Non-linear material, distinct tension/compression behaviors

I’d like to define a material with the following stress-strain relationship: As you can see, the tension and compression behaviors are quite different. It doesn’t seem to be possible to define a material beyond using Von Mises stresses, which to my understanding would not allow this definition. Can anyone confirm this?

Materials, Free Full-Text

Tension–compression asymmetry in amorphous silicon

Non-linear elastic longitudinal behaviour of continuous carbon fibres/epoxy matrix composite laminae: Material or geometrical feature? - ScienceDirect

Linear versus non-linear elastic behavior. Notes: (A) Stress-strain

Material nonlinearity - Technical Knowledge Base - Computers and Structures, Inc. - Technical Knowledge Base

eFatigue + Cast Iron Technical Background

Typical stress-strain curves for (a) linear elastic materials, (b)

Brittle-ductile transition stress of different rock types and its relationship with uniaxial compressive strength and Hoek–Brown material constant (mi)

Stress-strain relationship for wood under tension and compression

High Strain Rate Testing and Characterization of Materials