The figure provided is the force/width vs strain measured for a piece of fabric in uniaxial stress configuration (the thickness is unimportant but you can assume what you like e.g. 1mm).

The sample is stretched up to max 0.1 strain with constant rate (0.1/s) and then released at the same rate of deformation until the load frame cross-head is at the original location (associated with initial length of the sample). It will then get reloaded repeatedly to maximum 50 cycles. The data is shown at specific cycles (not all). As the sample is deformed its behavior changes.

1- I am looking for suitable constitutive models that may or may not be the right choice for the following data in the attached picture.

2- I am also looking to find if there are any material subroutines available in FE codes that are compatible with this response and/or an specific constitutive model.

I have done some literature search but I have not get to a desirable result as I am new to this field. Introducing any paper or document on this topic can help me to start my studies from an optimum point and save time.