MATHEMATICAL ANALYSIS FOR THE PERIDYNAMIC NONLOCAL CONTINUUM THEORY

166 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

NONLOCAL KORN-TYPE CHARACTERIZATION OF SOBOLEV VECTOR FIELDS (2012, background): “Significant progress has been made in this direction in [1, 10–12, 16, 22].”
Continuous and discontinuous finite element methods for a peridynamics model of mechanics (2011, background): “Finally, in Appendix A, we discuss the well-posedness of the variational formulation given in Section 4; in particular, we show that associated bilinear form is continuous and coercive; see also [10] [12] [17] [35] [36].”
ON THE ROLE OF THE INFLUENCE FUNCTION IN THE PERIDYNAMIC THEORY (2011, methodology): “In particular , this case has been analyzed in Zhou and Du (2010) and in Du and Zhou (2010).”
Peridynamic Theory of Solid Mechanics (2010, background): “Alali and Lipton [3], Du and Zhou [18, 19], and Emmrich and Weckner [20, 21] establish various existence and uniqueness results for the linear peridynamic balance of momentum.”
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, methodology): “An inspiration for this paper is to extend results of [29, 51] and [4, Chap.”
Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity (2013, background): “Results similar to those in Theorem 4 have been established for the peridynamic bond-based model; see for instance, [4,11,12].”