Home About us Contact
|
Home About us Contact | ||
|
|
||
Finite Strains (finite + strain)
Terms modified by Finite Strains Selected AbstractsA structural model for the seismicity of the Arudy (1980) epicentral area (Western Pyrenees, France)GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007Noalwenn Dubos-Sallée SUMMARY The Western Pyrenees presents a diffuse and moderate (M, 5.7) instrumental seismicity. It nevertheless historically suffered from strong earthquakes (I = IX MSK). The seismic sources of these events are not yet clearly identified. We focus on the Arudy (1980) epicentral area (M= 5.1) and propose here the reactivation of early Cretaceous normal faults of the Iberian margin as a potential source. The late Cretaceous inversion of this basin, first in a left-lateral strike-slip mode and then in a more frontal convergence, resulted in a pop-up geometry. This flower structure attests of the presence of a deep crustal discontinuity. The present-day geodynamic arrangement suggests that this accident is reactivated in a right lateral mode. This reactivation leads to a strain partitioning between the deep discontinuity that accommodates the lateral component of the motion and shallow thrusts, rooted on this discontinuity. These thrusts accommodate the shortening component of the strain. The distribution of the instrumental seismicity fits well the structural model of the Arudy basin. Whatever the compressive regional context, the structural behaviour of the system explains too the extensive stress tensor determined for the Arudy crisis if we interpret it in terms of strain ellipsoid. Indeed numerical modelling has shown that this concomitant activity of strike-slip and thrust faulting results in an extensive component that can rise 50 per cent of the finite strain. We identify too a 25,30 km long potential seismic source for the Arudy area. The size of the structure and its potential reactivation in a strike-slip mode suggest that a maximum earthquake magnitude of ,6.5 could be expected. The extrapolation of this model at the scale of the Western Pyrenees allows to propose other potential sources for major regional historical earthquakes. [source] An objective incremental formulation for the solution of anisotropic elastoplastic problems at finite strainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2001S. Chatti Abstract This paper presents an objective formulation for the anisotropic elastic,plastic problems at large strain plasticity. The constitutive equations are written in a rotating frame. The multiplicative decomposition of the deformation gradient is adopted and the formulation is hyperelastic based. Since no stress rates are present and the incremental constitutive law was formulated in a rotating frame, the formulation is numerically objective in the time integration. Explicit algorithm was proposed and has been optimized with regard to stability and accuracy. The incremental law was integrated in fast Lagrangian analysis of continua (FLAC) method to model anisotropic elastic,plastic problems at finite strain. Structural tests are carried out for isotropic and orthotropic materials. Copyright © 2001 John Wiley & Sons, Ltd. [source] Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heatINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008Dong Qian Abstract This paper focuses on the non-linear responses in thin cylindrical structures subjected to combined mechanical and thermal loads. The coupling effects of mechanical deformation and temperature in the material are considered through the development of a thermo-elasto-viscoplastic constitutive model at finite strain. A meshfree Galerkin approach is used to discretize the weak forms of the energy and momentum equations. Due to the different time scales involved in thermal conduction and failure development, an explicit,implicit time integration scheme is developed to link the time scale differences between the two key mechanisms. We apply the developed approach to the analysis of the failure of cylindrical shell subjected to both heat sources and internal pressure. The numerical results show four different failure modes: dynamic fragmentation, single crack with branch, thermally induced cracks and cracks due to the combined effects of pressure and temperature. These results illustrate the important roles of thermal and mechanical loads with different time scales. Copyright © 2008 John Wiley & Sons, Ltd. [source] Theory and finite element computation of cyclic martensitic phase transformation at finite strainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008Erwin Stein Abstract A generalized variational formulation, including quasi-convexification of energy wells for arbitrarily many martensitic variants in case of mono-crystals for linearized strains, was developed by Govindjee and Miehe (Comp. Meth. Appl. Mech. Eng. 2001; 191(3,5):215,238) and computationally extended by Stein and Zwickert (Comput. Mech. 2006; in press). This work is generalized here for finite strain kinematics with monotonous hyperelastic stress,strain functions in order to account for large transformation strains that can reach up to 15%. A major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation (PT) problems for multiple phase variants, n,2. A lower bound of the mixing energy is provided by the Reuss bound in case of linear kinematics and an arbitrary number of variants, shown by Govindjee et al. (J. Mech. Phys. Solids 2003; 51(4):I,XXVI). In case of finite strains, a generalized representation of free energy of mixing is introduced for a quasi-Reuss bound, which in general holds for n,2. Numerical validation of the used micro,macro material model is presented by comparing verified numerical results with the experimental data for Cu82Al14Ni4 monocrystals for quasiplastic PT, provided by Xiangyang et al. (J. Mech. Phys. Solids 2000; 48:2163,2182). The zigzag-type experimental stress,strain curve within PT at loading, called ,yield tooth', is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during PT. Copyright © 2007 John Wiley & Sons, Ltd. [source] Multiaxial fatigue of rubber: Part I: equivalence criteria and theoretical aspectsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 6 2005W. V. MARS ABSTRACT This paper investigates commonly used approaches for fatigue crack nucleation analysis in rubber, including maximum principal strain (or stretch), strain energy density and octahedral shear strain criteria. The ability of these traditional equivalence criteria, as well as a recent equivalence criterion (the cracking energy density) to predict multiaxial fatigue behaviour is explored. Theoretical considerations are also introduced relating to the applicability of various fatigue life analysis approaches. These include the scalar nature of traditional equivalence criteria, robustness of the criteria investigated for a wide range of multiaxial loadings, effects of crack closure and applications to non-proportional multiaxial loadings. It is shown that the notion of a stress or strain amplitude tensor used for the analysis of multiaxial loading in metals is not appropriate in the analysis of rubber due to nonlinearity associated with finite strains and near incompressibility. Taken together, these considerations illustrate that traditional criteria are not sufficiently consistent or complete to permit confident analysis of arbitrary multiaxial loading histories, and that an analysis approach specific to the failure plane is needed. Of the three traditional criteria, maximum principal strain is shown to match most closely to the cracking energy density criterion, in terms of a failure locus in principal stretch space. [source] On the structural age of the Rhoscolyn antiform, Anglesey, North WalesGEOLOGICAL JOURNAL, Issue 2 2004Hossein Hassani Abstract In the Rhoscolyn area of Anglesey, the late Precambrian interbedded psammites and pelites of the Monian Supergroup are folded into a kilometre-scale antiform, plunging about 25°NE and with an axial surface dipping about 40°NW. Numerous folds of up to a few tens of metres in wavelength are present on both limbs of this antiform. These smaller-scale folds also plunge about 25°NE but clearly belong to two separate episodes of folding, and it has become a matter of longstanding controversy as to whether the larger antiform belongs to the first or second of these episodes. Close examination of the cleavage/bedding asymmetries from all the lithologies, however, shows that the large antiform is a second-generation structure, and that on the gently dipping northwest limb, the sense of cleavage/bedding asymmetry of the earlier cleavage in the psammitic units has been almost uniformly and homogeneously reversed (so that it appears to be axial planar to the antiform), while in the pelitic units the sense of cleavage/bedding asymmetry of the earlier cleavage has been preserved. Many of the small-scale complexities of the observed cleavage/bedding relationships may be explained by appealing to differences in the timing of the formation of buckling instabilities relative to this reorientation of the early cleavage in the psammites during the second deformation. A first-order analysis of the finite strains from around the large-scale antiform shows that the orientation of the first cleavage prior to the second deformation was steeply dipping to the southeast. The second deformation correlates with the southeast-verging Caledonian deformation affecting the Monian and Ordovician units elsewhere in northwest Anglesey, while the northwest-verging first deformation event, which is not present in the Ordovician rocks, must have occurred before they were deposited. Copyright © 2004 John Wiley & Sons, Ltd. [source] Non-stationary plane problem of the successive origination of stress concentrators in a loaded body.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008Finite deformations, their superposition Abstract The first (for the given class of problems) results of solving non-stationary plane problems of non-simultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed. It is taken into account that the origination of a hole or an inclusion produces additional finite deformations (at least, at the vicinity of the hole) superimposed ,physically' on the finite initial ones. The problem is solved using the theory of repeated superposition of large deformations. It is supposed that the shape of stress concentrators is given at the moment of their origination. Calculations were made with the use of the specialized computer package ,Superposition' based on finite-element method. Stress fields are presented at different times. The change of maximal stresses in time is also presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Theory and finite element computation of cyclic martensitic phase transformation at finite strainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008Erwin Stein Abstract A generalized variational formulation, including quasi-convexification of energy wells for arbitrarily many martensitic variants in case of mono-crystals for linearized strains, was developed by Govindjee and Miehe (Comp. Meth. Appl. Mech. Eng. 2001; 191(3,5):215,238) and computationally extended by Stein and Zwickert (Comput. Mech. 2006; in press). This work is generalized here for finite strain kinematics with monotonous hyperelastic stress,strain functions in order to account for large transformation strains that can reach up to 15%. A major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation (PT) problems for multiple phase variants, n,2. A lower bound of the mixing energy is provided by the Reuss bound in case of linear kinematics and an arbitrary number of variants, shown by Govindjee et al. (J. Mech. Phys. Solids 2003; 51(4):I,XXVI). In case of finite strains, a generalized representation of free energy of mixing is introduced for a quasi-Reuss bound, which in general holds for n,2. Numerical validation of the used micro,macro material model is presented by comparing verified numerical results with the experimental data for Cu82Al14Ni4 monocrystals for quasiplastic PT, provided by Xiangyang et al. (J. Mech. Phys. Solids 2000; 48:2163,2182). The zigzag-type experimental stress,strain curve within PT at loading, called ,yield tooth', is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during PT. Copyright © 2007 John Wiley & Sons, Ltd. [source] A meshfree thin shell method for non-linear dynamic fractureINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007T. Rabczuk Abstract A meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straightforward. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of microstructure development in shearbands by energy relaxation of incremental stress potentials: Large-strain theory for standard dissipative solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Christian Miehe Abstract We propose a fundamentally new approach to the treatment of shearband localizations in strain softening elastic,plastic solids at finite strains based on energy minimization principles associated with microstructure developments. The point of departure is a general internal variable formulation that determines the finite inelastic response as a standard dissipative medium. Consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasi-hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables. The existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental stress potential in analogy to treatments of finite elasticity. Furthermore, localization phenomena are interpreted as microstructure developments on multiple scales associated with non-convex incremental stress potentials in analogy to elastic phase decomposition problems. These microstructures can be resolved by the relaxation of non-convex energy functionals based on a convexification of the stress potential. The relaxed problem provides a well-posed formulation for a mesh-objective analysis of localizations as close as possible to the non-convex original problem. Based on an approximated rank-one convexification of the incremental stress potential we develop a computational two-scale procedure for a mesh-objective treatment of localization problems at finite strains. It constitutes a local minimization problem for a relaxed incremental stress potential with just one scalar variable representing the intensity of the microshearing of a rank-one laminate aligned to the shear band. This problem is sufficiently robust with regard to applications to large-scale inhomogeneous deformation processes of elastic,plastic solids. The performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which report on the mesh independence of the results. Copyright © 2003 John Wiley & Sons, Ltd. [source] Energy driven crack propagation at finite strains based on the embedded strong discontinuity approachPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Radan Radulovic New advances in three-dimensional finite element modeling of crack propagation at finite strains are presented. The proposed numerical model is based on the Enhanced Assumed Strain concept. The enhanced part of the deformation gradient is associated with a displacement discontinuity. In contrast to previous works, a new, energy based criterion for crack propagation is presented. The necessity for a tracking algorithm for the crack path is avoided by using more than one discontinuity within each finite element. This leads to a strictly local formulation, i.e., no information about the neighboring elements are required. Further advantages of such a formulation are a symmetric tangent stiffness matrix and the reduction of locking effects. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Adaptive finite element procedures for elastoplastic problems at finite strainsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003A. Koch Dipl.-Ing. A major difficulty in the context of adaptive analysis of geometrically nonlinear problems is to provide a robust remeshing procedure that accounts both for the error caused by the spatial discretization and for the error due to the time discretization. For stability problems, such as strain localization and necking, it is essential to provide a step,size control in order to get a robust algorithm for the solution of the boundary value problem. For this purpose we developed an easy to implement step,size control algorithm. In addition we will consider possible a posteriori error indicators for the spatial error distribution of elastoplastic problems at finite strains. This indicator is adopted for a density,function,based adaptive remeshing procedure. Both error indicators are combined for the adaptive analysis in time and space. The performance of the proposed method is documented by means of representative numerical examples. [source] | |||||||||||||