مدل سازي و تحليل اجزاي محدود آسيب غير محلي به روش ميكرو-صفحه

چكيده انگليسي :

Micro Plane Modeling and Finite Element Analysis of Nonlocal Damage Neda Latifi Alavijeh n latifialavijeh@me iut ac ir July 21 2011 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiDr Mahmoud Kadkhodaei kadkhodaei@cc iut ac irDr Mohammad Mashayekhi mashayekhi@cc iut ac irAbstractIn many structures subjected to extreme loading conditions the initially smooth distribution of strain changesinto a highly localized one Typically the strain increments are concentrated in narrow bands while themajor part of the structure experiences unloading The size of the localized band and its evolution depend ondetails of the material microstructure Besides the mathematcal and numerical failure models must correctly reflect the energy dissipated in thefracture zone however continuum damage description of failure mechanisms generally exhibits strainsoftening In numerical simulations employing standard damage theory strain softening causes a severedependence on the size and orientation of the finite element discretization As a consequence upon meshrefinement the energy dissipated by the numerical model decreases and tends to extremely low values sometimes even to zero Therefore the numerical solution is not able to define the physical response of thematerial in a correct way On the other hand damage is an anisotropic material characteristic however it is considered to be isotropicin conventional damage models such as the primitive models of continuum damage mechanics The contribution of this research is to present an anisotropic continuum damage model based on the so calledmicroplane concept with its most reliable and thermodynamically consistent approach the V D split Theprevious research on such a topic has been carried out by the use of another approach of microplane theorywhich is called the V D T split Although the results of that research seem to be correct the model can not beconsidered as a thermodynamically consistent approach of the theory of microplane The aim to usemicroplane theory in damage modeling is its ability to incorporate anisotropic behavior of damage in anatural and simple way Choosing the implicit gradient enhanced approach as for nonlocal damage modeling the strain tensor has been considered as the nonlocal parameter A second partial differential equation has tobe solved in addition to the equations of equilibrium In practical simulations the differential equations governing the material response are solved numerically Additional nodal degrees of freedom are introduced which lead to a modified element formulation Firstly finite element analysis of the extended formulation has been carried out In order to do the finite elementanalysis the weak forms of equilibrium equations accompanied by the implicit gradient enhanced equationshave been simultaneously solved through discretization and linearization of the corresponding equations Theresult of this solution is to extend the stiffness matrix and the internal and external force vectors Solving thisset of nonlinear equations a consistent incremental iterative Newton Raphson solution procedure has beenapplied A UEL User element subroutine has been extended in order to introduce a new element which hasnot been available in ABAQUS library as well as using the software solver as the Newton Raphson optimumsolver among all of the possible solvers For a two dimensional plane strain example numerical solutions are presented They show the effectivenessof the gradient dependence as a measure against mesh sensitivity Upon mesh refinement the numericalsolution shows a consistent material response for different numbers of meshes Besides by increasing thecharacteristic length the material shows a less flexible behavior which seems to be more similar to the realmaterial behavior Keywords Nonlocal continuum Gradient enhanced Microplane theory Damage mechanics Finite elementmethod

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مدل سازي و تحليل اجزاي محدود آسيب غير محلي به روش ميكرو-صفحه

مكانيك آسيب , محيط پيوسته ي غير محلي , گراديان منحني