Elastic1DLinear

Background

The Elastic1DLinear class creates a uniaxial material class with the constitutive equation given as

\[ \sigma = E \, \epsilon \nonumber \]

where \(\sigma\) is the uniaxial stress, \(\epsilon\) is the uniaxial strain, and \(E\) is the elasticity modulus. The Figure shows the constitutive law of this material.

REFERENCE:

• Bathe K. Jurgen, "Finite Element Procedures", Chapter 4: pages 194, Table 4.3, 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 Elastic1DLinear material using json format, use:

• addMaterial(tag, name='Elastic1DLinear', 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 of elasticity.
      
    • 'nu' : is the Poisson’s ratio.
      
    • 'rho' : is the material density. Can be omitted for static analysis.

  Example

  A ELASTIC1DLINEAR material can be defined using the python interface as follows:
  SVL.addMaterial(tag=1, name='Elastic1DLinear', attributes={'E': 200.0, 'nu': 0.25, 'rho': 0.0})

  Application
  Please refer to the A01-DY_Lin_2D_Elastic_ZeroLength.py file located at 03-Validations/01-Debugging/ to see an example on how to define a Elastic1DLinear 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/01-Linear/Elastic1DLinear.cpp file provides the class implementation. A Elastic1DLinear material is created using the built-in json parse-structure provided in the Driver.hpp. A Elastic1DLinear is defined inside the "Materials" json field indicating its "Tag" as follows,

• {
      "Materials": {
          "Tag": {
              "name" : "ELASTIC1DLINEAR",
              "attributes": {
                  "E": double,
                  "nu": double,
                  "rho": double
              }
          }
      }
  }
  

  Variable	Description
  Tag	Unique material object identifier.
  E	Represents the elasticity modulus.
  nu	Represents the Poisson's ratio.
  rho	Represents the material density.

  
  

  Attention

  This material can only be assigned to one-dimensional elements such as: lin2DTruss2, kin2DTruss2, lin3DTruss2, kin3DTruss2 and ZeroLength1D elements.

  Example

  A uniaxial ELASTIC1DLINEAR material with elasticity modulus 200, Poisson's ratio 0.25, and no density is defined:
  { "Materials": { "1": { "name" : "ELASTIC1DLINEAR", "attributes": { "E" : 200.0, "nu" : 0.25, "rho": 0.0 } } } }