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Development of an Adaptive Model for Coupling the Meshfree Peridynamics to the Finite Element Method
, Ph.D. Dissertation Sharif University of Technology ; Kouchakzadeh, Mohammad Ali (Supervisor)
Abstract
The presence of spatial partial derivatives in the equations of classical continuum mechanics has led to the fact that methods based on this theory are not valid in displacement discontinuities (such as cracks). The peridynamic theory is a nonlocal formulation of solid mechanics which is most suited to model discontinuities and dynamic fractures in continuous or discrete media. By substituting integral expressions instead of partial differentials in the equations of motion, peridynamics provides an integrated model that is valid and the same in continuous, discontinuous, and discrete media.The capability of the peridynamic theory in modeling discontinuities and cracks has been demonstrated...
A variable horizon method for coupling meshfree peridynamics to FEM
, Article Computer Methods in Applied Mechanics and Engineering ; Volume 355 , 2019 , Pages 308-322 ; 00457825 (ISSN) ; Kouchakzadeh, M. A ; Sharif University of Technology
Elsevier B.V
2019
Abstract
Peridynamics is a nonlocal reformulation of solid mechanics which can reproduce the solution of classical continuum mechanics as its horizon approaches zero. Taking this idea into consideration, we proposed a new coupling approach between meshfree peridynamics and finite element method. An intermediate variable horizon element called “morakkab” is introduced to transfer force and momentum between peridynamic and FEM regions. In the original peridynamic formulation, artificial ghost forces will arise if the horizon varies with position; The creation of these artifacts is avoided by utilizing a modified peridynamic equation of motion based on the concept of co-family. The accuracy of the...