Increase in stiffness over time

[jmeier]

Dear Moose Community,

Concrete will increase its stiffness over time (and increase in strength, and shrink a little). Ignoring strength and shrinking, I'd like to model this increase in stiffness in a very simplified way just by increasing the Young's modulus of a linear-elastic material over time (using Executioner/Transient, SolidMechanics/QuasiStatic/strain = SMALL, SolidMechanics/QuasiStatic/incremental = true).

If I model a purely linear-elastic block under constant loading and increase the Young's modulus over time, the stresses will remain constant and the material will expand. Fixing the boundaries of this block and increasing the Young's modulus would increase the stress within the block. Both options seem not suitable to model the stiffness increase of concrete.

What is the best way to model this? Do I also have to apply a negative volumetric strain? If yes, how? Are there other options?

Thanks & kind regards,
Jörg

[GiudGiud]

@bwspenc

[bwspenc]

Hmm, this is tricky! It seems like what you want is to keep the stresses that have been incurred under prior loading constant, and then have the increased stiffness only affect additional incremental strains. I assume you're using ComputeFiniteStrainElasticStress. It currently computes the stress like this:

   intermediate_stress =
        elasticity_tensor_rotated * (_elastic_strain_old[_qp] + _strain_increment[_qp]);

You probably want something more like this:

   intermediate_stress =
        _stress_old[_qp] + elasticity_tensor_rotated * _strain_increment[_qp];

Maybe try this and see if that does what you want. I'm not really sure what the right way to do this is in general, but maybe we should consider doing something like that.

[jmeier]

Dear Ben, Thanks for your answer! Yes, I'm using ComputeFiniteStrainElasticStress. I will try your suggestion.

In the meantime: Is there a way to apply change of (plastic) strain in Moose for a Material (e.g. introduce a user-given plastic strain increments)?

[bwspenc]

@jmeier I was thinking about this some more, and we actually do just what I proposed in some cases for inelastic models. This code is in ComputeMultipleInelasticStress:

     if (_is_elasticity_tensor_guaranteed_isotropic || !_perform_finite_strain_rotations)
        _stress[_qp] =
            _elasticity_tensor[_qp] * (_elastic_strain_old[_qp] + elastic_strain_increment);
      else
      {
        if (_damage_model)
          _stress[_qp] = _undamaged_stress_old + _elasticity_tensor[_qp] * elastic_strain_increment;
        else
          _stress[_qp] = _stress_old[_qp] + _elasticity_tensor[_qp] * elastic_strain_increment;
      }

The last block is the one that applies an increment to the old stress, which only happens if the elasticity tensor is not isotropic. If I remember correctly, we do that because we do not rotate the elasticity tensor. You can actually run this model on elastic problems by supplying an empty list of inelastic models (i.e., inelastic_models = ""), but you'd get the same thing as you're getting now if you're using isotropic elasticity.

Regarding your second question: Probably the easiest way to do what you are asking is to have a user-defined eigenstrain model. You can set any of the components of the strain tensor that is used as an eigenstrain any way you like. That eigenstrain tensor is subtracted from the total strain before the stress calculation.

[jmeier]

Dear Ben, thank you so much! This looks very good. I'm going to use ComputeMultipleInelasticStress and probably have a look at a user-defined eigenstrain model later.