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IN THIS PAPER WE PRESENT A MOST PROMISING SCOPE OF THE EXACT QUASICONVEX ENERGY ENVELOPE IN MODELING THE GRANULAR MATERIALS WITH MICROSTRUCTRES. WE SHOW THAT IT IS POSSIBLE TO OBSERVE BOTH THE EXTENDED MICROSTRUCTURES AND LOCALIZED DEFORMATIONS IN GRANULAR MATERIALS USING A VARIATIONAL MODEL BASED ON THE MATHEMATICAL RELAXATION THEORY. THE VARIATIONAL MODEL IS DERIVED WITHIN THE FRAMEWORK OF COSSERAT CONTINUUM. THE COMPUTATIONAL ALGORITHM BASED ON FINITE ELEMENT METHOD IS USED TO CARRIED OUT NUMERICAL COMPUTATIONS. THE FEATURES OF THE PROPOSED MODEL ARE STUDIED FOR THREE REPRESENTATIVE EXAMPLES: THE COUETTE SHEAR CELL, THE RECTANGULAR SPECIMEN IN COMPRESSION AND THE INDENTATION OF A GRANULAR STRUCTURE. THE OBTAINED RESULTS DEOMONSTRATES ON THE POSSIBLE APPLICATIONS AND FEATURES OF EXACT QUASICONVEX ENERGY ENVELOPS IN MODELING THE GRANULAR MATERIALS.
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