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Recently, Verlinde has suggested a novel model of duality between thermodynamics and gravity which leads to an emergent phenomenon for the origin of gravity and general relativity. In this paper, we investigate some features of this model in the presence of noncommutative charged black hole by performing the method of coordinate coherent states representing smeared structures.We derive several quantities, e.g. temperature, energy and entropic force. Our approach clearly exhibits that the entropic force on a smallest fundamental cell of holographic surface with radius r 0 is halted. Accordingly, we can conclude that the black hole remnants are absolutely inert without gravitational interactions. So, the equivalence principle of general relativity is contravened due to the fact that it is now possible to find a difference between the gravitational and inertial mass.In other words, the gravitational mass in the remnant size does not emit any gravitational field, therefore it is experienced to be zero, contrary to the inertial mass. This phenomenon illustrates a good example for a feasible experimental confirmation to the entropic picture of Newton's Second law in very short distances.

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In this article, the effects of plastic anisotropy and damage on ductile crack initiation (ductile failure) are studied in a thermodynamically consistent framework. First, isotropic and anisotropic continuum damage models of Lemaitre are modified to incorporate anisotropic plasticity. In the next stage, a subroutine is developed to add the damage formulation to Abaqus finite element package. A highly ductile material with anisotropic plastic behavior, API 5L X100 pipeline steel, is selected for this study. Finite element analyses are done to simulate isotropic/anisotropic plasticity coupled with isotropic/anisotropic damage. Finite element results are compared with the result of tests on smooth and notched specimens, and the effects of anisotropic plasticity, anisotropic damage, geometry changes, triaxiality in stress and their mutual effects and interactions on post yield behavior and crack initiation are studied.

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