On assessing the tensile cracking pattern in brittle rocks and solids

Bulletin of Engineering Geology and the Environment - This work aims to identify fracture pattern and crack growth mode in brittle rocks and solids under induced tensile stresses, and further...     

Numerical analysis of peridynamic and classical models in transient heat transfer,employing Galerkin approach

The main scope of this research is to study transient heat transfer based on combined peridynamic theory and classical model. The principle of the energy conservation is used to develop the governing equation in case of existing both classical and peridynamic heat transfer mechanisms. The integro‐differential equation is developed containing the classical coefficient of heat conduction and peridynamic kernel function. To solve the equation, a spectral method based on a series solution in accordance with Gelerkin approach is implemented. Trapezoidal method is employed to compute the integral terms. Implicit Euler method is used to numerically solve the problem in time domain. In part of numerical studies, different kernel functions are attributed to the peridynamic coefficient of heat transfer. Relevant constraints are applied for making equivalency between classical and each of the peridynamic kernel functions. To ensure the accuracy of the numerical results, adequate convergence analyses are conducted. The results related to a few cases are compared to relevant data reported in the open literature showing good agreements. Moreover, comparisons are made to observe probable variations versus time. In case studies, effects of the nonlocal range on the heat transfer were studied.