Nonlocal elasticity and related variational principles

By C. Polizzotto. 2001

444 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2d62c6868a8502344f9c3d059fe6cd32e2a12fb3

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Continuous and discontinuous finite element methods for a peridynamics model of mechanics (2011, background): “Nonlocal theories in continuum mechanics have been introduced since at least the 1970s [18,19,25] and have recently become topical again [1–3,7,21,23,24,26,32,33].”
Nonlinear elasticity in nanostructured materials (2011, background): “Briefly, in nonlocal elasticity the algebraic constitutive equations are replaced by integral equations where the stress (or strain) at a given point depends on the strain (or stress) at that point as well as at all neighboring points in the material [50].”
Long-range cohesive interactions of non-local continuum faced by fractional calculus (2008, background): “In this context several strategies, which make use of variational formulations, have been recently proposed (Polizzotto, 2001, 2003).”
Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory (2017, unknown): “…relation for the two-phase constitutive model originally proposed by Eringen (1972a, 1987) has been recovered by other authors (Altan, 1989; Polizzotto, 2001; Pisano and Fuschi, 2003; Zhu and Dai, 2012; Benvenuti and Simone, 2013; Khodabakhshia and Reddy, 2015; Eptaimeros et al., 2016;…”
The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions (2010, background): “…2l ekj þ dkjk ehh ð12Þ where l ¼ b1l and k ¼ b1k, being l and k the Lamè elastic constants and b1 a dimensionless real coefficient, 0 6 b1 6 1, weighing the amount of local interactions (Polizzotto, 2001) in analogy to those non-local theories where the non-local elastic material is conceived as…”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, result): “[50]) who contributed to the field with important papers seem not to give explicit recognition that they were reformulating (and extending) the results already found by Piola.”