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Strain Problems (strain + problem)
Selected AbstractsExperimental and numerical studies on dynamic crack growth in layered slate rock under wedge impact loads: part II , non-plane strain problemFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2007M. R. ALAM ABSTRACT Dynamic crack propagation in non-plane strain (or 3D) slate blocks under wedge impact loads was investigated numerically in this part of the paper. A parabolic-shaped crack trajectory was taken into consideration to model the crack propagation in slate blocks for analyzing the impact splitting of layered slate rock. Major and minor axes of the parabola were determined from the condition of equal mode I stress intensity factors (SIFs) along the crack front. Mode I SIFs were determined for experimental breaking loads for each increment of crack growth in a manner similar to that mentioned in part I of this paper. These values were compared with the plane strain material fracture toughness value obtained from experimental studies and very good agreement was obtained between them, for the case of actual load applied on the specimen. Numerical analysis of a field problem, i.e., separation of a large-sized slate slab from the rock strata in a slate quarry using wedge impacting, was also carried out in this paper. It can be observed that a large magnitude of load is required to break large-sized slate blocks; but this load is applied through a number of smaller load-capacity actuators-in-parallel, requiring large power capacity for the hydraulic pumps. However, this required power could be reduced considerably if the load applied on the line of hydraulic actuators is cascaded across the (line of) actuators (starting from centrally placed actuators) with a small time delay (equal to the initial crushing time in slate rock). [source] A geometric-based algebraic multigrid method for higher-order finite element equations in two-dimensional linear elasticityNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2009Yingxiong Xiao Abstract In this paper, we will discuss the geometric-based algebraic multigrid (AMG) method for two-dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and higher-order finite element space. And then a geometric-based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high-order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd. [source] Modelling poroelastic hollow cylinder experiments with realistic boundary conditionsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2004S. Jourine Abstract A general poroelastic solution for axisymmetrical plane strain problems with time dependent boundary conditions is developed in Laplace domain. Time-domain results are obtained using numerical inversion of the Laplace transform. Previously published solutions can be considered as special cases of the proposed solution. In particular, we could reproduce numerical results for solid and hollow poroelastic cylinders with suddenly applied load/pressure (Rice and Cleary, Rev. Geophys. Space Phys. 1976; 14:227; Schmitt, Tait and Spann, Int. J. Rock Mech. Min. Sci. 1993; 30:1057; Cui and Abousleiman, ASCE J. Eng. Mech. 2001; 127:391). The new solution is used to model laboratory tests on thick-walled hollow cylinders of Berea sandstone subjected to intensive pressure drawdown. In the experiments, pressure at the inner boundary of the hollow cylinder is observed to decline exponentially with a decay constant of 3,5 1/s. It is found that solutions with idealized step-function type inner boundary conditions overestimate the induced tensile radial stresses considerably. Although basic poroelastic phenomena can be modelled properly at long time following a stepwise change in pressure, realistic time varying boundary conditions predict actual rock behaviour better at early time. Experimentally observed axial stresses can be matched but appear to require different values for , and , than are measured at long time. The proposed solution can be used to calculate the stress and pore pressure distributions around boreholes under infinite/finite boundary conditions. Prospective applications include investigating the effect of gradually changing pore pressure, modelling open-hole cavity completions, and describing the phenomenon of wellbore collapse (bridging) during oil or gas blowouts. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the numerical treatment of initial strains in biological soft tissuesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006E. Peña Abstract In this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress-free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible ,deformation gradient' field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress-free configuration, while in blood vessels the starting point is usually the load-free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are presented to show the performance of the strategies and to quantify the errors appearing in each of them. Copyright © 2006 John Wiley & Sons, Ltd. [source] A finite volume method for large strain analysis of incompressible hyperelastic materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005I. Bijelonja Abstract This paper describes development of a displacement,pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials. The method is based on the solution of the integral conservation equations governing momentum balance in total Lagrangian description. The incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body. A Mooney,Rivlin incompressible material model is used for material description. A collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape. A segregated approach is employed to solve resulting set of coupled non-linear algebraic equations, utilizing a SIMPLE based algorithm for displacement,pressure coupling. Comparisons of numerical and analytical results show a very good agreement. For the limited range of cell topologies tested the developed method appears to be locking free. Copyright © 2005 John Wiley & Sons, Ltd. [source] On solving large strain hyperelastic problems with the natural element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005B. Calvo Abstract In this paper, an extension of the natural element method (NEM) is presented to solve finite deformation problems. Since NEM is a meshless method, its implementation does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results (extremely important in three-dimensional problems). NEM has important advantages over other meshless methods, such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The ,-NEM extension generalizes this behaviour to non-convex boundaries. A total Lagrangian formulation has been employed to solve different problems with large strains, considering hyperelastic behaviour. Several examples are presented in two and three dimensions, comparing the results with the ones of the finite element method. NEM performs better showing its important capabilities in this kind of applications. Copyright © 2004 John Wiley & Sons, Ltd. [source] Non-uniform plastic deformation of micron scale objectsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003Christian F. Niordson Abstract Significant increases in apparent flow strength are observed when non-uniform plastic deformation of metals occurs at the scale ranging from roughly one to ten microns. Several basic plane strain problems are analysed numerically in this paper based on a new formulation of strain gradient plasticity. The problems are the tangential and normal loading of a finite rectangular block of material bonded to rigid platens and having traction-free ends, and the normal loading of a half-space by a flat, rigid punch. The solutions illustrate fundamental features of plasticity at the micron scale that are not captured by conventional plasticity theory. These include the role of material length parameters in establishing the size dependence of strength and the elevation of resistance to plastic flow resulting from constraint on plastic flow at boundaries. Details of the finite element method employed in the numerical analysis of the higher order gradient theory will be discussed and related to prior formulations having some of the same features. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||