The peridynamic equation of motion in non-local elasticity theory

The influence function in the peridynamic theory is used to weight the contribution of all the bonds participating in the computation of volume-dependent properties. In this work, we use influence functions to establish relationships between bond-based and state-based peridynamic models. We also demonstrate how influence functions can be used to modulate nonlocal effects within a peridynamic model independently of the peridynamic horizon. We numerically explore the effects of influence functions by studying wave propagation in simple one-dimensional models and brittle fracture in three-dimensional models.

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“…For p = 0, (i.e., the PMB model (3.7)) we recover the result of Emmrich and Weckner (2006), β 0 = 18K/5δ 2 .…”

Section: Second Examplesupporting

confidence: 77%

On the Role of the Influence Function in the Peridynamic Theory

Seleson

Parks

2011

Int J Mult Comp Eng

159

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“…For the special case of proportional materials [10,12,24], it follows from (3)-(5) that CðnÞ ¼ c n n jnj 3 ; i:e:; C ij ðnÞ ¼ c…”

Section: A Linearized Peridynamics Model For Microelastic Materialsmentioning

confidence: 99%

Continuous and discontinuous finite element methods for a peridynamics model of mechanics

Chen

Gunzburger

2011

Computer Methods in Applied Mechanics and Engineering

233

187

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“…It is explained in [21] how the general state-based PD material model converges to the continuum elasticity model as the ratio of the PD horizon to effective length scale decreases, assuming that the underlying deformation is sufficiently smooth. Some results on the existence and uniqueness of L 2 solutions of the PD models associated with bounded integral PD operators have been given in [8][9][10]. Though much of the focus of [1] is on developing homogenization theory for the PD model, some existence and uniqueness results are also provided, again for bounded integral PD operators.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis for the peridynamic nonlocal continuum theory

Du¹,

Zhou²

2010

ESAIM: M2AN

135

116

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Abstract.We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.Mathematics Subject Classification. 45A05, 46N20, 74B99.

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The peridynamic equation of motion in non-local elasticity theory

Abstract: Abstract. Non-local theories in solid mechanics that account for effects of long-range inter

Cited by 22 publications

References 34 publications

On the Role of the Influence Function in the Peridynamic Theory

On the Role of the Influence Function in the Peridynamic Theory

Continuous and discontinuous finite element methods for a peridynamics model of mechanics

Mathematical analysis for the peridynamic nonlocal continuum theory

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