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چكيده انگليسي :

Damage Modeling of Quasi Brittle Materials with Micro Plane Theory Meisam Asgari m asgari@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 irAbstractThe aim of this thesis is to extend a damage model for quasi brittle materials based on the so called Micro plane theory with its most important and thermodynamically consistent approach the V D split Micro planetheory yields a simple constitutive equation relating the macroscopic stress or strain tensor to theircomponents on different planes at each material point Traditional approaches of microplane theory such asthe normal tangential projection with one or two tangential components and the V D T split do not satisfy thesecond law of thermodynamics Among all approaches of microplane theory the formulation with V D splitis consistent with the second law of thermodynamics In this research the thermodynamically consistency ofthe V D micro plane model is clearly shown by extracting the same Material Jacobian Matrix as that of thelinear elasticity by extracting a symmetric material Jacobian matrix Damage mechanics is a new branch in mechanical engineering that deals with the science of growth andincreasing the size of microcracks and microvoids in engineering material in order to predict the materialresponse in a more precise way Because damage is naturally an anisotropic characteristic of material continuum damage mechanics which considers damage as an isotropic property of the material can notformulate the anisotropy of damage unless damage be considered as a complex forth or eighth order tensor ateach material point These assumptions in formulating anisotropic damage cause several complexities indealing with difficult mathematical calculations The aim to use Micro plane theory to formulate the damageis its ability to incorporate anisotropic behavior of damage in a natural and simple way In this research thedamage parameters of each Micro plane have been considered as dependent parameters to the normal vectorof the relevant Micro plane In previous researches the damage parameters have been simply assumed to bethe same for all of the micro planes In those researches the results seemed reasonable however in thepresent work not only the results are rational but also the model is a more reliable continuum based one The presented model is then implemented in a VUMAT subroutine in ABAQUS and is applied to solve somedefinite problems like simple shear and uniaxial tension The responses of quasi brittle materials under simple tension and simple shear are combined of two majorparts in the first part the material shows a linear elastic behavior which does not include damage In thesecond part which commences at the elastic limit an exponential softening response is observed based onexperimental tests on quasi brittle materials In order to appraise the results of the extracted model a macroscopic damage model based on linear elasticityand continuum damage mechanics is developed and implemented via a VUMAT subroutine in ABAQUS The results of these two models are compared and analyzed It is obvious from the results that the response ofMicroplane damage formulation is very similar to the results of macroscopic damage formulation Furthermore after progressive loading it is observed that the response of microplane damage modelconverges to the response of the macroscopic model Keywords Quasi brittle materials Microplane theory Damage mechanics

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مدل سازي آسيب مواد شبه ترد با استفاده از تئوري ميكرو- صفحه

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