A Morphing framework to couple non-local and local anisotropic continua

In this article, we develop a method to couple anisotropic local continua with anisotropic non-local continua with central long-range forces. First, we describe anisotropic non-local models based on spherical harmonic descriptions. We then derive compatible classic continuum models. Finally, we apply the morphing method to these anisotropic non-local models and present three-dimensional numerical examples to validate the efficiency of the technique.

[1]  Huajian Gao,et al.  On the Modified Virtual Internal Bond Method , 2005 .

[2]  O. Anderson,et al.  Elastic constants of the central force model for cubic structures: Polycrystalline aggregates and instabilities , 1971 .

[3]  Nicolas Sau,et al.  Micropolar Peridynamic Constitutive Model for Concrete , 2007 .

[4]  T. L. Warren,et al.  A non-ordinary state-based peridynamic method to model solid material deformation and fracture , 2009 .

[5]  Mario Di Paola,et al.  The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions , 2010 .

[6]  Janet M. Thornton,et al.  Real spherical harmonic expansion coefficients as 3D shape descriptors for protein binding pocket and ligand comparisons , 2005, Bioinform..

[7]  G. Failla,et al.  Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory , 2009 .

[8]  R. Lehoucq,et al.  Peridynamic Theory of Solid Mechanics , 2010 .

[9]  Jifeng Xu,et al.  Peridynamic analysis of damage and failure in composites. , 2006 .

[10]  P. Demmie An Approach to Modeling Extreme Loading of Structures using Peridynamics , 2006 .

[11]  Yonggang Huang,et al.  Finite element implementation of virtual internal bond model for simulating crack behavior , 2004 .

[12]  Stewart Andrew Silling,et al.  Linearized Theory of Peridynamic States , 2010 .

[13]  Hui-Ming Cheng,et al.  The present status and key problems of carbon nanotube based polymer composites , 2007 .

[14]  E. Madenci,et al.  Prediction of crack paths in a quenched glass plate by using peridynamic theory , 2009 .

[15]  Christian Rey,et al.  A morphing strategy to couple non-local to local continuum mechanics , 2012 .

[16]  Weber,et al.  Computer simulation of local order in condensed phases of silicon. , 1985, Physical review. B, Condensed matter.

[17]  S. Silling,et al.  Peridynamic States and Constitutive Modeling , 2007 .

[18]  Youn Doh Ha,et al.  Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites , 2012 .

[19]  S. Silling Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[20]  Xiurun Ge,et al.  Micromechanical consideration of tensile crack behavior based on virtual internal bond in contrast to cohesive stress , 2005 .