A cracking model for concrete and other brittle materials

This section describes the cracking constitutive model provided in Abaqus/Explicit for concrete and other brittle materials.

The following topics are discussed:

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Cracking model for concrete


The material library in Abaqus also includes a constitutive model for concrete based on theories of scalar plastic damage, described in Damaged plasticity model for concrete and other quasi-brittle materials, which is available in Abaqus/Standard and Abaqus/Explicit. In Abaqus/Standard plain concrete can also be analyzed with the smeared crack concrete model described in An inelastic constitutive model for concrete. Although this brittle cracking model can also be useful for other materials, such as ceramics and brittle rocks, it is primarily intended to model plain concrete. Therefore, in the remainder of this section, the physical behavior of concrete is used to motivate the different aspects of the constitutive model.

Reinforced concrete modeling in Abaqus is accomplished by combining standard elements, using this plain concrete cracking model, with “rebar elements”—rods, defined singly or embedded in oriented surfaces, that use a one-dimensional strain theory and that can be used to model the reinforcing itself. The rebar elements are superposed on the mesh of plain concrete elements and are used with standard metal plasticity models that describe the behavior of the rebar material. This modeling approach allows the concrete behavior to be considered independently of the rebar, so this section discusses the plain concrete cracking model only. Effects associated with the rebar/concrete interface, such as bond slip and dowel action, cannot be considered in this approach except by modifying some aspects of the plain concrete behavior to mimic them (such as the use of “tension stiffening” to simulate load transfer across cracks through the rebar).

It is generally accepted that concrete exhibits two primary modes of behavior: a brittle mode in which microcracks coalesce to form discrete macrocracks representing regions of highly localized deformation, and a ductile mode where microcracks develop more or less uniformly throughout the material, leading to nonlocalized deformation. The brittle behavior is associated with cleavage, shear and mixed mode fracture mechanisms that are observed under tension and tension-compression states of stress. It almost always involves softening of the material. The ductile behavior is associated with distributed microcracking mechanisms that are primarily observed under compression states of stress. It almost always involves hardening of the material, although subsequent softening is possible at low confining pressures. The cracking model described here models only the brittle aspects of concrete behavior. Although this is a major simplification, there are many applications where only the brittle behavior of the concrete is significant; and, therefore, the assumption that the material is linear elastic in compression is justified in those cases.