MOOSE_CODE

# This is strong form of 1D time-dependnet problem :
# \rho A \frac{\partial^2 u(x,t)}{\partial t^2} = \frac{\partial}{\partial x} \left( EA \frac{\partial u(x,t)}{\partial x} \right) + f(x,t)
# The weak form of governing equation is :
# \int \rho A v(x) \frac{\partial^2 u(x,t)}{\partial t^2} \, dx + \int \frac{\partial v(x)}{\partial x} EA \frac{\partial u(x,t)}{\partial x} \, dx - \left[ v(x) EA \frac{\partial u(x,t)}{\partial x} \right]_{x_0}^{x_L} = \int v(x) f(x,t) \, dx

# Only need to introduced new auxiliary variables : acceleration(acc) & Velocity(vel) when it's [solidmechanics/dynamics]

[Mesh] # yeild errors when adding subblock
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0.0
  xmax = 10.0
[]

[GlobalParams]
  displacements = 'disp'
[]

[Variables] #Block for the main variable (displacement), for auxiliary variables using [AxuVariables]
  [disp] # Define the interpolation functions
    order = FIRST
    family = LAGRANGE
  []
[]

# [AuxVariables]
#   [stress_theta]
#     order = CONSTANT
#     family = MONOMIAL
#   []
#   [strain_theta]
#     order = CONSTANT
#     family = MONOMIAL
#   []
# []

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        displacements = disp
        incremental = true
        add_variables = true # add displacement variables
        new_system = False
        strain = SMALL
        generate_output = 'max_principal_stress, max_principal_strain'
      []
    []
  []
[]

[BCs]
  [left_fixed]
    type = DirichletBC
    boundary = left
    variable = disp
    value = 0.0
  []
  [right_force]
    type = NeumannBC
    boundary = right
    variable = disp
    value = -1e5 # N (Applied force at the right end)
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 20e10 # Pa, the youngs_modulus of steel
    poissons_ratio = 0 # 1D problem
  []

  [linear_stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = Steady # means time-dependent
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]