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Small Strains (small + strain)

Distribution by Scientific Domains
Engineering70%
Polymers and Materials Science30%

Terms modified by Small Strains

  • small strain level
    		•

    Selected Abstracts

    Viscous behaviour of dry sand

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2007
    D. Pham Van Bang
    Abstract Tests on air-dried Hostun sand were performed on a newly developed triaxial apparatus, which allows static and dynamic measurements at ,Département Génie Civil et Bâtiment' (DGCB) of ENTPE. The prototype was designed to perform tests in order to investigate the viscous effects of sand from small strain (some 10,5m/m) up to intermediate strain (some 10,3m/m). The accuracy of the measuring system is ensured by the use of local non-contact displacements transducers and by the use of an internal load cell. The viscous behaviour of sand is experimentally studied for loose and dense specimens for confining pressure values from 80 up to 400 kPa and considering different histories of loading. Three types of viscous loading: creep periods; stress relaxation periods; and paths with stepwise changes in the strain rate are specifically analysed. The proposed viscous modelling is issued from a three-component general framework and is able to reproduce the experimental observations. More specifically, the peculiar behaviour of sand observed during a stepwise increase or decrease in the strain rate is detailed and modelled by the viscous evanescent (VE) model, developed at DGCB/ENTPE. Based on the three types of viscous tests, a simple relation is finally proposed for the viscous parameters of the VE model. Comparisons between data and simulations validate the approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Processability, morphology and mechanical properties of glass fiber reinforced poly(ether sulfone) modified by a liquid crystalline copolyester

    POLYMER COMPOSITES, Issue 6 2003
    M. García
    Ternary composites based on glass fiber reinforced polyethersulfone (gPES) modified by a liquid crystalline copolyester (R5) were obtained by injection molding at different nozzle temperatures and at LCP contents up to 20%. The blends showed two pure amorphous phases. The ability of R5 to improve processing was seen mainly in the increase in the MFI of the blends on 5% LCP addition, which was more than 75% and 16% with respect to that of pure gPES and PES, respectively. The best processing temperature appeared to be 330°C, as it led to the maximum skin fibrillation and provided both the best small strain and fracture mechanical properties. The blend processed at 330°C with 5% R5 showed the best balance of properties because, besides the highest relative processability increase, it led to maximum values in all mechanical properties measured. This was due to both the overall fibrillation of the skin and to its having the highest ductility. [source]

    Tailoring viscoelastic and mechanical properties of the foamed blends of EVA and various ethylene-styrene interpolymers

    POLYMER COMPOSITES, Issue 3 2003
    I-Chun Liu
    Foamed materials (EVA/ESI) have been prepared from blends of ethylene-vinyl acetate copolymer (EVA) and ethylene-styrene interpolymers (ESI) in the presence of various amounts of dicumyl peroxide (DCP). Four ESIs of different compositions were employed in this study; their styrene contents ranged from 30 to 73 wt% and their Tg ranged from ,2 to 33°C. It has been found that microcellular morphology, degree of crosslinking and expansion ratio were strongly affected by the DCP concentration and the type of ESI employed. A minimum degree of crosslinking was required for making good foams and the same degree of crosslinking could be achieved by employing a smaller amount of DCP for an EVA/ESI blend having a higher styrene content. In contrast to other EVA blends, such as EVA/LDPE, these EVA/ESI blends exhibited no existence of any optimum DCP concentration, and the , glass transition temperatures of the foams varied with the ESI type, covering a wide span from 0°C to 37°C. Therefore, it was possible to tailor the Tg of an EVA/ESI blend by choosing an appropriate type of ESI. Furthermore, by correctly tailoring the Tg, the EVA/ESI foam could be made into a rubbery material with a custom-designed damping factor. Tensile strength and modulus of the EVA/ESI foams increased generally with an increase in the styrene content, with the exception that ESIs with very low styrene content will confer on the blend a high modulus at small strain and a large elongation at break. [source]

    Hyperelastic modelling of small-strain stiffness anisotropy of cyclically loaded sand

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2010
    A. Gajo
    Abstract Experimental evidence shows that soil stiffness at very small strains is strongly anisotropic and depends on the stress level and void ratio. In particular, stiffness anisotropy varies considerably in sand when subjected to cyclic loading, following the stress cycles applied. To model this behaviour, an innovative hyperelastic formulation based on the elastoplastic coupling is incorporated in a new kinematic hardening elastoplastic model. The proposed hyperelastic,plastic model is the first to be capable of correctly simulating all aspects of the small-strain behaviour of granular materials subjected to monotonic and cyclic loads. This hyperelastic formulation is generally applicable to any elastoplastic model. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    A small-strain overlay model

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2009
    T. Benz
    Abstract The paper begins with a discussion of the phenomenon of small-strain stiffness and presents the small-strain overlay model, a simple model that takes into account the non-linear stiffness of soils at small strains. The new model can enhance already established elastoplastic formulations for non-linear stiffness variation at small strains in a similar way that intergranular strain enhances the hypoplastic model. The overlay model is driven by the material's strain history and only two additional material constants, both with clear physical meaning. Therefore, the proposed model is a step towards the incorporation of small-strain stiffness into routine design. In this paper, the new small-strain overlay model is formulated. Its ability to take into account the influence of various strain histories on soil stiffness is illustrated in several examples. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A hypoplastic constitutive model for clays

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2005
    D. Ma
    Abstract This paper presents a new constitutive model for clays. The model is developed on the basis of generalized hypoplasticity principles, which are combined with traditional critical state soil mechanics. The positions of the isotropic normal compression line and the critical state line correspond to the Modified Cam clay model, the Matsuoka,Nakai failure surface is taken as the limit stress criterion and the non-linear behaviour of soils with different overconsolidation ratios is governed by the generalized hypoplastic formulation. The model requires five constitutive parameters, which correspond to the parameters of the Modified Cam clay model and are simple to calibrate on the basis of standard laboratory experiments. This makes the model particularly suitable for practical applications. The basic model may be simply enhanced by the intergranular strain concept, which allows reproducing the behaviour at very small strains. The model is evaluated on the basis of high quality laboratory experiments on reconstituted London clay. Contrary to a reference hypoplastic relation, the proposed model may be applied to highly overconsolidated clays. Improvement of predictions in the small strain range at different stress levels is also demonstrated. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    A note on formulas for localized failure of frictional materials in compression and biaxial loading modes

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2001
    Matthias Lambrecht
    Abstract The paper investigates aspects of the localization analysis of frictional materials. We derive closed formulas and diagrams for the inclination angle of critical discontinuity surfaces which develop in homogeneous compression and biaxial loading tests. The localization analysis is based on a Drucker,Prager-type elastoplastic hardening model for non-associated plastic flow at small strains, which we represent in spectral form. For this type of constitutive model, general analytical formulas for the so-called critical hardening modulus and the inclination angle of critical discontinuity surfaces are derived for the plane strain case. The subsequent treatment then specializes these formulas for the analysis of compression and biaxial loading modes. The key contribution here is a detailed analysis of plane strain deformation modes where the localized failure occurs after subsequent plastic flow. The derived formulas and diagrams can be applied to the checking of an accompanying localization analysis of frictional materials in finite-element computations. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002
    Christian Miehe
    Abstract The paper investigates computational procedures for the treatment of a homogenized macro-continuum with locally attached micro-structures of inelastic constituents undergoing small strains. The point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro-structure as a generalized standard medium in terms of an energy storage and a dissipation function. Consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi-hyperelastic micro-stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. We specify the local variational formulation for a setting of smooth single-surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables. The existence of the quasi-hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity. Focusing on macro-strain-driven micro-structures, we develop a new incremental variational formulation of the global homogenization problem where a quasi-hyperelastic macro-stress potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. It is shown that this global minimization problem determines the state of the micro-structure for finite increments of time. We consider three different settings of the global variational problem for prescribed linear displacements, periodic fluctuations and constant stresses on the boundary of the micro-structure and discuss their numerical solutions based on a spatial discretization of the fine-scale displacement fluctuation field. The performance of the proposed methods is demonstrated for the model problem of von Mises-type elasto-visco-plasticity of the constituents and applied to a comparative study of micro-to-macro transitions of inelastic composites. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    The effect of annealing on the nonlinear viscoelastic response of isotactic polypropylene

    POLYMER ENGINEERING & SCIENCE, Issue 4 2003
    Aleksey D. Drozdov
    Three series of tensile relaxation tests are performed on isotactic polypropylene at room temperature in the vicinity of the yield point. In the first series of experiments, injection-molded samples are used without thermal pre-treatment. In the second and third series, the specimens are annealed at 130°C for 4 and 24 hours, respectively. Constitutive equations are derived for the time-dependent response of semicrystalline polymers at isothermal loading with small strains. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross-links, entanglements and crystalline lamellae). Under loading, junctions slide with respect to their positions in the bulk material (which reflects the viscoplastic behavior), whereas active strands separate from their junctions and dangling strands merge with the network at random times (which reflects the viscoelastic response). The network is thought of as an ensemble of meso-regions (MRs) with various activation energies for detachment of chains from temporary nodes. Adjustable parameters in the stress-strain relations are found by fitting the observations. The experimental data demonstrate that the relaxation spectrum (characterized by the distribution of MRs with various potential energies) is independent of mechanical factors, but is altered at annealing. For specimens not subjected to thermal treatment, the growth of longitudinal strain does not affect the volume fraction of active MRs and the attempt rate for detachment of chains from their junctions. For annealed samples, the concentration of active MRs increases and the attempt rate decreases with strain. These changes in the time-dependent response are attributed to broadening of the distribution of strengths of lamellae at annealing. [source]

    Theory and Numerics of Rate-Dependent Incremental Variational Formulations in Ferroelectricity

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
    Daniele Rosato
    This paper is concerned with macroscopic continuous and discrete variational formulations for domain switching effects at small strains, which occur in ferroelectric ceramics. The developed new three,dimensional model is thermodynamically,consistent and determined by two scalar,valued functions: the energy storage function (Helmholtz free energy) and the dissipation function, which is in particular rate,dependent. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for ferroelectric ceramics. The rate,dependent character of the dissipation function allows us also to reproduce the experimentally observed rate dependency of the above mentioned hysteresis phenomena. An important aspect is the numerical implementation of the coupled problem. The discretization of the two,field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of a benchmark problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]