Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.