Chang-Mander nonlinear concrete model - con_cm

It is the implementation of Chang & Mander's [Chang & Mander, 1994] concrete model, which puts particular emphasis on the transition of the stress-strain relation upon crack opening and closure, contrary to other similar models that assume sudden crack closure with rapid change in section modulus. The concrete in tension is modelled with a cyclic behaviour similar to that in compression, and the model envelopes for compression and tension have control on the slope of the stress-strain behaviour at the origin, and the shape of both the ascending and descending (i.e., pre-peak and post-peak) branches of the stress-strain behaviour.

Eight model calibrating parameters must be defined in order to fully describe the mechanical characteristics of the material:

Compressive strength - fc
This is the cylinder (100x200 mm) compressive stress capacity of the material. Its value typically varies from 15 MPa up to 45 MPa. The default value is 28 MPa.

Tensile strength - ft
This is the tensile stress capacity of the material. It can usually be estimated as , where kt varies from 0.5 (concrete in direct tension) to 0.75 (concrete in flexural tension), as suggested by Priestley et al. [1996]. When this value is reached, the concrete is assumed to abruptly loose its tensile resistance, without any sort of tension softening. The default value is 2.2 MPa (see note below).

Modulus of elasticity - Ec
This is the initial elastic stiffness of the material. Its value usually oscillates between 10000 and 30000 MPa. The default value is 22960 MPa.

Strain at peak compressive stress -
This is the strain corresponding to the point of unconfined peak compressive stress (fc). For normal strength plain concrete, this value is usually considered to lie within the range of 0.002 to 0.0022. The default value is 0.002 mm/mm.

Strain at peak tensile stress -
This is the strain corresponding to the point of unconfined peak tensile stress (ft). For normal strength plain concrete, this value is usually considered to lie within the range of 0.0002 to 0.00022. The default value is 0.0002 mm/mm.

Non-dimensional critical compressive strain -x_cr^-
This is a normalised non-dimensional critical compressive strain value that determine the shape of the descending branches of the curve, this value is usually considered to lie within the range of 1.1 to 1.5. The default value is 1.3.

Non-dimensional critical tensile strain -x_cr⁺
This is a normalised non-dimensional critical tensile strain value that determine the shape of the descending branches of the curve, this value is usually considered to lie within the range of 1 to 5. The default value is 3.

Specific weight -
This is the specific weight of the material. The default value is 24 kN/m3.

Notes

1. Values of compressive strength capacity obtained through testing of concrete cubes are usually 25 to 10 percent higher than their cylinder counterparts, for cylinder concrete strength of 15 to 50 MPa, respectively.
2. The non-dimensional critical strain values, r for compression and xcr for tension, determined the shape of the descending branches of the curve. Users are advised to view the plot on the New Material dialog box, in order to understand how the curve changes with different values of the parameters.