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THIS WORK PRESENTS A DETAILED DESCRIPTION OF THE FORMULATION AND IM-PLEMENTATION OF THE ATOMISTIC FINITE ELEMENT METHOD AFEM, EXEMPLI-FIED IN THE ANALYSIS OF ONE- AND TWO-DIMENSIONAL ATOMIC DOMAINS GOV-ERNED BY THE LENNARD JONES INTERATOMIC POTENTIAL. THE METHODOLOGY TO SYNTHESIZE ELEMENT STIFFNESS MATRICES AND LOAD VECTORS, THE POTENTIAL ENERGY MODIFICATION OF THE ATOMISTIC FINITE ELEMENTS (AFE) TO ACCOUNT FOR BOUNDARY EDGE EFFECTS, THE INCLUSION OF BOUNDARY CONDITIONS IS CARE-FULLY DESCRIBED. THE CONCEPTUAL RELATION BETWEEN THE CUT-OFF RADIUS OF INTERATOMIC POTENTIALS AND THE NUMBER OF NODES IN THE AFE IS ADDRESSED AND EXEMPLIFIED FOR THE 1D CASE. FOR THE 1D CASE ELEMENTS WITH 3, 5 AND 7 NODES WERE ADDRESSED. THE AFEM HAS BEEN USED TO DESCRIBE THE ME-CHANICAL BEHAVIOR OF ONE-DIMENSIONAL ATOMIC ARRAYS AS WELL AS TWO-DIMENSIONAL LATTICES OF ATOMS. THE EXAMPLES ALSO INCLUDED THE ANALYSIS OF PRISTINE DOMAINS, AS WELL AS DOMAINS WITH MISSING ATOMS, DEFECTS, OR VACANCIES. RESULTS ARE COMPARED WITH CLASSICAL MOLECULAR DYNAMIC SIMULATIONS (MD) PERFORMED USING A COMMERCIAL PACKAGE. THE RESULTS HAVE BEEN VERY ENCOURAGING IN TERMS OF ACCURACY AND IN THE COMPUTA-TIONAL EFFORT NECESSARY TO EXECUTE BOTH METHODOLOGIES, AFEM AND MD. THE METHODOLOGY CAN BE EXPANDED TO MODEL ANY DOMAIN DESCRIBED BY AN INTERATOMIC ENERGY POTENTIAL.
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