The recently emerged idea of incorporating strain or displacement discontinuities into standard finite element interpolations has triggered the development of powerful techniques that allow efficient ...modeling of regions with highly localized strains, e.g. of fracture process zones in concrete or shear bands in metals or soils. Following the pioneering work of Ortiz, Leroy, and Needleman, a number of studies on elements with embedded discontinuities were published during the past decade. It was demonstrated that local enrichments of the displacement and/or strain interpolation can improve the resolution of strain localization by finite element models. The multitude of approaches proposed in the literature calls for a comparative study that would present the diverse techniques in a unified framework, point out their common features and differences, and find their limits of applicability. There are many aspects in which individual formulations differ, such as the type of discontinuity (weak/strong), variational principle used for the derivation of basic equations, constitutive law, etc. The present paper suggests a possible approach to their classification, with special attention to the type of kinematic enhancement and of internal equilibrium condition. The differences between individual formulations are elucidated by analyzing the behavior of the simplest finite element – the constant-strain triangle (CST). The sources of stress locking (spurious stress transfer) reported by some authors are analyzed. It is shown that there exist three major classes of models with embedded discontinuities but only one of them gives the optimal element behavior.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Presented are results of molecular dynamics simulations that demonstrate flow gating through a polymer-grafted nanopore as a function of effective solvent quality. Analysis of density and flow ...profiles from the simulations show that the difference in drag force exerted on the flowing solvent due to different polymer brush configurations produces the effective fluid gating. Shear-induced permeability changes through these nanopores has also been investigated. These results establish a critical starting point in nanofluidics from which continuum modeling can be developed to design this emerging class of smart nanoporous materials with tailor-made properties.
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A micromechanical damage model considering progressive partial debonding is presented to investigate the effective elastoplastic-damage behavior of partially debonded particle reinforced ductile ...matrix composites (PRDMCs). The effective, evolutionary elastoplastic-damage responses of three-phase composites, consisting of perfectly bonded spherical particles, partially debonded particles and a ductile matrix, are micromechanically derived on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. The effects of random dispersion of particles are accommodated. Further, the evolutionary partial debonding mechanism is governed by the internal stresses of spherical particles and the statistical behavior of the interfacial strength. Specifically, following
Zhao and Weng (1996), a partially debonded elastic spherical isotropic inclusion is replaced by an equivalent, transversely isotropic yet perfectly bonded elastic spherical inclusion. The Weibull's probabilistic function is employed to describe the varying probability of progressive partial particle debonding. The proposed effective yield criterion, together with the assumed overall associative plastic flow rule and the hardening law, forms the analytical framework for the estimation of the effective elastoplastic-damage behavior of ductile matrix composites. Finally, the present predictions are compared with the predictions based on Ju and Lee's (2000) complete particle debonding model, other existing numerical predictions, and available experimental data. It is observed that the effects of partially debonded particles on the stress–strain responses are significant when the damage evolution becomes rapid.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
A framework for continuum elastoplastic-damage modelling, which employs irreversible thermodynamics and internal state variables, is investigated. The damage part of the modelling involves the ...gradient of damage quantity which, together with the equations of motion, are issued from a new formulation of the principle of virtual power recently proposed. It is shown how the plastic part of the modelling takes its standard format. Next, we consider in detail the variational formulation and subsequent numerical implementation of the elastoplastic-damage models. The development of an algorithm consistent with the present formulation is given where, for the plastic part, it leaves the standard return mapping algorithms unchanged. Application is made to different classical rate-independent and rate-dependent plastic models with the presence of a damage mechanism. The numerical implementation in the context of the finite element method is discussed in detail and a set of representative applications and numerical examples is given.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
A compliant tower in the ocean environment is modelled as a beam undergoing coupled transverse and axial motion. The equations of motion are non-linear and coupled and are derived here. The beam is ...assumed to be supported by a linear-elastic torsional spring at one end and with a point mass at the other end. Such a model is representative of numerous applications. The equations of motion and boundary conditions are obtained using Hamilton's variational principle. It is assumed that strains are small but the rotation is moderate compared to the strain so that the equations of motion for the axial and transverse motion are non-linearly coupled. The free response in vacua and the free response in water are considered in particular. The fluid forces, the added mass and drag forces, are modelled using a semi-empirical Morison equation. The resulting non-linear coupled partial differential equations are solved numerically using the finite difference approach. In Part 2 of this work, various forced responses are studied.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The principle of virtual power is used to derive the equilibrium field equations of a porous solid saturated with a fluid, including second density-gradient effects; the intention is the elucidation ...and extension of the effective stress principle of Terzaghi and Fillunger. In the context of a first density-gradient theory for a saturated solid we interpret the porewater pressure as a Lagrange multiplier in the expression for the deformation energy, assuring that the saturation constraint is verified. We prove that this saturation pressure is distributed among the constituents according to their respective volume fraction (Delesse law) only if they are both tru density-preserving.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Many models for the flexural and membranal behaviour of piezoelectric plates are available in the literature. They are based on different assumptions concerning the strain, stress, electric and ...electric-displacement fields inside the plate. A critical comparison among such models is presented here in a completely analytic way, in order to assess the accuracy of the results they provide and determine their range of applicability. The comparison is made by using a class of case-study problems, whose analytical solutions in the framework of the linear theory of piezoelectricity are available, as benchmarks for the solutions supplied by the plate models. The evaluated models are also here rationally derived from the three-dimensional theory of piezoelectricity, and a consistent treatment of the stress and electric-displacement relaxation conditions is proposed.
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In this paper, a continuum-based shape design sensitivity formulation for a frictional contact problem with a rigid body is proposed using a meshless method. The contact condition is imposed using ...the penalty method that regularizes the solution of variational inequality. The shape dependency of the contact variational form with respect to the design velocity field is obtained. The dependency of the response with respect to the shape of the rigid body is also considered. It is shown that the sensitivity equation needs to be solved at the final converged load step for the frictionless contact problem, whereas for the frictional contact case the sensitivity solution is needed at the converged configuration of each load step because the sensitivity of the current load step depends on that of the previous load step. The continuum-based contact formulation and consistent linearization is critical for accurate shape design sensitivity results. The accuracy of the proposed method is compared with the finite difference result and excellent agreement is obtained for a door seal contact example. A design optimization problem is formulated and solved to reduce the contact gap opening successfully in a demonstration of the proposed method.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We consider a perforated elastic plate in which identical traction-free holes form square or hexagonal periodic arrays. The optimization problem of finding the hole shape in this structure that ...maximizes either of its effective moduli is posed as a full scale inverse problem of elasticity. In this context, only limiting cases of a single hole and cellular solids with thin cell walls have been studied thus far. Here, we cover the gap between these cases numerically solving the problem by the genetic algorithm approach. A new time-saving scheme of the fitness evaluation provides reliable data even near the percolation limit. The presented numerical results comprehensively describe the optimal behavior of perforated plates in terms of equivalent homogeneous medium. Similar, though less sophisticated approach was used by the author Vigdergauz, (Int. J. Solids Struct. 38 (2001) 6851) to optimize an isolated inclusion in a plate.
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