the perturbed compound poisson risk model with two sided jumps in this paper we consider a perturbed compound poisson risk model with two sided jumps the downward jumps represent the claims following an arbitrary distribution while the upward jumps are also allowed to represent the random gains assuming that the density function of the upward jumps has a rational laplace transform the laplace transforms and defective renewal equations for the discounted penalty functions are derived and the asymptotic estimate for the probability of ruin is also studied for heavy tailed downward jumps finally some explicit expressions for the discounted penalty functions as well as numerical examples are given

a new frictional time integration algorithm for large slip multi body frictional contact problems in this paper a new frictional time integration suitable for large slip multibody frictional contact problems is presented the algorithm is introduced within the simple context of a model problem the sliding motion of a particle onto a rough surface time integration of frictional traction is performed introducing a new slip path parametrization which is defined independently of the local surface finite element parametrization used in the spatial triangularization the key point of the algorithm is that now in presence of large slips problems associated with slip motions such that a full incremental slip path is not within a single surface element are completely bypassed remarkably the algorithm is defined on the sole basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization geometrically the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path the algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a newton raphson iterative solution scheme the algorithm can easily be extended to large slip multi body frictional contact problems involving finite strains

monotonic continuous time random walks with drift and stochastic reset events in this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes we focus our attention on monotonic continuous time random walks with a constant drift the process increases between the reset events either by the effect of the random jumps or by the action of the deterministic drift as a result of all these combined factors interesting properties emerge like the existence for any drift strength of a stationary transition probability density function or the faculty of the model to reproduce power law like behavior general formulas for two extreme statistics the survival probability and the mean exit time are also derived to corroborate in an independent way the results of the paper monte carlo methods were used these numerical estimations are in full agreement with the analytical predictions

nurbs enriched contact finite elements abstract a novel enrichment of finite elements for contact computations based on isogeometric analysis is presented each body is divided into two parts an enriched contact surface and the bulk domain together with surfaces that are not in contact the latter part comprises the large majority of the domain and is treated in the usual manner with standard linear basis function preserving the efficiency of classical finite element techniques the enriched contact surface is discretized using nurbs basis functions of at least second order allowing for a locally differentiable surface representation this avoids the problem of suddenly changing normal vectors between element boundaries on the contact surface following the concept of isogeometric analysis the smooth basis functions are not only used to describe the surface geometry but also to approximate the solution on the surface this leads to higher accuracy in the contact integral evaluation numerical results are presented for 2d and 3d contact computations including frictionless sliding adhesive peeling and cohesive debonding the presented contact element enrichment exhibits a major gain in numerical accuracy and stability without loss of efficiency compared to standard linear finite elements the enrichment technique offers some advantages over hermite and higher order lagrangian contact element enrichment techniques such as locally differentiable surface representations in 3d while featuring competitive accuracy and performance

beyond the poisson renewal process a tutorial survey after sketching the basic principles of renewal theory and recalling the classical poisson process we discuss two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of mittag leffler and of wright type we compare these three processes with each other

diffusion of epicenters of earthquake aftershocks omori s law and generalized continuous time random walk models the epidemic type aftershock sequence etas model is a simple stochastic process modeling seismicity based on the two best established empirical laws the omori law power law decay ensuremath sim 1 t 1 ensuremath theta of seismicity after an earthquake and gutenberg richter law power law distribution of earthquake energies in order to describe also the space distribution of seismicity we use in addition a power law distribution ensuremath sim 1 r 1 ensuremath mu of distances between triggered and triggering earthquakes the etas model has been studied for the last two decades to model real seismicity catalogs and to obtain short term probabilistic forecasts here we present a mapping between the etas model and a class of ctrw continuous time random walk models based on the identification of their corresponding master equations this mapping allows us to use the wealth of results previously obtained on anomalous diffusion of ctrw after translating into the relevant variable for the etas model we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock specifically we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks the different regimes are fully characterized by the two exponents ensuremath theta and ensuremath mu our predictions are checked by careful numerical simulations we stress the distinction between the bare omori law describing the seismic rate activated directly by a mainshock and the renormalized omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock and so on in particular we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed omori exponent is less than 1 because this signals the operation of the renormalization of the bare omori law also at the origin of seismic diffusion in the etas model we present predictions and insights provided by the etas to ctrw mapping which suggest different ways for studying seismic catalogs finally we discuss the present evidence for our predicted subdiffusion of seismicity triggered by a main shock stressing the caveats and limitations of previous empirical works

an unbiased computational contact formulation for 3d friction to high accuracy as is shown a new 3d friction formulation is also proposed that is a direct extension of the 1d setup expressing the friction variables in the parameter space used for the curvilinear surface description the new formulation resorts to classical expressions in the continuum limit the current approach uses c 1 smooth contact surface representations based on either hermite or nurbs interpolation a penalty regularization is considered for the impenetrability and tangential sticking constraints the new unbiased friction formulation is illustrated by several 2d and 3d examples which include an extensive analysis of the model parameters a convergence study and the comparison with a classical biased master slave contact algorithm

simulating anisotropic frictional response using smoothly interpolated traction fields this paper develops a constitutive description and a computational treatment of anisotropic friction within the context of the finite element method the theoretical approach makes use of structural tensors that characterize texture are convected with the material surfaces and represent the symmetries that reflect changes in relative orientation of the surfaces in the discrete setting the texture is mapped using techniques adapted from discrete differential geometry and computer graphics in addition the traction fields are interpolated smoothly on the surfaces and the stick slip condition is enforced sharply via lagrange multipliers

three dimensional isogeometrically enriched finite elements for frictional contact and mixed mode debonding abstract we present an isogeometric enrichment technique for three dimensional finite element computations applied to frictional contact and mixed mode debonding this is an extension of previous work that focused on two dimensional and frictionless problems to offer a more complete view of the enriched element s performance a comparison of the results to tri variate isogeometric discretizations and standard lagrangian elements is also included here the enrichment is applied by discretizing parts of the surface that require higher accuracy with isogeometric basis functions while the rest of the body uses lagrangian shape functions by using an isogeometric surface representation the higher continuity across element boundaries and higher order of interpolation can be exploited at the same time the generation of tri variate isogeometric meshes is avoided a convergence study without any surface effects involving only volume integrals shows that the enriched elements can also be beneficial for these problems the major advantage of the isogeometric element enrichment over standard tri linear elements is demonstrated in contact problems including normal and tangential tractions for both mixed mode cohesive debonding and frictional contact the enrichment increases robustness and leads to more accurate results than standard linear lagrangian elements all computations are also compared to results using tri variate isogeometric discretizations to give a complete picture of the element s performance it is also shown that the proposed enrichment formulation has advantages in mesh generation

subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3d this paper presents a strategy to parameterize contact surfaces of arbitrary mesh topology in 3d with at least c1 continuity for both quadrilateral and triangular meshes in the regular mesh domain four quadrilaterals or six triangles meet in one node even c2 continuity is attained therefore we use subdivision surfaces for which non physical pressure jumps are avoided for contact interactions they are usually present when the contact kinematics is based on facet elements discretizing the interacting bodies the properties of subdivision surfaces give rise to basically four different implementation strategies each strategy has specific features and requires more or less efforts for an implementation in a finite element program one strategy is superior with respect to the others in the sense that it does not use nodal degrees of freedom of the finite element mesh at the contact surface instead it directly uses the degrees of freedom of the smooth surface thereby remarkably it does not require an interpolation we show how the proposed method can be used to parameterize adaptively refined meshes with hanging nodes this is essential when dealing with finite element models whose geometry is generated by means of subdivision techniques three numerical 3d problems demonstrate the improved accuracy robustness and performance of the proposed method over facet based contact surfaces in particular the third problem adopted from biomechanics shows the advantages when designing complex contact surfaces by means of subdivision techniques copyright 2004 john wiley sons ltd

an unbiased nitsche s approximation of the frictional contact between two elastic structures most of the numerical methods dedicated to the contact problem involving two elastic bodies are based on the master slave paradigm it results in important detection difficulties in the case of self contact and multi body contact where it may be impractical if not impossible to a priori nominate a master surface and a slave one in this work we introduce an unbiased finite element method for the finite element approximation of frictional contact between two elastic bodies in the small deformation framework in the proposed method the two bodies expected to come into contact are treated in the same way no master and slave surfaces the key ingredient is a nitsche based formulation of contact conditions as in chouly et al math comput 84 1089 1112 2015 we carry out the numerical analysis of the method and prove its well posedness and optimal convergence in the h 1 norm numerical experiments are performed to illustrate the theoretical results and the performance of the method

skew symmetric nitsche s formulation in isogeometric analysis dirichlet and symmetry conditions patch coupling and frictionless contact abstract a simple skew symmetric nitsche s formulation is introduced into the framework of isogeometric analysis iga to deal with various problems in small strain elasticity essential boundary conditions symmetry conditions for kirchhoff plates patch coupling in statics and in modal analysis as well as signorini contact conditions for linear boundary or interface conditions the skew symmetric formulation is parameter free for contact conditions it remains stable and accurate for a wide range of the stabilization parameter several numerical tests are performed to illustrate its accuracy stability and convergence performance we investigate particularly the effects introduced by nitsche s coupling including the convergence performance and condition numbers in statics as well as the extra outlier frequencies and corresponding eigenmodes in structural dynamics we present the hertz test the block test and a 3d self contact example showing that the skew symmetric nitsche s formulation is a suitable approach to simulate contact problems in iga

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

a contact smoothing method for arbitrary surface meshes using nagata patches abstract this paper presents a contact surface smoothing method combined with the node to segment discretization technique to solve large deformation frictional contact problems between deformable bodies the nagata patch interpolation is used to smooth the surface mesh providing a master surface with quasi g 1 continuity between patches moreover the local support of the interpolation method allows to deal with surface meshes of arbitrary topology regular and irregular finite element discretizations as well as hybrid meshes the non physical oscillations in the contact force evolution induced by the faceted contact surface representation are reduced using the proposed smoothing method furthermore the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces while providing an important improvement in convergence behaviour four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method the results show a significant improvement in the accuracy robustness and performance of the numerical simulations using the smoothing approach when compared with the piecewise faceted contact surface description

a family of simple two pass dual formulations for the finite element solution of contact problems simple stable unbiased algorithms for two pass two body contact have until now eluded researchers in computational mechanics this work examines the subject starting from an interpolation scheme proposed in an earlier work this method though stable and unbiased results in an exceedingly complex algorithm in three dimensions motivated by the need for simplicity a new formulation of the contact problem is introduced which results in a family of simple stable geometrically unbiased elements the starting point of these elements is any algorithm which is stable for the signorini problem a number of example problems are presented to compare the performance of the elements

isogeometric dual mortar methods for computational contact mechanics in recent years isogeometric analysis iga has received great attention in many fields of computational mechanics research especially for computational contact mechanics an exact and smooth surface representation is highly desirable as a consequence many well known finite element methods and algorithms for contact mechanics have been transferred to iga in the present contribution the so called dual mortar method is investigated for both contact mechanics and classical domain decomposition using nurbs basis functions in contrast to standard mortar methods the use of dual basis functions for the lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional lagrange multiplier degrees of freedom from the global system this condensed system is smaller in size and no longer of saddle point type but positive definite a very simple and commonly used element wise construction of the dual basis functions is directly transferred to the iga case the resulting lagrange multiplier interpolation satisfies discrete inf sup stability and biorthogonality however the reproduction order is limited to one in the domain decomposition case this results in a limitation of the spatial convergence order to o h3 2 in the energy norm whereas for unilateral contact due to the lower regularity of the solution optimal convergence rates are still met numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order lagrange polynomials

spatial behavior of anomalous transport we present a general derivation of one dimensional spatial concentration distributions for anomalous transport regimes such transport can be captured in the framework of a continuous time random walk with a broad transition time distribution this general theory includes a fokker planck equation as a particular limiting case all of the concentration profiles as well as the associated temporal first passage time distributions can be written in terms of a single special function that belongs to the class of fox functions in addition we consider the first two moments of the spatial concentration distributions and determine not only their scaling behavior with time but also the coefficients and correction terms

multiplicative processes and power laws takayasu sato and takayasu phys rev lett 79 966 1997 revisited the question of stochastic processes with multiplicative noise which have been studied in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we briefly explain the physical mechanism leading to a power law probability distribution function and provide a list of references for these results dating back from a quarter of century we explain how the formulation in terms of the characteristic function developed by takayasu sato and takayasu can be extended to exponents ensuremath mu g2 which explains the reason for the lucky coincidence the multidimensional generalization of the results of takayasu sato and takayasu and the present status of the problem are briefly summarized the discovery of stretched exponential tails in the presence of the cutoff introduced by takayasu sato and takayasu is explained theoretically we end by briefly listing applications

continuous time random walk model for financial distributions we apply the formalism of the continuous time random walk to the study of financial data the entire distribution of prices can be obtained once two auxiliary densities are known these are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump we have applied the formalism to data on the u s dollar deutsche mark future exchange finding good agreement between theory and the observed data

uncoupled continuous time random walks solution and limiting behavior of the master equation a detailed study is presented for a large class of uncoupled continuous time random walks ctrws the master equation is solved for the mittag leffler survival probability the properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed finally some common objections found in the literature are thoroughly reviewed

a continuum based finite element formulation for the implicit solution of multibody large deformation frictional contact problems in this paper a formulation is presented for the finite element treatment of multibody large deformation frictional contact problems the term multibody is used to mean that when two bodies mechanically contact both may be deformable a novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first before deriving the corresponding finite element equations this feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general in particular the approach yields a characterization of the frictional constraint assuming a coulomb law suitable for arbitrary discretizations in either two or three dimensions a geometric framework is constructed within which both frictionless and frictional response are naturally described making subsequent finite element discretization a straightforward substitution of finite dimensional solution spaces for their continuum counterparts to our knowledge this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature the development includes exact linearization of the statement of virtual work which enables optimal convergence properties for newton raphson solution strategies and which appears to be highly desirable if not essential for the general robustness of implicit finite element techniques since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non linear behaviour this assertion is substantiated through presentation of a variety of examples in both two and three dimensions

stochastic multiplicative processes with reset events we study a stochastic multiplicative process with reset events it is shown that the model develops a stationary power law probability distribution for the relevant variable whose exponent depends on the model parameters two qualitatively different regimes are observed corresponding to intermittent and regular behavior in the boundary between them the mean value of the relevant variable is time independent and the exponent of the stationary distribution equals ensuremath 2 the addition of diffusion to the system modifies in a nontrivial way the profile of the stationary distribution numerical and analytical results are presented

on the equivalence between jensen shannon divergence and michelson contrast this paper focuses on the link between a visible linear and local distortion in a pictorial scene and its cost in terms of information theory quantities in particular a formal relation between the michelson visual contrast and the jensen shannon divergence jsd will be provided a universal just noticeable threshold is also derived by maximizing jsd constrained to the greatest michelson contrast of an invisible distortion such a threshold is independent of both distortion parameters and the probability density function of the degraded image it is then able to measure the bits budget to be spent for leaving the distortion invisible some tests on both synthetic and real distorted images validate the theoretical findings they confirm that the proposed universal threshold is really able to get the lower bound of human perception and then it may be useful for many applications such as bit allocation in coding procedures and automatic parameters setting in restoration algorithms

isogeometric contact analysis geometric basis and formulation for frictionless contact this paper introduces an isogeometric framework for the numerical analysis of contact problems in this approach nurbs is utilized as basis for geometric representation and analysis the contact surfaces and the underlying solids are parameterized in an identical paradigm the use of nurbs geometry eliminates at the onset the geometric discontinuities induced by the traditional faceted approximation contact detection is carried out patch wise instead of element wise leading to an efficient and robust numerical algorithm a strategy for smoothing sharp corners is also described the algorithm does not rely on fillets but entails only a minor perturbation to the nurbs parameters a variationally consistent surface to surface formulation is developed in the context of frictionless contact numerical examples are presented to demonstrate the performance and utility of the method

a large deformation frictional contact formulation using nurbs based isogeometric analysis this paper focuses on the application of nurbs based isogeometric analysis to coulomb frictional contact problems between deformable bodies in the context of large deformations a mortar based approach is presented to treat the contact constraints whereby the discretization of the continuum is performed with arbitrary order nurbs as well as c0 continuous lagrange polynomial elements for comparison purposes the numerical examples show that the proposed contact formulation in conjunction with the nurbs discretization delivers accurate and robust predictions results of lower quality are obtained from the lagrange discretization as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface copyright 2011 john wiley sons ltd

fractal random walks we consider a class of random walks on lattices and in continuous spaces having infinite mean squared displacement per step the probability distribution functions considered generate fractal self similar trajectories the characteristic functions structure functions of the walks are nonanalytic functions and satisfy scaling equations

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

isogeometric collocation for large deformation elasticity and frictional contact problems abstract isogeometric collocation methods have been recently proposed as an alternative to standard galerkin approaches as they provide a significant reduction in computational cost for higher order discretizations in this work we explore the application of isogeometric collocation to large deformation elasticity and frictional contact problems we first derive the non linear governing equations for the elasticity problem with finite deformation kinematics and provide details on their consistent linearization some numerical examples demonstrate the performance of collocation in its basic and enhanced versions differing by the enforcement of neumann boundary conditions for problems with strong singularities enhanced collocation is shown to outperform basic collocation and to lead to a spatial convergence behavior very similar to galerkin whereas for weaker or no singularities enhanced and basic collocation may give very similar results a large deformation contact formulation is subsequently developed and tested in the frictional setting where collocation confirms the excellent performance already obtained for the frictionless case finally it is shown that the contact formulation in the collocation framework passes the contact patch test to machine precision in a three dimensional setting with arbitrarily inclined non matching discretizations thus outperforming most of the available contact formulations and all those with pointwise enforcement of the contact constraints

a computational contact formulation based on surface potentials this work presents the theory and numerical implementation of a contact formulation based on surface potentials the new theory formulates contact based on distance dependent surface interaction potentials and distinguishes between three interaction classes point interaction short range surface interaction and long range surface interaction here the focus is placed on frictionless contact although the first class readily admits frictional sticking contact as is also shown the proposed contact theory provides a unified framework for various contact formulations ranging from numerical constraint formulations like penalty barrier cross constrained and augmented lagrange multiplier methods to physical interaction formulations like cohesive zone models as well as electrostatic gravitational and van der waals interaction apart from recovering classical penalty and barrier formulations the new theory also naturally leads to a modified penalty and barrier method the formulation also recovers classical one pass contact algorithms however the real advantages lie in a novel two pass contact algorithm denoted the two half pass contact algorithm since each pass only accounts for the contact forces acting on the slave body this implies that traction continuity is only satisfied in theory but not imposed a priori in the algorithm instead it is obtained naturally to high accuracy as is demonstrated by several 2d and 3d numerical examples these include sliding contact peeling contact and electrostatic attraction between deformable solids among the examples is a detailed comparison between the new formulation and classical one pass approaches it is further shown that the new contact formulation passes the contact patch test

anomalous diffusion under stochastic resettings a general approach we present a general formulation of the resetting problem which is valid for any distribution of resetting intervals and arbitrary underlying processes we show that in such a general case a stationary distribution may exist even if the reset free process is not stationary as well as a significant decreasing in the mean first passage time we apply the general formalism to anomalous diffusion processes which allow simple and explicit expressions for poissonian resetting events

a computational formulation for constrained solid and liquid membranes considering isogeometric finite elements abstract a geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements and is suitable for both solid and liquid membranes the curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane in the latter case this avoids the use of local cartesian coordinates at the element level consequently no transformation of derivatives is required the formulation considers a split of the in plane and out of plane membrane contributions which allows the construction of a stable formulation for liquid membranes with constant surface tension the proposed membrane formulation is general and accounts for dead and live loading as well as enclosed volume area and contact constraints the new formulation is illustrated by several challenging examples considering linear and quadratic lagrange elements as well as isogeometric elements based on quadratic nurbs and cubic t splines it is seen that the isogeometric elements are much more accurate than standard lagrange elements the gain is especially large for the liquid membrane formulation since it depends explicitly on the surface curvature

contact treatment in isogeometric analysis with nurbs abstract we study nurbs based isogeometric analysis of contact problems and compare with standard c 0 continuous lagrange finite elements a knot to surface kts algorithm is developed to treat the contact constraints with nurbs contact surface discretizations qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems quantitative studies based on the hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard kts approach the improved mortar based kts algorithm delivers robust and accurate results for nurbs discretizations based on numerical examples we conclude that nurbs based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over c 0 continuous finite elements

diffusion with optimal resetting we consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r we consider several generalisations of the model of m r evans and s n majumdar 2011 diffusion with stochastic resetting phys rev lett 106 160601 i a space dependent resetting rate r x ii resetting to a random position z drawn from a resetting distribution p z iii a spatial distribution for the absorbing target pt x as an example of i we show that the introduction of a non resetting window around the initial position can reduce the mean time to absorption provided that the intial position is sufficiently far from the target we address the problem of optimal resetting that is minimising the mean time to absorption for a given target distribution for an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows

a novel three dimensional contact finite element based on smooth pressure interpolations this article proposes a new three dimensional contact finite element which employs continuous and weakly coupled pressure interpolations on each of the interacting boundaries the resulting formulation circumvents the geometric bias of one pass methods as well as the surface locking of traditional two pass node on surface methods a lagrange multiplier implementation of the proposed element is validated for frictionless quasi static contact by a series of numerical simulations published in 2001 by john wiley sons ltd

an unbiased nitsche s formulation of large deformation frictional contact and self contact in this paper we propose an extension of nitsche s method for frictional contact in large elastic deformations in fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces conversely to the master slave strategy this enables to take into account within the same formalism contact of two elastic bodies as well as self contact we provide a numerical study of the performance and robustness of the method

a yield limited lagrange multiplier formulation for frictional contact an analogy with rigid plasticity is used to develop a constitutive framework for quasi static frictional contact between finitely deforming solids within this setting a lagrange multiplier method is used to impose a sharp distinction between stick and slip the scope of the multipliers is limited by a constitutivelydefined yield function and a finite element based predictor corrector scheme is employed to efficiently determine the regions of stick and slip and the associated tractions selected simulations of planar quasi static problems are presented to validate the method and illustrate its capabilities