Plane stress problems in nonlocal elasticity: finite element solutions with a strain-difference-based formulation

Abstract An enhanced computational version of the finite element method in the context of nonlocal strain-integral elasticity of Eringen-type is discussed. The theoretical bases of the method are illustrated focusing the attention on numerical and computational aspects as well as on the construction of the nonlocal elements matrices. Two numerical examples of plane stress nonlocal elasticity are presented to show the potentials and the limits of the promoted approach.

[1]  Paolo Fuschi,et al.  A nonhomogeneous nonlocal elasticity model , 2006 .

[2]  Paolo Fuschi,et al.  Nonlocal integral elasticity: 2D finite element based solutions , 2009 .

[3]  Harm Askes,et al.  Implicit gradient elasticity , 2006 .

[4]  C. Polizzotto Unified thermodynamic framework for nonlocal/gradient continuum theories , 2003 .

[5]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[6]  A. Waas,et al.  Non-local modeling of epoxy using an atomistically-informed kernel , 2013 .

[7]  A. Eringen,et al.  Theory of Nonlocal Elasticity and Some Applications , 1984 .

[8]  P. Fuschi,et al.  Closed form solution for a nonlocal elastic bar in tension , 2003 .

[9]  Dominik Rogula,et al.  Introduction to Nonlocal Theory of Material Media , 1982 .

[10]  E. Aifantis,et al.  Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results , 2011 .

[11]  David R. Owen,et al.  FINITE ELEMENT PROGRAMMING , 1980, The Finite Element Method Using MATLAB.

[12]  Castrenze Polizzotto,et al.  A unifying variational framework for stress gradient and strain gradient elasticity theories , 2015 .

[13]  Andrei V. Metrikine,et al.  Mechanics of generalized continua : one hundred years after the Cosserats , 2010 .

[14]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[15]  Z. Bažant,et al.  Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories , 1993 .

[16]  John Peddieson,et al.  Application of nonlocal continuum models to nanotechnology , 2003 .

[17]  Paolo Fuschi,et al.  A strain-difference-based nonlocal elasticity model , 2004 .

[18]  A. Eringen,et al.  Nonlocal Continuum Field Theories , 2002 .

[19]  E. Aifantis On the role of gradients in the localization of deformation and fracture , 1992 .

[20]  J. Awrejcewicz,et al.  Improved Continuous Models for Discrete Media , 2010 .

[21]  Paolo Fuschi,et al.  Finite element solutions for nonhomogeneous nonlocal elastic problems , 2009 .

[22]  Anthony M. Waas,et al.  Non-local continuum modeling of carbon nanotubes: physical interpretation of non-local kernels using atomistic simulations , 2011 .

[23]  F. Scarpa,et al.  On the asymptotic crack-tip stress fields in nonlocal orthotropic elasticity , 2014 .

[24]  C. Polizzotto,et al.  A method to transform a nonlocal model into a gradient one within elasticity and plasticity , 2014 .

[25]  E. Aifantis Update on a class of gradient theories , 2003 .

[26]  Anthony M. Waas,et al.  Construction of multi-dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data , 2014 .

[27]  A. Cemal Eringen,et al.  Stress concentration at the tip of crack , 1974 .

[28]  Castrenze Polizzotto,et al.  Nonlocal elasticity and related variational principles , 2001 .

[29]  R. C. Picu On the functional form of non-local elasticity kernels , 2002 .

[30]  Castrenze Polizzotto,et al.  Stress gradient versus strain gradient constitutive models within elasticity , 2014 .

[31]  Milan Jirásek,et al.  Nonlocal integral formulations of plasticity and damage : Survey of progress , 2002 .

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

[33]  A. Eringen On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .