Softening Model 1 - GCMLab/GCMLab-FEM GitHub Wiki

The stress field is related to the elastic strains through the constitutive law,

in which is the 4^th order linear elasticity tensor.

The modulus of elasticity is a non-linear softening law according to the first invariant of the strain tensor such that

As of June 2023, the softening model fails to converge beyond the ultimate strength of the component under analysis. It cannot consistently capture post-peak softening behaviour. For instance, in the analysis of tension problem, the softening behaviour can be captured by utilizing a finite element mesh with just one element, as strain localization does not occur within a single element. However, when the number of elements is increased, the softening model fails to converge beyond the ultimate strength.

• One-dimensional problems:

  

  in which E is the modulus of elasticity (Young's modulus) and

  

• Two-dimensional problems:

  

  Plane strain

  

  in which is Poisson's ratio.

  Plane stress