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Carnegie Mellon Center for Nonlinear Analysis
Mathematical Analysis of the Nonlocal State Based Peridynamic Models


Kun Zhou
Penn State University
Department of Mathematics

Abstract: We develop a calculus for nonlocal operator of vector-valued functions. It allows us to reduce the regularity requirements associated with the classical identities. We then use the nonlocal calculus to reformulate the linear peridynamic state models, and to show that under certain stability condition and some mild requirements on the influence functions, the state model is well-posed, and its energy space is equivalent to the L2 space. We also relate the local limit of the linear peridynamic state model to the Navier equation of linear elasticity with arbitrary Poisson ratio.