The concrete material model predicts the failure of brittle materials. Both cracking and crushing failure modes are accounted for. TB,CONCR accesses this material model, which is available with the reinforced concrete element SOLID65.

The criterion for failure of concrete due to a multiaxial stress state can be expressed in the form (Willam and Warnke):

(2–1)

where:

If Equation 2–1 is satisfied, the material will crack or crush.

A total of five input strength parameters (each of which can be temperature dependent) are needed to define the failure surface as well as an ambient hydrostatic stress state. These are presented in Table 2.1: Concrete Material Table.

Table 2.1: Concrete Material Table

(Input on TBDATA Commands with TB,CONCR)
Label	Description	Constant
ft	Ultimate uniaxial tensile strength	3
fc	Ultimate uniaxial compressive strength	4
fcb	Ultimate biaxial compressive strength	5
	Ambient hydrostatic stress state	6
f1	Ultimate compressive strength for a state of biaxial compression superimposed on hydrostatic stress state	7
f2	Ultimate compressive strength for a state of uniaxial compression superimposed on hydrostatic stress state	8

However, the failure surface can be specified with a minimum of two constants, f_t and f_c. The other three constants default to Willam and Warnke:

(2–2)

(2–3)

(2–4)

However, these default values are valid only for stress states where the condition

(2–5)

(2–6)

is satisfied. Thus condition Equation 2–5 applies to stress situations with a low hydrostatic stress component. All five failure parameters should be specified when a large hydrostatic stress component is expected. If condition Equation 2–5 is not satisfied and the default values shown in Equation 2–2 thru Equation 2–4 are assumed, the strength of the concrete material may be incorrectly evaluated.

When the crushing capability is suppressed with f_c = -1.0, the material cracks whenever a principal stress component exceeds f_t.

Both the function F and the failure surface S are expressed in terms of principal stresses denoted as σ₁, σ₂, and σ₃ where:

(2–7)

(2–8)

and σ₁ σ₂ σ₃. The failure of concrete is categorized into four domains:

In each domain, independent functions describe F and the failure surface S. The four functions describing the general function F are denoted as F₁, F₂, F₃, and F₄ while the functions describing S are denoted as S₁, S₂, S₃, and S₄. The functions S_i (i = 1,4) have the properties that the surface they describe is continuous while the surface gradients are not continuous when any one of the principal stresses changes sign. The surface will be shown in Figure 2.1: 3D Failure Surface in Principal Stress Space and Figure 2.3: Failure Surface in Principal Stress Space with Nearly Biaxial Stress.