51 citations · 199 across the 12 of their papers we have counts for
12 papers
Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures
Huaiqian You, Xiao Xu, Yue Yu +3
Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation…
Multi-Output Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Uncertainties
Mingyuan Yang, John T. Foster
Physics-informed neural networks (PINNs) have recently been used to solve various computational problems which are governed by partial differential equations (PDEs). In this paper,…
Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves
Xiao Xu, Marta D'Elia, Christian Glusa +1
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models ha…
Coupling of IGA and Peridynamics for Air-Blast Fluid-Structure Interaction Using an Immersed Approach
Masoud Behzadinasab, Georgios Moutsanidis, Nathaniel Trask +2
We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena…
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
Yu Leng, Xiaochuan Tian, Leszek Demkowicz +2
We present a Petrov-Gelerkin (PG) method for a class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm…
A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems
Xiao Xu, Christian Glusa, Marta D'Elia +1
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem wher…
A machine-learning framework for peridynamic material models with physical constraints
Xiao Xu, Marta D'Elia, John T. Foster
As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an…
A unified, stable and accurate meshfree framework for peridynamic correspondence modeling. Part II: wave propagation and enforcement of stress boundary conditions
Masoud Behzadinasab, John T. Foster, Yuri Bazilevs
The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the corresponden…
Deriving peridynamic influence functions for one-dimensional elastic materials with periodic microstructure
Xiao Xu, John T. Foster
The influence function in peridynamic material models has a large effect on the dynamic behavior of elastic waves and in turn can greatly effect dynamic simulations of fracture pro…
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
Yu Leng, Xiaochuan Tian, Nathaniel A. Trask +1
In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilata…
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Yu Leng, Xiaochuan Tian, Nathaniel Trask +1
Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation…
On the stability of the generalized, finite deformation correspondence model of peridynamics
Masoud Behzadinasab, John T. Foster
A class of peridynamic material models known as constitutive correspondence models provide a bridge between classical continuum mechanics and peridynamics. These models are useful…