No Compression or No Tension

The modified elastic behavior is obtained by first solving for the principal stresses assuming linear elasticity and then setting the appropriate principal stress values to zero. The associated stiffness matrix components will also be set to zero. These models are not history dependent: the directions in which the principal stresses are set to zero are recalculated at every iteration.

The no compression effect for a one-dimensional stress case such as a truss or a layer of a beam in a plane is illustrated in Figure 1. No compression and no tension definitions modify only the elastic response of the material.

A no compression elastic case with an imposed strain cycle.

In Abaqus/Explicit, you can define a cutoff for principal stress values to remove the influences of low-level oscillating stresses. If a cutoff stress ${\sigma }_t^{cutoff}\ge 0$ is defined for a no tension elasticity material, the principal stress values larger than the cutoff stress are set to ${\sigma }_t^{cutoff}$ , and principal stress values smaller than or equal to the cutoff stress are not affected. If a cutoff stress ${\sigma }_c^{cutoff}\le 0$ is defined for a no compression elasticity material, the principal stress values smaller than the cutoff stress are set to ${\sigma }_t^{cutoff}$ , and principal stress values larger than or equal to the cutoff stress are not affected. The default value is based on a small fraction (10^–4) of the dilatational wave modulus of the material.

Using no compression or no tension elasticity can make a model unstable: convergence difficulties might occur. Sometimes these difficulties can be overcome by overlaying each element that uses the no compression (or no tension) model with another element that uses a small value of Young's modulus (small in comparison with the Young's modulus of the element using modified elasticity). This technique creates a small “artificial” stiffness, which can stabilize the model.