Product: ABAQUS/Standard
Hashin's damage initiation criteria and energy-based damage evolution law are tested with a linearly elastic material.
This verification test consists of a set of one- and two-element models subjected to uniaxial tension or compression for various angles (off-axis angles) between the fiber direction and the direction in which the load is applied. The default maximum degradation (equal to 1.0) is used for first-order elements, and the value of the maximum degradation of 0.95 was specified using the *SECTION CONTROLS, MAX DEGRADATION option for the second-order elements.
The degradation of the material stiffness starts when Hashin's initiation criterion is reached for at least one of the failure modes. The damage variables, for the damage modes for which the initiation criteria are satisfied, evolve according to an energy-based evolution law with linear softening. Once the damage variable reaches the maximum degradation specified, no further damage takes place.
The results for the off-axis angles equal to 0° (fiber tension and compression) and 90° (matrix tension and compression) were verified to agree with analytical results.
Figure 2.2.21–1 and Figure 2.2.21–2 show the unidirectional stress for tension and compression, respectively, at which the initiation criterion is satisfied as a function of the off-axis angle. In these figures the numerical predictions agree very well with the analytical results and also show good agreement with the experimental data reported in Jones (1999).
CPS4 elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
CPS4R elements are subjected to uniaxial compression; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
CPS6 elements are subjected to uniaxial compression; off-axis angle, 90°. The maximum degradation is equal to 0.95.
CPS6M elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
CPS8 elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
CPS8R elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
M3D8 elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
M3D8R elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
M3D9 elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
S4R elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial compression; off-axis angle, 15°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial compression; off-axis angle, 30°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial compression; off-axis angle, 45°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial compression; off-axis angle, 60°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial compression; off-axis angle, 75°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial compression; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
S8R elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
S8R5 elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
S9R5 elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 0.95.
SC6R elements are subjected to uniaxial compression; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
CPS3 elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
CPS4 elements are subjected to uniaxial tension; off-axis angle, 30°. The maximum degradation is equal to 1.0 (default).
CPS4I elements are subjected to uniaxial tension; off-axis angle, 60°. The maximum degradation is equal to 1.0 (default).
CPS4R elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
CPS4R elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
M3D3 elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
M3D4R elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
M3D6 elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 0.95.
M3D9R elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 0.95.
S3 elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
S3R elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
S4 elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 15°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 30°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 45°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 60°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 75°. The maximum degradation is equal to 1.0 (default).
S4R elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
S4R5 elements are subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 1.0 (default).
SC8R elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
STRI3 elements are subjected to uniaxial tension; off-axis angle, 0°. The maximum degradation is equal to 1.0 (default).
STRI65 elements subjected to uniaxial tension; off-axis angle, 90°. The maximum degradation is equal to 0.95.
The default and nondefault degradation behaviors are tested. By default, elements are deleted if the damage variable for each failure mode and at each material point reaches the default maximum degradation value, 
. The *SECTION CONTROLS, ELEMENT DELETION=NO option and the *SECTION CONTROLS, MAX DEGRADATION option can be used to modify the default behavior.
Each model consists of nine elements. A linear elastic material is assigned to all the elements except one, for which a fiber reinforced damage model is used. The specimen is subjected to biaxial extension, which is followed by biaxial compression. For each of the elements three different cases are tested:
default behavior (, and elements are deleted if the deletion criteria are satisfied);
default value of maximum degradation (), and the elements remain active even if the deletion criteria are satisfied (*SECTION CONTROLS, ELEMENT DELETION=NO); and
the maximum degradation of 0.99 is specified, and the elements remain active even if the deletion criteria are satisfied (*SECTION CONTROLS, ELEMENT DELETION=NO, MAX DEGRADATION=0.99).
In the first step (biaxial extension) the fiber tensile and matrix tensile modes are completely damaged. In the subsequent biaxial compression step the remaining two failure modes (fiber and matrix compressive modes) are completely damaged as well. The evolutions of damage variables stop when the value of 
is reached. Once the maximum degradation is reached at all material points for all failure modes, the elements are deleted when deletion is requested and remain active when element deletion is not requested.
CPS4 elements are tested with default behavior (*SECTION CONTROLS, ELEMENT DELETION=YES, 
).
CPS4 elements are tested with nondefault behavior (*SECTION CONTROLS, ELEMENT DELETION=NO, 
).
CPS4 elements are tested with nondefault behavior (*SECTION CONTROLS, ELEMENT DELETION=NO, MAX DEGRADATION=0.99).
M3D4 elements are tested with default behavior (*SECTION CONTROLS, ELEMENT DELETION=YES, 
).
M3D4 elements are tested with nondefault behavior (*SECTION CONTROLS, ELEMENT DELETION=NO, 
).
M3D4 elements are tested with nondefault behavior (*SECTION CONTROLS, ELEMENT DELETION=NO, MAX DEGRADATION=0.99).
S4 elements are tested with default behavior (*SECTION CONTROLS, ELEMENT DELETION=YES, 
).
S4 elements are tested with nondefault behavior (*SECTION CONTROLS, ELEMENT DELETION=NO, 
).
S4 elements are tested with nondefault behavior (*SECTION CONTROLS, ELEMENT DELETION=NO, MAX DEGRADATION=0.99).
Hashin's damage initiation criteria with energy-based evolution law are tested with different types of procedures.
This verification test consists of small models (up to nine elements) that are used with various procedure types. The element removal and reactivation using the *MODEL CHANGE option are tested by removing the element, reactivating it in the subsequent step, and verifying that all the state variables are reset correctly. The dynamic and Riks analyses are tested by comparing the numerical results with the analytical results. Finally, the linear perturbation procedures are tested by performing a general step in which the material properties are degraded before the perturbation step and then comparing the results with those obtained using a material without damage with appropriately modified parameters.
The results agree well with exact analytical results or numerical results obtained using undamaged material.
Riks analysis.
Model change.
Frequency extraction analysis.
Frequency extraction analysis (model without damage).
Dynamic analysis.
Steady-state dynamics.
Steady-state dynamics (model without damage).
