ABAQUS/Explicit offers a general capability for modeling progressive damage and failure of materials. In the most general case, modeling material failure requires the specification of the following:
the undamaged response of the material (“Material data definition,” Section 9.1.2);
a damage initiation criterion (“Damage initiation,” Section 11.6.2); and
a damage evolution response, including a choice of element removal (“Damage evolution and element removal,” Section 11.6.3).
ABAQUS/Explicit offers a general framework for material failure modeling that allows the combination of multiple failure mechanisms acting simultaneously on the same material. Material failure refers to the complete loss of load-carrying capacity that results from progressive degradation of the material stiffness. The stiffness degradation process is modeled using damage mechanics.
To help understand the failure modeling capabilities in ABAQUS/Explicit, consider the response of a typical metal specimen during a simple tensile test. The stress-strain response, such as that illustrated in Figure 11.6.1–1, will show distinct phases.
The material response is initially linear elastic,
, followed by plastic yielding with strain hardening, 
. Beyond point 
there is a marked reduction of load-carrying capacity until rupture, 
. The deformation during this last phase is localized in a neck region of the specimen. Point identifies the material state at the onset of damage, which is referred to as the damage initiation criterion. Beyond this point, the stress-strain response is governed by the evolution of the degradation of the stiffness in the region of strain localization. In the context of damage mechanics can be viewed as the degraded response of the curve 
that the material would have followed in the absence of damage.Thus, in ABAQUS/Explicit the specification of a failure mechanism consists of four distinct parts:
the definition of the effective (or undamaged) material response (
),
a damage initiation criterion (),
a damage evolution law (), and
a choice of element deletion whereby elements can be removed from the calculations once the material stiffness is fully degraded (
).
A damage initiation criterion establishes the condition that must be satisfied for the material to reach a critical state corresponding to the onset of progressive damage. ABAQUS offers a variety of choices of damage initiation criteria, each associated with distinct types of material failure. They can be classified in the following categories:
Damage initiation criteria for the fracture of metals, including ductile and shear criteria.
Damage initiation criteria for the necking instability of sheet metal. These include forming limit diagrams (FLD and FLSD) intended to assess the formability of sheet metal and the Marciniak-Kuczynski (M-K) criterion to numerically predict necking instability in sheet metal taking into account the deformation history.
These criteria are discussed in “Damage initiation,” Section 11.6.2. Each damage initiation criterion has an associated output variable to indicate whether the criterion has been met during the analysis. A value of 1.0 or higher indicates that the initiation criterion has been met.
More than one damage initiation criterion can be specified for a given material. If multiple damage initiation criteria are specified for the same material, they are treated independently. Once a particular initiation criterion is satisfied, the material stiffness is degraded according to the specified damage evolution law for that criterion; in the absence of a damage evolution law, however, the material stiffness is not degraded. A failure mechanism for which no damage evolution response is specified is said to be inactive. ABAQUS/Explicit will evaluate the initiation criterion for an inactive mechanism for output purposes only, but the mechanism will have no effect on the material response.
| Input File Usage: | *DAMAGE INITIATION, CRITERION=criterion 1 |
| Repeat this option as often as necessary to define multiple damage initiation criteria. |
The damage evolution law describes the rate of degradation of the material stiffness once the corresponding initiation criterion has been reached. ABAQUS/Explicit assumes that the degradation of the stiffness associated with each active failure mechanism can be modeled using a scalar damage variable, 
(
), where 
represents the set of active mechanisms. At any given time during the analysis the stress tensor in the material is given by the scalar damage equation
is the overall damage variable and 
is the effective (or undamaged) stress tensor computed in the current increment. are the stresses that would exist in the material in the absence of damage. The material has lost its load-carrying capacity when 
. By default, an element is removed from the mesh if all of the section points at any one integration location have lost their load-carrying capacity.The overall damage variable, , captures the combined effect of all active mechanisms and is computed in terms of the individual damage variables, , according to a user-specified rule.
ABAQUS supports different models of damage evolution and provides controls associated with element deletion due to material failure, as described in “Damage evolution and element removal,” Section 11.6.3. All of the available models use a formulation intended to alleviate the strong mesh dependency of the results that can arise from strain localization effects during progressive damage.
| Input File Usage: | Use the following option immediately after the corresponding *DAMAGE INITIATION option to specify the damage evolution behavior: |
*DAMAGE EVOLUTION |
The failure modeling capability can be used with any elements in ABAQUS/Explicit that include mechanical behavior (elements that have displacement degrees of freedom).
For coupled temperature-displacement elements the thermal properties of the material are not affected by the progressive damage of the material stiffness until the condition for element deletion is reached; at this point the thermal contribution of the element is also removed.
The damage initiation criteria for sheet metal necking instability (FLD, FLSD, and M-K) are available only for elements that include mechanical behavior and use a plane stress formulation (i.e., plane stress, shell, continuum shell, and membrane elements).
