You will need to export the ABAQUS results as text file "report". Copy this text file into MATLAB's working directory and use any number of txt read commands in MATLAB to read from the appropriate portion of the report. A simple coding will need to be used to read the entries in the matrix of interest in the ABAQUS report and write in a corresponding matrix in MATLAB.
Alternatively you can use the txt import wizard in MATLAB for this but I am not sure if this will be simpler or not.
The easiest way to do that is to export the Abaqus results in a *rpt (Report file and then read it into Matlab using dlmread command). You have to export manually the report file.
Importing models and results from other commercial codes is a tedious task. Especially if the code has to be maintained, or is applied to large models.
My society is selling a finite element toolbox in MATLAB, named SDT, and we provide an extension to import models and results from other codes named FEMLink, you can check it out if interested,