Ordinary state-based peridynamic model for geometrically nonlinear analysis

Abstract

This study presents a novel ordinary state-based peridynamic model for geometrically nonlinear analysis. A new definition of logarithmic bond stretch for large deformations has been proposed. The peridynamic formulations for one-dimensional, two-dimensional and three-dimensional structures are obtained based on the principle of virtual displacements by using Total Lagrange formulation. The capability of the developed peridynamic model is demonstrated by predicting large deformations for a bar, a plate, and a three-dimensional structure. To further demonstrate the capabilities of the proposed model, damage on a plate and a three-dimensional structure are simulated.

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

“…Peridynamics can be applicable for both elastic and plastic materials [6][7][8][9][10], composite and polycrystalline materials [11][12][13][14][15][16], multiphysics [17][18][19], large deformation problems [20], topology optimization [21] and multiscale modeling [22,23]. Peridynamics can also be suitable for structural idealization to analyze slender structures by using PD beam models [24][25][26][27] or thin wall structures by using PD plate and shell models [27][28][29][30][31][32].…”

An energy-based peridynamic model for fatigue cracking

“…Meanwhile, the interaction passing a point inside the crack can be counted as 1 interaction. For a horizon size 3.015 x    , there are 48 interactions passing the unit crack surface, in which 24 interactions passing the crack tips [31,49]. Therefore, the total number of interactions passing the unit crack surface can be counted as 24 24 / 2 36…”

“…Peridynamics can be applicable for both elastic and plastic materials and large deformation problems [26][27][28][29][30][31]. It is also applied for composite and polycrystalline materials [32][33][34][35][36].…”

Peridynamic model for visco-hyperelastic material deformation in different strain rates

“…in which N c represents the number of interactions creating a unit crack surface. For 2-D model with a horizon size of δ = 3.015 x, the total number of interactions passing through a unit crack surface can be calculated as N c = 36 [42,43]. Therefore, the failure criteria for each interaction can be expressed as…”