strain relationship. The results for all elements are identical.

Figure 5 shows stress-strain in the only cracking direction (direction 2) for elements CAX4R, C3D8R, CPS4R, CPE4R, and B21 (row (d) in Figure 1). The tension softening data are defined by specifying the postfailure stress/displacement relationship. The results for all but the axisymmetric element are identical. The axisymmetric result is slightly different because the characteristic length computed by Abaqus/Explicit is different in the axisymmetric case.

Figure 6 shows stress-strain in the only cracking direction (direction 2) for elements CAX4R, C3D8R, CPS4R, CPE4R, and B21 (row (e) in Figure 1). The tension softening data are defined by specifying the failure stress, σt⁢uI, and the Mode 1 fracture energy, GfI. The results for all but the axisymmetric element are identical. The axisymmetric result is slightly different because the characteristic length computed by Abaqus/Explicit is different in the axisymmetric case.

Figures

Figure 1. Deformed shapes for one-element cracking model tests.

Figure 2. Stress-strain in three cracking directions: CAX4R and C3D8R elements.

Figure 3. Stress-strain in two cracking directions: CAX4R, C3D8R, CPS4R, and CPE4R elements.

Figure 4. Stress-strain in single cracking direction (stress-strain specified): CAX4R, C3D8R, CPS4R, CPE4R, and B21 elements.

Figure 5. Stress-strain in single cracking direction (stress/displacement specified): CAX4R, C3D8R, CPS4R, CPE4R, and B21 elements.

Figure 6. Stress-strain in single cracking direction (failure stress and fracture energy specified): CAX4R, C3D8R, CPS4R, CPE4R, and B21 elements.