Peridynamic State-Based Models and the Embedded-Atom Model

Abstract

Abstract. We investigate connections between nonlocal continuum models and molecular dynamics. A continuous upscaling of molecular dynamics models of the form of the embedded-atom model is presented, providing means for simulating molecular dynamics systems at greatly reduced cost. Results are presented for structured and structureless material models, supported by computational experiments. The nonlocal continuum models are shown to be instances of the state-based peridynamics theory. Connections relating multibody peridynamic models and upscaled nonlocal continuum models are derived.

Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations

“…In Table 2, we present the influence functions used for the numerical studies in Section 5.1, and indicate their regularity and the corresponding constant c (cf. (26)). In Section 5.1, we present computational results comparing the performance of the different algorithms in numerical integration, for different QoIs.…”

“…The GPMB model (26) reduces to the PMB model [4] for ω(∥ · ∥) ≡ 1. 2 We study influence functions with different regularities, having a finite support.…”

“…Moreover, influence functions have been used in [37,38] to weight the contribution of bonds to the interaction between a PD point and its neighborhood. Influence functions have also been used to connect PD models in [26,37] and to introduce damage mechanisms in [38][39][40][41].…”

“…Under such discretization, peridynamic governing equations possess similar computational structure as molecular dynamics equations; thus, peridynamics has been implemented in molecular dynamics software [23,24]. In fact, peridynamics can be connected to molecular dynamics through a continuous upscaling process, as demonstrated in [25,26]. Other discretization approaches for the strong form of peridynamic equations have been proposed in the literature.…”

Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems

“…Also see other related engineering applications [16,35,37,51,50], the review and news articles [18,21,41] for a comprehensive discussion, and the recent book [43]. In addition, we witness a major effort to meet the need for a mathematical theory for PD applications and related nonlocal problems addressing, for instance, conditioning analysis, domain decomposition and variational theory [2,3,4], volume constraints [18], nonlinearity [23,24,25,42], discretization [1,4,28,63], numerical methods [17,19,22,54], and various other aspects [5,20,26,27,33,39,40,44,45,46,56,57,65].…”