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On Defect Energy in Elasticity

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image of Multidiscipline Modeling in Materials and Structures

In plane elasticity, a general expression for a mutual work difference integral (MWDI) derived from two stress fields is introduced. Once two physical stress fields are known beforehand, the relevant MWDI can be evaluated exactly from the coefficients in the complex potentials. A biaxial tension model for evaluating defect energy is introduced. A particular MWDI from two fields, one is for the damaged medium under remote biaxial tension and other is for an infinite perfect plate under the same remote biaxial tension, can be defined as a suitable measure of stiffness for the damaged medium, which is called the defect energy (E(α)). The suggested model can deal with the cracks, holes, and elastic inclusions in a unique way. The model can also evaluate the defect energies for different damages exactly without dependence on the orientation of damages. Physically, the higher is the defect energy achieved, the more are the involved damages in the medium. The defect energy may be negative, which means a more rigid inclusion is included in the medium. For 3D-elasticity, a triaxial tension model is introduced for evaluating the defect energy for the damaged medium. For some particular cases, for example, the dissimilar elastic spherical inclusion, or the elliptic flat crack, the relevant defect energies are evaluated.


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