Nonlocal constitutive laws generated by matrix functions: Lattice Dynamics Models and their Continuum Limits
نویسندگان
چکیده
We analyze one-dimensional discrete and quasi-continuous linear chains of N >> 1 equidistant and identical mass points with periodic boundary conditions and generalized nonlocal interparticle interactions in the harmonic approximation. We introduce elastic potentials which define by Hamilton’s principle discrete “Laplacian operators” (“Laplacian matrices”) which are operator functions (N ×N -matrix functions) of the Laplacian of the Born-von-Karman linear chain with next neighbor interactions. The non-locality of the constitutive law of the present model is a natural consequence of the non-diagonality of these Laplacian matrix functions in the N dimensional vector space of particle displacement fields where the periodic boundary conditions (cyclic ∗Corresponding author, e-mail : [email protected], www : http://bit.ly/champs-fractelysees
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