33 research outputs found

    Neuroendocrinology: A science for psychosomatic medicine

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    From fractal media to continuum mechanics

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    This paper presents an overview of modeling fractal media by continuum mechanics using the method of dimensional regularization. The basis of this method is to express the balance laws for fractal media in terms of fractional integrals and, then, convert them to integer-order integrals in conventional (Euclidean) space. Following an account of this method, we develop balance laws of fractal media (continuity, linear and angular momenta, energy, and second law) and discuss wave equations in several settings (1d and 3d wave motions, fractal Timoshenko beam, and elastodynamics under finite strains). We then discuss extremum and variational principles, fracture mechanics, and equations of turbulent flow in fractal media. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions and reduce to conventional forms for continuous media with Euclidean geometries upon setting the dimensions to integers. We also point out relations and potential extensions of dimensional regularization to other models of microscopically heterogeneous physical systems

    Impact damage assessment by using peridynamic theory

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    This study presents an application of peridynamic theory for predicting residual strength of impact damaged building components by considering a reinforced panel subjected to multiple load paths. The validity of the approach is established first by simulating a controlled experiment resulting in mixed-mode fracture of concrete. The agreement between the PD prediction and the experimentally observed behavior is remarkable especially considering the simple material model used for the concrete. Subsequently, the PD simulation concerns damage assessment and residual strength of a reinforced panel under compression after impact due to a rigid penetrator
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