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Title of Journal: Comput Mech

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Abbravation: Computational Mechanics

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Springer Berlin Heidelberg

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DOI

10.1007/978-1-4615-6790-5_1

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1432-0924

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The total and updated lagrangian formulations of s

Authors: Guy L Bergel Shaofan Li
Publish Date: 2016/05/11
Volume: 58, Issue: 2, Pages: 351-370
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Abstract

The peridynamics theory is a reformulation of nonlocal continuum mechanics that incorporates material particle interactions at finite distances into the equation of motion Statebased peridynamics is an extension of the original bondbased peridynamics theory wherein the response of an individual particle depends collectively on its interaction with neighboring particles through the concept of state variables In this paper the more recent nonordinary statebased Peridynamics formulations of both the total referential Lagrangian approach as well as the updated spatial Lagrangian approach are formulated In doing so relations of the state variables are defined through various nonlocal differential operators in both material and spatial configurations in the context of finite deformation Moreover these nonlocal differential operators are mathematically and numerically shown to converge to the local differential operators and they are applied to derive new force states and deformation gradients

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  2. A first order method for the Cauchy problem for the Laplace equation using BEM
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