48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 2007
DOI: 10.2514/6.2007-2314
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Damage and Failure Analysis based on Peridynamics - Theory and Applications

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Cited by 12 publications
(6 citation statements)
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“…A computer solution to one of the Kalthoff-Winkler problems (Kalthoff & Winkler, 1988), which is regarded in the computational fracture mechanics community as an important benchmark problem, is presented in Silling (2003). Additional examples, as well as more details about the numerical method, are discussed in Silling and Askari (2005), Weckner, Askari, Xu, Razi, and Silling (2007).…”
Section: Summary Of the Literaturementioning
confidence: 99%
“…A computer solution to one of the Kalthoff-Winkler problems (Kalthoff & Winkler, 1988), which is regarded in the computational fracture mechanics community as an important benchmark problem, is presented in Silling (2003). Additional examples, as well as more details about the numerical method, are discussed in Silling and Askari (2005), Weckner, Askari, Xu, Razi, and Silling (2007).…”
Section: Summary Of the Literaturementioning
confidence: 99%
“…As can be seen from equation (27), the micromodulus needed for triclinic materials is significantly more involved than the one for orthotropic materials (see Mikata [1]). Substituting equation ( 27) into equation ( 18), we obtaiñ…”
Section: Triclinic Peridynamic Materialsmentioning
confidence: 99%
“…After examining the resulting equations, it can be seen that, out of 54 equations represented by equation ( 32), 18 equations are repeated. Therefore, equation (32) represents a system of 36 equations for 36 unknown constants p i , q i , r i , l i , m i , and n i (i = 1, ., 6) used for defining the micromodulus C(j) given in equation (27). Substituting equation ( 27) into the resulting equation obtained from equation (32), performing some algebra, and solving the resulting equation for the 36 unknown constants p i , q i , r i , l i , m i , and n i (i = 1, ., 6), we finally obtain…”
Section: Triclinic Peridynamic Materialsmentioning
confidence: 99%
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“…Therefore, theoretical and numerical challenges arise from how to mathematically impose inhomogeneous Neumann-type boundary conditions properly in the nonlocal model. For instance, in the peridynamic theory of solid mechanics [54,33,19,4,61,59,32,39,28,36,40,56], the classical description of material deformation locally via a deformation gradient is replaced by a nonlocal interaction described with integral operators. In these models, it has been shown that the careless imposition of traction conditions on the nonlocal boundary induces an unphysical strain energy concentration, leading in turn to the material being softer near the boundary.…”
Section: Introductionmentioning
confidence: 99%