Background

The Concrete1DFiber class creates a uniaxial material with the constitutive equation given as

\[ \sigma = \begin{cases} E_t \, \epsilon \quad\quad & \text{, for } 0 \leq \epsilon \leq \epsilon_t, \\ f_c \frac{\epsilon}{\epsilon_{cc}}\left(2 - \frac{\epsilon}{\epsilon_{cc}} \right) & \text{, for } -\epsilon_{cc} \leq \epsilon \leq 0,\\ f_c \left( 1 - \frac{\epsilon - \epsilon_{cc}}{\epsilon_{cu} - \epsilon_{cc}} \right) & \text{, for } \epsilon \leq -\epsilon_{cc} \end{cases} \]

where \(\sigma\) is the uniaxial stress, \(\epsilon\) is the uniaxial strain, and \(f_c\) is the concrete compressive strength, \(\epsilon_{cc}\) is the concrete strain at maximum strength, and \(\epsilon_{cu}\) is the concrete strain at crushing strength. The Figure shows the constitutive law of this material. No hysteresis behavior is present for this formulation.

REFERENCE:

Mohd Hisham Mohd Yassin, "Nonlinear Analysis of Prestressed Concrete Structures under Monotonic and Cycling Loads", PhD dissertation, University of California, Berkeley, 1994.

Pre-Analysis

The python Pre-Analysis in the 01-Pre_Process/Method/Attach.py file provides with an interface to populate the Entities dictionary. This file contains several functions to populate specific fields. For example, to create a Concrete1DFiber material using json format, use:

addMaterial(tag, name='Concrete1DFiber', attributes):
- tag : The identifier of this material, i.e., tag > -1
- name : Seismo-VLAB material class name
- attributes : Specific properties for the created material, for example
  - 'fc' : is the concrete compressive strength at 28 days.
  - 'ecc' : is the concrete strain at maximum strength.
  - 'fcu' : is the concrete crushing strength.
  - 'ecu' : concrete strain at crushing strength.
  - 'ratio' : ratio between unloading slope at and initial slope.
  - 'ft' : is the concrete tensile strength.
  - 'Et' : is the tension softening stiffness (absolute value).
  - 'nu' : is the Poisson’s ratio.
  - 'rho' : is the material density.
Example

A CONCRETE1DFIBER can be defined using the python interface as follows:
SVL.addMaterial(tag=1, name='Concrete1DFiber', attributes={'fc': -5.73, 'ecc': -0.003, 'fcu': -1.146, 'ecu': -0.021, 'ratio': 0.05, 'ft': 0.28, 'Et': 430.0})

Application
Please refer to the A17-DY_1D_Material_Fiber_Concrete.py file located at 03-Validations/01-Debugging/ to see an example on how to define a PlasticPlaneStrainBA material.

On the contrary, the 01-Pre_Process/Method/Remove.py file provides with an interface to depopulate the Entities dictionary. For example, to remove an already define Material, use:

delMaterial(tag):
- tag : The identifier of the material to be removed, i.e., tag > -1

Run-Analysis

The C++ Run-Analysis in the 02-Run_Process/02-Materials/03-Fiber/Concrete1DFiber.cpp file provides the class implementation. A Concrete1DFiber is created using the built-in json parse-structure provided in the Driver.hpp. A Concrete1DFiber is defined inside the "Materials" json field indicating its "Tag" as follows,

{
    "Materials": {
        "Tag": {
            "name" : "CONCRETE1DFIBER",
            "attributes": {
                "fc": double,
                "ecc": double,
                "fcu": double
                "ecu": double,
                "ratio": double,
                "ft": double
                "Et": double,
                "nu": double,
                "rho": double
            }
        }
    }
}

Variable	Description
`Tag`	Unique material object identifier.
`fc`	The concrete compressive strength at 28 days.
`ecc`	The concrete strain at maximum strength.
`fcu`	The concrete crushing strength.
`ecu`	The concrete strain at crushing strength.
`ratio`	Ratio between unloading slope at and initial slope.
`ft`	The concrete tensile strength.
`Et`	The tension softening stiffness (absolute value).
`nu`	Represents the Poisson's ratio.
`rho`	Represents the material density.

Attention: This material can only be assigned to section such as the Fib3DLineSection.; Compressive concrete parameters should be input as negative values.; The initial slope for this model is \(E_c = \displaystyle{\frac{2 f_c}{\epsilon_{cc}}}\).

Example

A uniaxial CONCRETE1DFIBER with compressive strength 5.73, strain at maximum strength 0.003, concrete crushing strength 0.021, ratio 0.05, and tensile strength and softening stiffness of 0.28, 430 respectively:
{ "Materials": { "1": { "name" : "CONCRETE1DFIBER", "attributes": { "fc": -5.73, "ecc": -0.003, "fcu": -1.146, "ecu": -0.021, "ratio": 0.05, "ft": 0.28, "Et": 430.0, "nu" : 0.25, "rho": 0.0 } } } }