Elastic1DGap

Background

The Elastic1DGap class creates a uniaxial material with the constitutive equation given as

\[ \sigma = \begin{cases} 0, & \epsilon \leq \epsilon_g \\ E(\epsilon - \epsilon_g), & \epsilon \geq \epsilon_g \end{cases} \]

where \(\sigma\) is the uniaxial stress, \(\epsilon\) is the uniaxial strain, \(E\) is the elasticity modulus, \(\epsilon_g\) is gap from which the material will take stress, and \(\epsilon_y\) is the yielding strain. The Figure shows the constitutive law of this material. No hysteresis behavior is present for this formulation.

REFERENCE:

• Bathe, K. Jurgen, "Finite Element Procedures", Chapter 6: pages 485-491, Prentice-Hall, 1996.

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 Elastic1DGap material using json format, use:

• addMaterial(tag, name='Elastic1DGap', 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
    • 'E' : is the elastic modulus.
      
    • 'gap' : is the gap or separation.
      
    • 'behavior' : is the gap behavior (0: tension, 1: compression).

  Example

  A ELASTIC1DGAP can be defined using the python interface as follows:
  SVL.addMaterial(tag=1, name='Elastic1DGap', attributes={'E': 50.0, 'gap': 0.2, 'behavior': 0})

  Application
  Please refer to the A16-DY_1D_Material_Fiber_Elastic_Gap.py file located at 03-Validations/01-Debugging/ to see an example on how to define a Elastic1DGap 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/02-NonLinear/Elastic1DGap.cpp file provides the class implementation. A Elastic1DGap is created using the built-in json parse-structure provided in the Driver.hpp. A Elastic1DGap is defined inside the "Materials" json field indicating its "Tag" as follows,

• {
      "Materials": {
          "Tag": {
              "name" : "ELASTIC1DGAP",
              "attributes": {
                  "E": double,
                  "gap": double,
                  "behavior": int
              }
          }
      }
  }
  

  Variable	Description
  Tag	Unique material object identifier.
  E	Represents the elasticity modulus.
  gap	Represents the gap (strain or separation)
  behavior	Represents if it is a tension (0) or compressive (1) gap.

  
  

  Attention

  This material should only be assigned to ZeroLength1D.

  To create a compression-only gap element, NEGATIVE values need to be specified for fy and gap.

  Example

  A uniaxial compressive ELASTIC1DGAP with elasticity modulus 50, and a gap of 0.2 is defined:
  { "Materials": { "1": { "name" : "ELASTIC1DGAP", "attributes": { "E" : 50.0, "gap" : 0.2, "behavior" : 1 } } } }