Boundary conditions for strain based loading

Hi,

I would like to perform a loading on a 2D specimen using a commercial software to obtain a stress-strain curve for  shape memory alloy (using the Ginzburg-Laundau model). To obtain the stress-strain curve following methods can be applied (refer to the figure for the nomenclature of boundaries)

(a) Displacement based loading: Constraint (Dirichlet boundary condition) the boundary 1 (in x and y direction) and load the boundary 4 in the x direction.

(b) Stress based loading: Constraint (Neumann boundary condition) the boundary 1 (in x and y direction) and apply stress flux (Neumann boundary condition) on the boundary 4 in the x direction.

(c) Strain based loading: Increment the strain loading using constant strain rate in the x direction as

    strain (x component) = strain (x component) + strain rate * time

I am mainly interested in the strain based loading here. If boundary 1 is constrained, the stress curve oscillates between the first and third quadrant in the stress-strain curve. I am wondering what are the boundary conditions to be used for the strain based loading on boundaries 1, 2, 3, and 4? 

Nomenclature of boundaries in the rectangular domain is attached in the jpg file.

I would appreciate if you could share your expertise.

Warm regards,

RPD