a hybrid finite element formulation of the linear biphasic equations for hydrated soft tissue a hybrid finite element method has been developed for application to the linear biphasic model of soft tissues the biphasic model assumes that hydrated soft tissue is a mixture of two incompressible immiscible phases one solid and one fluid and employs mixture theory to derive governing equations for its mechanical behaviour these equations are time dependent involving both fluid and solid velocities and solid displacement and will be solved by spatial finite element and temporal finite difference approximation the first step in the derivation of this hybrid method is application of a finite difference rule to the solid phase thus obtaining equations with only velocities at discrete times as primary variables a weighted residual statement of the temporally discretized governing equations employing c continuous interpolations of the solid and fluid phase velocities and discontinuous interpolations of the pore pressure and elastic stress is then derived the stress and pressure functions are chosen so that the total momentum equation of the mixture is satisfied they are jointly referred to as an equilibrated stress and pressure field the corresponding weighting functions are chosen to satisfy a relationship analogous to this equilibrium relation the resulting matrix equations are symmetric as an illustration of the hybrid biphasic formulation six noded triangular elements with complete linear several incomplete quadratic and complete quadratic stress and pressure fields in element local co ordinates are developed for two dimensional analysis and tested against analytical solutions and a mixed penalty finite element formulation of the same equations the hybrid method is found to be robust and produce excellent results preferred elements are identified on the basis of these results

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

a constructive approach of invariants of behavior laws with respect to an infinite symmetry group application to a biological anisotropic hyperelastic material with one fiber family abstract in this paper six new invariants associated with an anisotropic material made of one fiber family are calculated by presenting a systematic constructive and original approach this approach is based on the development of mathematical techniques from the theory of invariants definition of the material symmetry group definition of the generalized reynolds operator calculation of an integrity basis for invariant polynomials comparison between the new constructed invariants and the classical ones

implicit explicit schemes for nonlinear consolidation abstract a general analytical procedure capable of performing linear and nonlinear consolidation analysis of saturated porous media is proposed a brief review of the coupled field equations is included and the constitutive assumptions are stated explicitly time integration of the resulting nonlinear semidiscrete finite element equations is performed by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers it is shown that the algorithm can be simply and concisely implemented the technique allows for a convenient selection of implicit and explicit elements and for a convenient implicit explicit split of the various operators appearing in the equations the procedure proves to be extremely effective in dealing with consolidation problems numerical results which demonstrate the versatility and accuracy of the proposed procedures are presented

finite element formulations for hyperelastic transversely isotropic biphasic soft tissues abstract this paper presents a finite element model for the three dimensional 3 d nonlinear analysis of soft hydrated tissues such as articular cartilage in diarthrodial joints under physiologically relevant loading conditions a biphasic continuum description is used to represent the soft tissue as a two phase mixture of incompressible inviscid fluid and a hyperelastic transversely isotropic solid alternate mixed penalty and velocity pressure finite element formulations are used to solve the nonlinear biphasic governing equations including the effects of a strain dependent permeability and a hyperelastic solid phase under finite deformation the resulting first order nonlinear system of equations are discretized in time using an implicit finite difference scheme and solved using the newton raphson method a significant contribution of this work is the implementation and testing of a biphasic description with a transversely isotropic hyperelastic solid phase this description considers a helmholtz free energy function of five invariants of the cauchy green deformation tensor and the preferred direction of the material allowing for asymmetric behavior in tension and compression an exponential form is suggested and a set of material parameters is identified to represent the response of soft tissues in ranges of deformation and stress observed experimentally after demonstrating the behavior of this constitutive model in simple tension and compression a sample problem of unconfined compression is used to further validate the finite element implementation

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

yangian of the queer lie superalgebra consider the complex matrix lie superalgebra with the standard generators where define an involutory automorphism of by the twisted polynomial current lie superalgebra has a natural lie co superalgebra structure we quantise the universal enveloping algebra as a co poisson hopf superalgebra for the quantised algebra we give a description of the centre and construct the double in the sense of drinfeld we also construct a wide class of irreducible representations of the quantised algebra

hybrid and mixed penalty finite elements for 3 d analysis of soft hydrated tissue solution of biomechanics problems involving three dimensional 3 d behaviour of soft tissue on geometries representative of such tissue in vivo will require the use of numerical methods toward this end a pair of tetrahedral finite elements has been developed the equations which are used to model the tissue behaviour for both elements are those commonly known as the linear biphasic equations this model assumes that hydrated soft tissue is a mixture of two incompressible immiscible phases and employs mixture theory to derive governing equations for its mechanical behaviour the finite element techniques applied to these equations for the two elements are the mixed penalty method and the hybrid method both elements are described here and the special requirements for 3 d analysis are discussed results obtained by solving canonical problems in two and three dimensions using both elements are presented and compared both elements are found to produce excellent results the hybrid element is also noted to have advantages for non linear analyses involving finite deformation which will require solution in the future

a polyconvex framework for soft biological tissues adjustment to experimental data the main goal of this contribution is to provide a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues the advantage of our approach is that only a few parameters are necessary to approximate a variety of stress strain curves and to satisfy the condition of a stress free reference configuration a priori in the framework of polyconvexity the proposed polyconvex stored energies are embedded into the concept of structural tensors and the representation theorems for isotropic tensor functions are utilized as an example the medial layer of a human abdominal aorta is investigated modeled by some of the proposed polyconvex functions and compared with experimental data hereby the economic fitting to experimental data and hence the easy handling of the functions is shown

the tournament scheduling problem with absences abstract we study time scheduling problems with allowed absences as a new kind of graph coloring problem one may think of a sport tournament where each player each team is permitted a certain number t of absences we then examine how many rounds are needed to schedule the whole tournament in the worst case this upper limit depends on t and on the structure of the graph g whose edges represent the games that have to be played but also on whether or not the absences are announced before the tournament starts therefore we actually have two upper limits for the number of required rounds we have t g for pre scheduling if all absences are pre fixed and we have ol t g for on line scheduling if we have to stay flexible and deal with absences when they occur we conjecture that t g g 2 t and that ol t g g 2 t the first conjecture is stronger than the total coloring conjecture while the second is weaker than the on line list edge coloring conjecture our conjectures hold for all bipartite graphs for complete graphs we prove them partially lower and upper bounds to t g and ol t g for general multigraphs g are established too

nonlinear transient phenomena in saturated porous media abstract in this report the transient static and dynamic response of saturated porous medium is analyzed the saturated porous medium viewed as a two phase system whose state is described by the stresses displacements velocities and accelerations within each phase the coupled field and constitutive equations based on mixture s theories are presented and solved numerically by the use of the finite element method time integration is achieved by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers the procedure allows for a convenient selection of implicit and explicit elements and for an implicit explicit split of the various operators appearing in the differential equations accuracy and versatility of the proposed procedure are demonstrated by applying it to obtain solution to various dynamic and pseudo static one and two dimensional initial value problems

dynamics of porous media at finite strain we present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation momentum and mass conservation laws are written in lagrangian form by a pull back from the current configuration to the reference configuration following the solid matrix motion a complete formulation based on the motion of the solid and fluid phases is first presented then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so called v p formulation which is subsequently implemented in a finite element model we show how the resulting finite element matrix equations can be consistently linearized using a compressible neo hookean hyperelastic material with a kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures as well as the strong convergence profile exhibited by the iterative algorithm

on the mechanical energy and effective stress in saturated and unsaturated porous continua abstract this paper has two objectives a to formulate a mechanical theory of porous continua within the framework of strong discontinuity concept commonly employed for the analysis of strain localization in inelastic solids and b to introduce an effective stress tensor for three phase solid water air partially saturated porous continua emerging from principles of thermodynamics to achieve the first objective strong forms of the boundary value problems are compared between two formulations the first in which the velocity jump at the solid fluid interface is treated as a strong discontinuity problem and the second in which the strong discontinuity is smeared in the representative volume element as for the second objective an effective cauchy stress tensor of the form 1 k k s p 1 emerges from the formulation where is the total stress tensor k and ks are the bulk moduli of the solid matrix and solid phase respectively and p is the mean pore water and pore air pressures weighted according to the degree of saturation we show from the first and second laws of thermodynamics that this effective stress tensor is power conjugate to the solid rate of deformation tensor and that it includes the mechanical power required to compress the solid phase

a variational approach for materially stable anisotropic hyperelasticity abstract in this work we propose an anisotropic stored energy function which satisfies a priori the legendre hadamard condition which is strongly related to the material stability of the constitutive equations in the linearized case this condition implies positive wave speeds the legendre hadamard condition plays also an important role for the local existence of solutions in the neighborhood of stationary points we apply the proposed hyperelastic energies to soft tissues and compare the formulation with existing models which have been used for the calculation of medial collateral ligament and arterial walls in our numerical and analytical investigations we discuss the distribution of wave speeds for a sequence of deformation states containing some essential stress strain characteristics of the compared models

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

a contact finite element formulation for biological soft hydrated tissues as part of the highly complex numerical simulation of human joints a finite element formulation for contact between layers of articular cartilage has been developed a biphasic description of the cartilage is used where the material is considered to be a porous permeable solid matrix with fluid flowing through it governing equations and contact boundary conditions are summarized for this material before developing the finite element formulation from a galerkin weighted residual statement lagrange multipliers are introduced to enforce the two kinetic continuity equations across the contact surface and an iterative scheme is employed to determine the current contact area numerical examples are presented which demonstrate both that the appropriate continuity across the contact surface is enforced and that the contact surface definition is accurate

optimal complete diallel crosses summary optimality of complete diallel crosses in incomplete blocks is investigated optimal complete diallel crosses are characterized and such binary plans are derived using nested balanced incomplete block designs a table of optimal complete diallel crosses for up to 15 lines is also provided

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

reflection equation and twisted yangians with any involutive antialgebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra a hopf algebraic treatment of the reflection equation of this type and its universal solution is given applications to the twisted yangians are considered

a mixture approach to the mechanics of skin skin can be considered to be a mixture of a solid and a fluid a general theory for the description of the behaviour of mixtures is presented and applied to a mixture of a solid and a fluid a numerical procedure is presented to solve the non linear field equations describing such a mixture the abilities of the procedure are demonstrated by means of a confined compression test

two finite element approaches for darcy and darcy brinkman flow through deformable porous media mixed method vs nurbs based isogeometric continuity abstract porous media problems with coupled finite deformations and flow are still quite challenging if large deformations occur a non homogeneous porosity field is almost inevitable as the porosity can vary due to deformation or due to flow and pore pressure from a numerical point of view this significantly changes the mathematical description of the problem in this contribution we will analyze the consequences of the occurrence of porosity gradients on the finite element formulations of saturated two phase porous media for darcy and darcy brinkman flow we will present two approaches which are capable of fulfilling the numerical requirements for convergence the first will be an approach based on nurbs shape functions the second is a mixed formulation including the porosity as primary solution field in addition we will propose a method to include no penetration or no slip constraints into the monolithic system using a dual lagrange multiplier method the potential of the proposed methods for solving porous flow structure interaction undergoing large deformations will be illustrated by numerical examples

improved convected particle domain interpolation method for coupled dynamic analysis of fully saturated porous media involving large deformation abstract based on the u p form governing equations and the convected particle domain interpolation technique the improved convected particle domain interpolation based material point method ccpdi is developed in this paper for the coupled dynamic and contact analysis of fully saturated porous media involving large deformation the numerical artifact noises due to material points crossing computational grid boundaries that usually occur in large deformation are eliminated by using the smoother interpolation functions presented in the convected particle domain interpolation technique the discrete equations are derived in the framework of the generalized interpolation material point method the boundary load tracking algorithm and a modified contact algorithm are proposed based on the definition of particle domains to apply accurately the surface loads on the motive boundaries and to capture correctly the contact time behaviors in large deformation problems respectively simulations of several representative one and two dimensional problems are presented to demonstrate the accuracy and effectiveness of the proposed methods compared to those obtained by using the coupling material point method and or finite element method the simulation results illustrate that the proposed ccpdi method can be successfully used in simulating the large deformation coupled dynamic responses of the solid skeleton and fluid phase in fully saturated porous media and the large deformation impact between solid and saturated porous bodies

examples of braided groups and braided matrices matrix braided groups are developed as an analog of the coordinate functions on a group or supergroup the 1 in the super case is replaced by braid statistics there are braided group analogs of all the classical simple lie groups as well as braided matrix groups and braided matrices b r for every regular solution r of the quantum yang baxter equations a direct verification of b r is provided and some of the simplest examples are computed in detail

bethe subalgebras in twisted yangians we study analogues of the yangian of the lie algebra mathfrak g mathfrak l n for the other classical lie algebras mathfrak s mathfrak o n and mathfrak s mathfrak p n we call them twisted yangians they are coideal subalgebras in the yangian of mathfrak g mathfrak l n and admit homomorphisms onto the universal enveloping algebras u mathfrak s mathfrak o n and u mathfrak s mathfrak p n respectively in every twisted yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical lie algebra the images in u mathfrak s mathfrak o n and u mathfrak s mathfrak p n of these subalgebras are also maximal commutative

a new invariant based method for building biomechanical behavior laws application to an anisotropic hyperelastic material with two fiber families abstract in this article we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers this approach is based on mathematical techniques from the theory of invariants definition of the material symmetry group analytical calculation of a set of generators using the noether s theorem analytical calculation of an integrity basis comparison between the proposed invariants and the classical ones

finite element formulation for transient pore pressure dissipation a variational approach abstract a finite element formulation for solving general three dimensional consolidation problems using variational concepts is presented the formulation involves coupled displacement and pore pressure fields and has been numerically implemented to analyze boundary value problems of axisymmetric torsionless and plane strain configurations three numerical examples are discussed

algebraic structures related to reflection equations quadratic algebras related to the reflection equations are introduced they are quantum group comodule algebras the quantum group fq gl 2 is taken as the example the properties of the algebras centre representation realizations real forms fusion procedure etc as well as the generalizations are discussed

a large strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics this paper presents a finite element formulation suitable for large strain modeling of biological tissues and uses this formulation to implement an accurate finite element model for mitral valve leaflet tissue first an experimentally derived strain energy function is obtained from literature this function is implemented in finite elements using the mixed pressure displacement formulation a modification is made to aid in maintaining positive definiteness of the stiffness matrix at low strains the numerical implementation is shown to be accurate in representing the analytical model of material behavior the mixed formulation is useful for modeling of soft biological tissues in general and the model presented here is applicable to finite element simulation of mitral valve mechanics

a generalized orthotropic hyperelastic material model with application to incompressible shells in the present paper a new orthotropic hyperelastic constitutive model is proposed which can be applied to the numerical simulation of a wide range of anisotropic materials and particularly biological soft tissues the model represents a non linear extension of the orthotropic st venant kirchhoff material and is described in each principal material direction by an arbitrary isotropic tensor function coupled with the corresponding structural tensor in the special case of isotropy this constitutive formulation reduces to the valanis landel hypothesis and may therefore be considered as its generalization to the case of orthotropy constitutive relations and tangent moduli of the model are expressed in terms of eigenvalue bases of the right cauchy green tensor c and obtained for the case of distinct and coinciding eigenvalues as well for the analysis of shells the model is then coupled with a six five in incompressible case parametric shell kinematics able to deal with large strains as well as finite rotations the application of the developed finite shell element is finally illustrated by a number of numerical examples copyright 2001 john wiley sons ltd

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

on the mechanics of solids with a growing mass a general constitutive theory of the stress modulated growth of biomaterials is presented with a particular accent given to pseudo elastic soft living tissues the governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics the multiplicative decomposition of the deformation gradient into its elastic and growth parts is employed to study the growth of isotropic transversely isotropic and orthotropic biomaterials an explicit representation of the growth part of the deformation gradient is given in each case which leads to an effective incremental formulation in the analysis of the stress modulated growth process the rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function physically appealing structures of the stress dependent evolution equations for the growth induced stretch ratios are proposed