Erratum: “A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems” [ASME Journal of Applied Mechanics, 1997, 64(1), pp. 23–31]

1998 ◽  
Vol 65 (4) ◽  
pp. 1068-1068
Author(s):  
Jungki Lee ◽  
Ajit Mal
Keyword(s):  
Integral Equation ◽  
Crack Interaction ◽  
Applied Mechanics ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Multiple Inclusion ◽  
Asme Journal

A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems

1997 ◽  
Vol 64 (1) ◽  
pp. 23-31 ◽  
Author(s):  
Jungki Lee ◽  
Ajit Mal
Keyword(s):  
Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Interfacial Stress ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Integral Methods ◽  
Multiple Inclusion ◽  
Interface Layers ◽  
Volume Integral Equation Method

A volume integral equation method is introduced for the solution of elastostatic problems in heterogeneous solids containing interacting multiple inclusions, voids, and cracks. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions and cracks. The influence of interface layers on the interfacial stress field is investigated. The stress intensity factors for microcracks in the presence of interacting inclusions or voids are also calculated for a variety of model geometries. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and boundary integral methods.

The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials

2014 ◽  
Vol 1030-1032 ◽  
pp. 223-227
Author(s):  
Lin Fan ◽  
Song Rong Qian ◽  
Teng Fei Ma
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Numerical Integration ◽  
Integration Method ◽  
Equation Of Motion ◽  
Numerical Integration Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Method Of Molecular Dynamics ◽  
Classic Theory

In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

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