The effect of long-range forces on the dynamics of a bar

By Olaf Weckner, R. Abeyaratne. 2005

257 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/eee6781000641a46f172e732f9f3866f8c691bd8

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Peridynamic Theory of Solid Mechanics (2010, background): “As shown in [75], this C is related to the Young’s modulus E that would be measured in the static extension of a long bar by”
Crack nucleation in a peridynamic solid (2010, background): “(24) On the other hand, the tangent modulus (Weckner and Abeyaratne 2005) is given by E = δ∫ 0 ξ2C(ξ) dξ.”
An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis (2015, background): “According to the requirements concluded in [5,7,9,34], the kernel function gðξ; δÞ which reflects the distribution of the intensity of long-range forces in materials should hold the following relations:”
Convergence, adaptive refinement, and scaling in 1D peridynamics (2009, unknown): “We note that the smoothing regularization of the micromodulus function given in [39] is not necessary.”
On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity (2007, background): “From studying particular nonlinear dispersion relations for the one-dimensional infinite peridynamic bar, it has already been known that the peridynamic integral operator equals for smooth functions a differential operator of infinite order that is the series of derivatives of even order (cf. Weckne”
A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks (2018, methodology): “Some representative studies were conducted using peridynamics, such as the dynamic fracture of homogeneous and heterogeneous bar (Weckner and Abeyaratne 2005a; Weckner and Emmrich 2005b), damage and fracture of membranes and fibers (Kilic et al. 2009; Cheng et al. 2018), brittle fracture of…”
Peridynamics via finite element analysis (2007, background): “012 has been proposed that does not require spatial derivatives to be evaluated within a body [1–6].”
Peridynamic States and Constitutive Modeling (2007, background): “Recent theoretical work on the peridynamic model includes the study of discontinuities and other mathematical aspects of deformations in one-dimensional constitutively linear bodies [5, 6].”