Impenetrability Condition Research Articles

Hybrid particle methods in frictionless impact‐contact problems

AbstractThe dual particle dynamic (DPD) methods which employ two sets of particles have been demonstrated to have better accuracy and stability than the co‐locational particle methods, such as the smooth particle hydrodynamics (SPH). The hybrid particle method (HPM) is an extension of the DPD method. Besides the advantages of the DPD method, the HPM possesses features which better facilitate the simulation of large deformations. This paper presents the continued development of the HPM for the numerical solution of two‐dimensional frictionless contact problems. The interface contact force algorithm which employs a modified kinematic constraints method is used to determine the contact tractions. In this method, both the impenetrability condition and the traction condition are simultaneously enforced. In the original kinematic constraints method, only the former condition is satisfied. A new formulation to find stress derivatives at stress‐free corners by imposing stress‐free boundary conditions is also developed. The results for 1‐D and 2‐D contact problems indicate good accuracy for the contact formulation as well as the corner treatment when compared to analytical solutions and explicit finite element results using the commercial code LS‐DYNA. Copyright © 2004 John Wiley & Sons, Ltd.

Numerical analysis of a new Eulerian–Lagrangian finite element method applied to steady‐state hot rolling processes

AbstractA finite element code for steady‐state hot rolling processes of rigid–visco‐plastic materials under plane–strain conditions was developed in a mixed Eulerian–Lagrangian framework. This special set up allows for a direct calculation of the local deformations occurring at the free surfaces outside the contact region between the strip and the work roll. It further simplifies the implementation of displacement boundary conditions, such as the impenetrability condition. When applied to different practical hot rolling situations, ranging from thick slab to ultra‐thin strip rolling, the velocity–displacement based model (briefly denoted as vu‐model) in this mixed Eulerian–Lagrangian reference system proves to be a robust and efficient method.The vu‐model is validated against a solely velocity‐based model (vv‐model) and against elementary methods based on the Kármán–Siebel and Orowan differential equations. The latter methods, when calibrated, are known to be in line with experimental results for homogeneous deformation cases. For a massive deformation it is further validated against the commercial finite‐element software package Abaqus/Explicit. It is shown that the results obtained with the vu‐model are in excellent agreement with the predictions of the vv‐model and that the vu‐model is even more robust than its vv‐counterpart. Throughout the study we assumed a rigid cylindrical work roll; only for the homogeneous test case, we also investigated the effect of an elastically deformable work roll within the frame of the Jortner Green's function method.The new modelling approach combines the advantages of conventional Eulerian and Lagrangian modelling concepts and can be extended to three dimensions in a straightforward manner. Copyright © 2004 John Wiley & Sons, Ltd.

Deriving the similarities between Japanese and Italian: a case study in comparative syntax

This article explores a way of explaining rather surprising similarities between Japanese and Italian, in contradistinction with English. These similarities include (i) the presence of null subjects and quirky subjects, (ii) the absence of expletive elements, (iii) the existence of relatively free word order, (iv) the possibility of long-distance NP movement in restructuring constructions, and (v) the lack of so-called “subject condition effects” with respect to extraction. Capitalizing on the analysis of functional categories in terms of [±L(exical)] and [±F(unctional)] features [Huang, 1982, Logical Relations in Chinese and the Theory of Grammar. Doctoral dissertation, MIT, Cambridge, MA; Fukui, 1995, The principles-and-parameters approach: a comparative syntax of English and Japanese. In: Shibatani, M., Bynon, T. (Eds.), Approaches to Language Typology. Oxford University Press, Oxford, p. 327], it is proposed that T in Japanese/Italian is specified as [+F, +L] (i.e., a functional category with lexical nature, which induces no feature checking), as opposed to T in English whose feature specification is [+F, −L] (i.e., a “pure” functional category inducing feature checking). It is then demonstrated that the proposed parameter, as it interacts with various principles of universal grammar, gives a unified account for the similarities between Japanese and Italian, while successfully distinguishing these two (types of) languages from English. The parameter also leads to an important modification of the Phase Impenetrability Condition [Chomsky, 2000. Minimalist inquiries: the framework. In: Martin, R., Michaels, D., Uriagereka, J. (Eds.), Step by Step: Essays on Minimalist Syntax in Honor of Howard Lasnik. MIT Press, Cambridge, MA, p. 89], thus opening up a refreshing way of looking at the differences, first noted by Rizzi [1982, Issues in Italian Syntax. Foris, Dordrecht], between English and Italian with respect to the wh-island constraint. Implications and advantages of the “tripartite” approach to comparative syntax are also discussed in detail.

Impenetrability condition for a degenerate point of a one-term symmetric differential operator of even order

Let , , , be real functions not vanishing on their definition intervals. For fixed and one considers the differential expressions of arbitrary even order degenerate at the point . Let and be the minimal symmetric operators induced by and in the Hilbert spaces and , respectively. “Sewing together” the differential expressions and at one obtains a new differential expression , , which is degenerate at the same point, an interior point of . Under certain constraints on and the differential expression gives rise to a minimal symmetric operator in which is a symmetric extension of the orthogonal sum . The point is called in this paper an interior barrier for . Conditions ensuring the equality are found. It is natural to call an interior barrier an impenetrable interior interface if this equality holds and it is a penetrable interior interface if it fails. The main result of this paper is as follows: the point is an impenetrable interior interface if , and this condition is best possible in a certain sense.

The Phase Impenetrability Condition, the Vacuous Movement Hypothesis, and that- t effects

This paper proposes a new analysis of that- t effects, which have resisted any principled minimalist account. It is shown that given the Vacuous Movement Hypothesis, that- t effects straightforwardly follow from the Phase Impenetrability Condition, an independently motivated principle in the minimalist program. The proposed analysis receives further support from the fact that it accounts for adverb effects and crosslinguistic variations with that- t effects.

Three-dimensional frictional dynamic contact analysis for predicting low-velocity impact damage in composite laminates

The low-velocity impact and impact induced damage in composite laminates are studied in this paper by using the finite element technique. A three-dimensional (3D) dynamic contact model with friction is presented. The contact constraints of the model are described in the velocity field, instead of the displacement field as conventionally. This alternative description of the contact constraints may better satisfy the impenetrability condition and decrease the numerical oscillations in the computation. The sliding and friction, which are controlled by Coulomb friction law, are included in the contact-impact model. The semi-discrete finite element equation is solved by Newmark Algorithm with modifications based on the elastic wave propagation theory. An augmented Lagrange iteration with adaptive penalty is developed to ensure the convergence and the accurate solution of the contact problem. A technique for searching the contact point pair in 3D finite element analysis is proposed. Based on the results of contact-impact analysis, the damage predicting in composite laminates has been made. Numerical examples are given to demonstrate the validity and efficiency of the numerical algorithms and the computational strategies developed in this paper.

A Newton method for rigid body frictional impact with multiple simultaneous impact points

In this paper a mathematical formulation and a numerical algorithm for the analysis of frictional impact of rigid bodies with multiple simultaneous contact points are developed. A direct approach is used where the impenetrability condition and Coulomb's law of friction are formulated as equations, which are not differentiable in the usual sense, and solved together with the equations of motion and necessary kinematical relations using Newton's method. An experiment has also been performed where a possible mechanism for the difference between static and dynamic friction is observed and results are compared with computations using the present algorithm.

Expletives and agreement in Scandinavian passives

The paper deals with variation found among the Scandinavian languages and English concerning word order and agreement in passives. The variation concerns, among other things, whether the language does or does not have (a) participle agreement, (b) the order expletive-aux-NP-participle, (c) an expletive passive double object construction, (d) the order wh-expletive-participle, and (e) so-called complex passives. This is argued to be the result of variation along a set of parameters, including whether the expletive has φ-features, whether the participle head has φ-features, and whether it also has an EPP-feature. The framework is that of Chomsky (2001), assuming Agree, hence not assuming obligatory spec-head agreement with covert movement to check φ-features or Case. Certain apparent cases of obligatory spec-head agreement in Swedish and Norwegian are discussed and explained as the result of an economy condition. A modification is proposed concerning the phase impenetrability condition.

Modeling impact induced delamination of woven fiber reinforced composites with contact/cohesive laws

The dynamic delamination in woven glass fiber reinforced plastic (GRP) composite is studied with a 3D finite deformation anisotropic viscoplastic model in conjunction with contact/cohesive laws. The large deformation of the material during impact loading is described through an anisotropic plasticity model in total Lagrangian co-ordinates whose coefficients are determined experimentally. The interaction between lamina is analyzed through a contact/interface model. The tensile and shear tractions in zero thickness interface elements, embedded between lamina, are calculated from interface cohesive law. The interface cohesive law describes the evolution of these tractions in terms of normal and tangential displacement jumps and other interface parameters. The compressive traction at the interface is calculated through the impenetrability condition employed in the contact module. Once the effective displacement jump exceeds a specified critical value, the interface elements are assumed to have failed, i.e., delamination is said to have taken place. Three interface cohesive laws are proposed to describe the delamination process. It is assumed that loading of interface takes place reversibly up to a specified value of the displacement jump followed by irreversible loading beyond this value. This feature represents a partial damage of the interface in the event of unloading. Dynamic delamination in the woven GRP composite is studied through analyses of plate-on-plate impact experiments. The heterogeneity of composite materials leading to wave dispersion and scattering is modeled by considering a layered composition of the GRP plate. Each lamina is assumed to be made of three layers of materials. The middle layer of half the thickness of lamina is considered as GRP and the two end layers of equal thicknesses are considered to be of matrix material, i.e., polyester resin. The possible delamination of the composite material under compressive shock loading is shown to occur due to local shear effects. This is modeled by considering waviness of the interface between lamina. Interfaces with flat as well as two types of wavy structures are analyzed. Analyses are carried out to establish the effect of critical displacement jump, mixed mode coupling parameter employed in interface laws, interface waviness and the effect of interface laws. The response of GRP composite during impact is characterized in terms of the free surface velocity, delamination event vs. time and interface normal and shear stresses. The interface normal and shear stresses are obtained directly from the interface cohesive laws, as well as, by extrapolating continuum stresses from integration points of the neighboring triangular elements to the interface. It is shown that the finite element model predicts the response of the material in confirmation with the available experimental results. The wave dispersion and scattering effects are obtained in the form of attenuation of shock stress and free surface velocity. The model predicts partial delamination during compressive shock loading above a certain threshold due to local shear and mode coupling.

Convection in Slab and Spheroidal Geometries

Abstract: Three‐dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing‐length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise‐parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion.Fluid motions in both geometries exhibit a Kolmogorov‐like k−5/3 range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non‐local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Theory of Supercoiled Elastic Rings with Self-Contact and Its Application to DNA Plasmids

Methods are presented for obtaining exact analytical representations of supercoiled equilibrium configurations of impenetrable elastic rods of circular cross-section that have been pretwisted and closed to form rings, and a discussion is given of applications in the theory of the elastic rod model for DNA. When, as here, self-contact is taken into account, and the rod is assumed to be inextensible, intrinsically straight, transversely isotropic, and homogeneous, the important parameters in the theory are the excess link Δℒ (a measure of the amount the rod was twisted before its ends were joined), the ratio ω of the coefficients of torsional and flexural rigidity, and the ratio d of cross-sectional diameter to the length of the axial curve C. Solutions of the equations of equilibrium are given for cases in which self-contact occurs at isolated points and along intervals. Bifurcation diagrams are presented as graphs of Δℒ versus the writhe of C and are employed for analysis of the stability of equilibrium configurations. It is shown that, in addition to primary, secondary, and tertiary branches that arise by successive bifurcations from the trivial branch made up of configurations for which the axial curve is a circle, there are families of equilibrium configurations that are isolas in the sense that they are not connected to bifurcation branches by paths of equilibrium configurations compatible with the assumed impenetrability of the rod. Each of the isolas found to date is connected to a bifurcation branch by a path which, although made up of solutions of the governing equations, contains regions on which the condition of impenetrability does not hold.

Study of Frictional Impact Using a Nonsmooth Equations Solver

In this paper a mathematical formulation and a numerical algorithm for the analysis of impact of rigid bodies against rigid obstacles are developed. The paper concentrates on three-dimensional motion using a direct approach where the impenetrability condition and Coulomb’s law of friction are formulated as equations, which are not differentiable in the usual sense, and solved together with the equations of motion and necessary kinematical relations using Newton’s method. An experiment has also been performed and compared with predictions of the algorithm, with favorable results. [S0021-8936(00)01402-1]

Discontinuous Time-Integration Method for Dynamic Contact/Impact Problems

A new time-integration method is proposed using the generalized derivative concept to simulate the dynamic phenomena with sudden constraint occurring in dynamic contact/impact problems. By the adoption of the generalized derivative concept and the jump assumption, discontinuity can be incorporated in time integration, and as a result, the algorithm does not need any other special consideration of jumps in dynamic field variables due to sudden constraint, such as dynamic contact-release conditions. To observe the characteristics of the proposed time-integration method, stability and convergence analyses are carried out. The analyses prove that the proposed method with linear approximation in the time domain yields unconditional stability and third-order accuracy. In numerical tests, several dynamic contact/impact problems are analyzed by straightforward application of the proposed time-integration method with the exterior penalty method. From the tests, it is shown that the proposed time-integration method can be used successfully with the penalty method in numerical simulations of dynamic contact/impact problems. YNAMIC contact/impact problems1 are often encountered in mechanical and structural systems. Because the impact phenomena induce stiffness degradation and local failure in structural systems, the impact behavior of safety-relate d structural systems must be precisely analyzed. For example, the impact analysis of laminated composite structures is very important. Composite structures are susceptible to impact loading even though they have been used extensively in aerospace and the other applications due to their good material properties. Especially in the case of low-velocity impact2'3 there may be significant internal damage resulting in a substantial drop in the stiffness and strength of the structures, although no apparent damage is detected by visual inspection, leading directly to safety-related problems of structures. To simulate contact/impact problems, several studies have been carried out, and it has been pointed out that the impenetrability condition alone in the contact area is not sufficient in the numerical simulations of dynamic contact/impact problems. The sudden constraint induces the jumps in dynamic field variables, which makes it difficult to satisfy the velocity and the acceleration compatibility between the target and impactor under discrete time integration, such as the Newmark method.4 As a result, straightforward application of the impenetrability condition without any other treatment produces undesirable oscillations. This is a somewhat different issue in solving static contact problems. To alleviate this problem, several studies were performed. Hughes et al.5 devised the discrete dynamic contact/impact conditions for a lumped-mass case and enforced the conditions. Taylor and Papadopoulos6 assumed that the velocities and accelerations on the contact points are independent of the displacements in the Newmark time-integration method and enforced the velocity and the acceleration compatibility. Chaudhary and Bathe7 adopted the special parameters of the Newmark timeintegration method to satisfy the momentum conservation principle of the isolated particle. Lee8 proposed an iterative scheme for satisfying the velocity and the acceleration compatibility on the contact

Oblique penetration of a rigid projectile into an elastic-plastic target

The main objective of the present work is to develop an approximate solution of the problem of oblique penetration of a rigid projectile into an elastic-plastic target of finite thickness. This is accomplished by generalizing the work on normal penetration reported in [1]. Here, an irrotational isochoric velocity field is considered that consists of three parts, each of which together satisfy the condition of impenetrability at the projectile's surface. The first part is associated with the longitudinal motion of the projectile, the second part with the transverse motion, and the third part with the projectile rotation in the plane defined by the initial longitudinal projectile velocity and the normal to the target surface. The target material is assumed to be incompressible and the target region is subdivided into an elastic region ahead of the projectile, and a rigid-plastic region near the projectile. Using the above potential velocity field, inertia effects are included and the linear momentum equation is solved exactly in the elastic region. In the plastic region, the linear momentum equation is integrated numerically along the instantaneous streamlines to determine the pressure field on the projectile surface. Then the decelerating force and moment applied to the projectile are solved numerically. The model developed here predicts the residual velocity, the ballistic limit, as well as the residual angle of obliquity. Moreover, this model is able to describe the phenomenon of ricochet. It is shown that the agreement of the theory with experiments is good even though no adjustable parameters are used. Also, a user-friendly computer program has been developed that is available for distribution along with a Users' Manual.

Penetration of a rigid projectile into an elastic-plastic target of finite thickness

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.

Effects of diisopropyl phosphofluoridate, sarin and soman on the accessibility of proteins, in the electroplax membrane, to lactoperoxidase-catalyzed iodination

Anticholinesterases (anti-ChE) have some effects on biological properties including behavior, vision, and electroencephalograms, which are often long lasting and which do not appear to be due to cholinesterase (ChE; EC 3.1.1.7) inhibition, but which may be due to alterations in the organization and/or functioning of the cellular membrane. We assessed the effects of anti-ChE agents on the asymmetric organization of proteins in the innervated (excitable) and in the non-innervated (non-excitable) plasma membrane of the electroplax from the electric eel. Lactoperoxidase-catalyzed iodination (LCI) was carried out under impenetrable conditions in intact electroplax (where protein exposure on the external surface is monitored) and in split electroplax (where total protein labeling on both the external and internal monolayers of the plasma membrane bilayer is monitored). Labeling in split electroplax was much greater than in intact electroplax for all molecular weight groupings of proteins (30,000 to > 200,000). The anti-ChE agents diisopropyl phosphofluoridate (DFP; 10 −3 M), sarin (10 −4 M) and soman (10 −4 M, 10 −6 M, 2.5 × 10 −9 M) did not alter permeability, protein content or the electrophoretic pattern of the plasma membrane proteins of the electroplax. DFP, sarin and 10 −6M soman (but not 2.5 × 10 −9M or 10 −4M soman) increased labeling of some of the molecular weight fractions in the non-innervated plasma membrane as monitored by LCI in intact electroplax. Under these same conditions, DFP and 10 −4M soman increased labeling in the innervated plasma membrane while 10 −6M soman decreased labeling. When LCI was carried out in split electroplax, 10 −4M soman caused a decrease in labeling in both the innervated and non-innervated plasma membrane indicating a decrease of exposed proteins on the cytoplasmic surface of the plasma membrane. These concentrations of the anti-ChE agents caused almost complete ChE inhibition in the electroplax cells, except for 2.5 × 10 −9 M soman which caused little or no inhibition. These results suggest that alterations in protein asymmetry, as monitored by LCI of accessible proteins, are not directly due to ChE inhibition. These changes in organization of membrane proteins could contribute to a variety of effects of anti-ChE agents which are not due to ChE inhibition.

Contact‐impact by the pinball algorithm with penalty and Lagrangian methods

AbstractContact‐impact algorithms, which are sometimes called slideline algorithms, are a computationally time‐consuming part of many explicit simulations of non‐linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.

Diffusion in solids under strain, with emphasis on polymer membranes

AbstractA solute diffusing through a solid gives rise to a change in volume. This swelling can be viewed as a strain, and it is possible to obtain the accompanying stress using elasticity theory. The theory provides two ways by which stresses can be generated. The first comes from the condition of impenetrability where the system generates stress to exclude certain configurations during deformation. The second is due to imposed restrictions on the geometry during the swelling process. Larché and Cahn have provided the thermodynamics for such systems, from which the chemical potential can be used to obtain a phenomenological expression for flux and an expression for the solubility. These two are sufficient to obtain the sorption response in most systems. Solutions have been obtained here.

A theory of friction

A rather general theory of friction, inspired from the classical theory of plasticity is proposed. It includes the contact impenetrability condition as a by-product.

Computation and cognition: issues in the foundations of cognitive science

AbstractThe computational view of mind rests on certain intuitions regarding the fundamental similarity between computation and cognition. We examine some of these intuitions and suggest that they derive from the fact that computers and human organisms are both physical systems whose behavior is correctly described as being governed by rules acting on symbolic representations. Some of the implications of this view are discussed. It is suggested that a fundamental hypothesis of this approach (the “proprietary vocabulary hypothesis”) is that there is a natural domain of human functioning (roughly what we intuitively associate with perceiving, reasoning, and acting) that can be addressed exclusively in terms of a formal symbolic or algorithmic vocabulary or level of analysis.Much of the paper elaborates various conditions that need to be met if a literal view of mental activity as computation is to serve as the basis for explanatory theories. The coherence of such a view depends on there being a principled distinction between functions whose explanation requires that we posit internal representations and those that we can appropriately describe as merely instantiating causal physical or biological laws. In this paper the distinction is empirically grounded in a methodological criterion called the “cognitive impenetrability condition.” Functions are said to be cognitively impenetrable if they cannot be influenced by such purely cognitive factors as goals, beliefs, inferences, tacit knowledge, and so on. Such a criterion makes it possible to empirically separate the fixed capacities of mind (called its “functional architecture”) from the particular representations and algorithms used on specific occasions. In order for computational theories to avoid being ad hoc, they must deal effectively with the “degrees of freedom” problem by constraining the extent to which they can be arbitrarily adjusted post hoc to fit some particular set of observations. This in turn requires that the fixed architectural function and the algorithms be independently validated. It is argued that the architectural assumptions implicit in many contemporary models run afoul of the cognitive impenetrability condition, since the required fixed functions are demonstrably sensitive to tacit knowledge and goals. The paper concludes with some tactical suggestions for the development of computational cognitive theories.