The book covers all basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact ...kinematics and resolution schemes both for sequential and parallel computer architectures. The book is self-consistent and is intended for people working on implementation and improvement of contact algorithms in a finite element software. The book contains numerous examples and figures to make the material accessible for a broad audience. The book combines extended introductory parts with new developments, so it is accessible for freshmen in computational contact and is of interest for established researchers. Using a new tensor algebra, we introduce some original notions in contact kinematics and extend the classical formulation of contact elements. We discuss robust and efficient contact detection algorithms both for sequential and parallel computer architectures. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are given. Many validation problems and tests are presented.
The Mohr–Coulomb (M–C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids. This criterion has been extensively used in rock and soil ...mechanics as it correctly accounts for the effects of hydrostatic pressure as well as the Lode angle parameter. It turns out that these two parameters, which are critical for characterizing fracture of geo-materials, also control fracture of ductile metals (Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins et al. 1980). The local form of the M–C criterion is transformed/extended to the spherical coordinate system, where the axes are the equivalent strain to fracture
, the stress triaxiality η, and the normalized Lode angle parameter
. For a proportional loading, the fracture surface is shown to be an asymmetric function of
. A detailed parametric study is performed to demonstrate the effect of model parameters on the fracture locus. It was found that the M–C fracture locus predicts almost exactly the exponential decay of the material ductility with stress triaxiality, which is in accord with theoretical analysis of Rice and Tracey (1969) and the empirical equation of Hancock and Mackenzie (1976), Johnson and Cook (1985). The M–C criterion also predicts a form of Lode angle dependence which is close to parabolic. Test results of two materials, 2024-T351 aluminum alloy and TRIP RA-K40/70 (TRIP690) high strength steel sheets, are used to calibrate and validate the proposed M–C fracture model. Another advantage of the M–C fracture model is that it predicts uniquely the orientation of the fracture surface. It is shown that the direction cosines of the unit normal vector to the fracture surface are functions of the “friction” coefficient in the M–C criterion. The phenomenological and physical sound M–C criterion has a great potential to be used as an engineering tool for predicting ductile fracture.
The computational modeling of failure mechanisms in solids due to fracture based on
sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a
...diffusive crack modeling based on the introduction of a crack phase field. Following our recent work C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically-consistent phase field models of fracture: Variational principles and multi-field fe implementations, International Journal for Numerical Methods in Engineering DOI:10.1002/nme.2861 on phase-field-type fracture, we propose in this paper a new variational framework for rate-independent diffusive fracture that bases on the introduction of a
local history field. It contains a maximum reference energy obtained in the deformation history, which may be considered as a measure for the maximum tensile strain obtained in history. It is shown that this local variable drives the evolution of the crack phase field. The introduction of the history field provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a new algorithmic treatment of diffusive fracture. Here, we propose an extremely
robust operator split scheme that successively updates in a typical time step the history field, the crack phase field and finally the displacement field. A regularization based on a viscous crack resistance that even enhances the robustness of the algorithm may easily be added. The proposed algorithm is considered to be the canonically simple scheme for the treatment of diffusive fracture in elastic solids. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples.
Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the ...traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh. This book will cover the fundamental and practical application of LBM. The first part of the book consists of three chapters starting form the theory of LBM, basic models, initial and boundary conditions, theoretical analysis, to improved models. The second part of the book consists of six chapters, address applications of LBM in various aspects of computational fluid dynamic engineering, covering areas, such as thermo-hydrodynamics, compressible flows, multicomponent/multiphase flows, microscale flows, flows in porous media, turbulent flows, and suspensions.
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