nonlinear scattering theory at low energy abstract we study the scattering theory of a conservative nonlinear one parameter group of operators on a hilbert space x relative to a group of linear unitary operators under certain hypotheses the scattering operator carries a neighborhood of 0 in x into x the theory is designed to apply to the semilinear schrodinger and klein gordon equations

stabilization of partitioned solution procedure for pore fluid soil interaction analysis on montre que la solution decalee conventionnelle des problemes d interaction fluide sol dans les pores souffre de restrictions sur la stabilite on presente une forme stabilisee de la procedure de solution decalee de ce probleme on recommande cette procedure pour l implementation des problemes d interaction sol fluide

diffusion in poro elastic media existence uniqueness and regularity theory is developed for a general initial boundary value problem for a system of partial differential equations which describes the biot consolidation model in poro elasticity as well as a coupled quasi static problem in thermoelasticity additional effects of secondary consolidation and pore fluid exposure on the boundary are included this quasi static system is resolved as an application of the theory of linear degenerate evolution equations in hilbert space and this leads to a precise description of the dynamics of the system

standard staggered and staggered newton schemes in thermo hydro mechanical problems the aim of the paper is to compare the rates of iteration convergence of two staggered numerical schemes one using successive substitutions and the other the newton method in the case of very weakly coupled problems the newton method is one order faster but there are specific cases when it is slower than the standard staggered algorithm in both cases a convergence condition must be verified the behaviour of the investigated staggered procedures in case of thermo hydro mechanical problems are shown on examples

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

well posedness and existence of bound states for a coupled schrodinger gkdv system abstract we derive some new results concerning the cauchy problem and the existence of bound states for a class of coupled nonlinear schrodinger gkdv systems in particular we obtain the existence of strong global solutions for initial data in the energy space h 1 r h 1 r generalizing previous results obtained in tsutsumi 1993 11 corcho and linares 2007 13 and dias et al submitted for publication 14 for the nonlinear schrodinger kdv system

three dimensional finite element simulation of three phase flow in a deforming fissured reservoir the development of a capacity to predict the exploitation of structurally complicated and fractured oil reservoirs is essential for the rational use of investment capital a poor understanding of how the reservoir behaves during production may lead to inept costly and inefficient development schemes the mathematical formulation of a three phase three dimensional fluid flow and rock deformation in fractured reservoirs is hence presented the present formulation consisting of both the equilibrium and multiphase mass conservation equations accounts for the significant influence of coupling between the fluid flow and solid deformation an aspect usually ignored in the reservoir simulation literature a galerkin based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time the final set of equations which contain the additional cross coupling terms as compared to similar existing models are highly non linear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables a field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme the results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered

a note on the 2d generalized zakharov kuznetsov equation local global and scattering results abstract we consider the generalized two dimensional zakharov kuznetsov equation u t x u x u k 1 0 where k 3 is an integer number for k 8 we prove local well posedness in the l 2 based sobolev spaces h s r 2 where s is greater than the critical scaling index s k 1 2 k for k 3 we also establish a sharp criteria to obtain global h 1 r 2 solutions a nonlinear scattering result in h 1 r 2 is also established assuming the initial data is small and belongs to a suitable lebesgue space

construction of solutions to the subcritical gkdv equations with a given asymptotical behavior we consider the subcritical generalized korteweg de vries equation ut uxx u4 x 0 t x r let rj t x qcj x xj cjt j 1 n be n soliton solutions to this equation denote u t the kdv linear group and let v be in an adequate weighted sobolev space we construct a solution u t to the generalized korteweg de vries equation such that limt u t u t v j 1nrj t h1 0

a mathematical framework for finite strain elastoplastic consolidation part 1 balance laws variational formulation and linearization a mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented strong and weak forms of the boundary value problem are derived using both the material and spatial descriptions the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure balance laws are written for the soil water mixture following the motion of the soil matrix alone it is shown that the motion of the fluid phase only affects the jacobian of the solid phase motion and therefore can be characterized completely by the motion of the soil matrix furthermore it is shown from energy balance consideration that the effective or intergranular stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil water mixture finally it is shown that the mathematical model is amenable to consistent linearization and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method

von neumann stability analysis of biot s general two dimensional theory of consolidation von neumann stability analysis is performed for a galerkin finite element formulation of biot s consolidation equations on two dimensional bilinear elements two dimensionless groups the time factor and void factor are identified and these quantities along with the time integration weighting are used to explore the stability implications for variations in physical property and discretization parameters the results show that the presence and persistence of stable spurious oscillations in the pore pressure are influenced by the ratio of time step size to the square of the space step for fixed time integration weightings and physical property selections in general increasing the time step or decreasing the mesh spacing has a smoothing effect on the discrete solution however special cases exist that violate this generality which can be readily identified through the von neumann approach the analysis also reveals that explicitly dominated schemes are not stable for saturated media and only become possible through a decoupling of the equilibrium and continuity equations in the case of unsaturated media a break down in the von neumann results has been shown to occur due to the influence of boundary conditions on stability 1998 john wiley sons ltd

fractional step methods for index 1 differential algebraic equations in the numerical solution of ordinary differential systems the method of fractional steps also known as operator splitting yields high order accurate schemes based on separate computationally convenient treatments of distinct physical effects such schemes are equally desirable but much less accurate for semi explicit index 1 differential algebraic equations daes in the first half of this note it is shown that email protected ve application to daes of standard splitting schemes suffers from order reduction both first and second order schemes are only first order accurate for daes in the second half of this note a new family of higher order splitting schemes for semi explicit index 1 daes is developed the new schemes are based on a deferred correction paradigm in which an error equation is solved numerically and therefore inherit a simple computationally convenient structure higher order convergence of the new schemes is proved and numerical results confirm the expected order of accuracy in addition to establishing efficiency

nonlinear small data scattering for the generalized korteweg de vries equation abstract we study the longtime stability of small solutions to the ivp for the generalized korteweg de vries equation we obtain a lower bound for the degrees of nonlinearity of the perturbation which guarantees that the small solutions of the nonlinear problem behave asymptotically like the solutions of the associated linear problem this behavior allows us to establish a nonlinear scattering result for small perturbations with these degrees for a class of small data we improve the value of this lower bound the new crucial ingrediants in our proofs are the l p decay estimates of the half derivative of the airy kernel

on convergence conditions of partitioned solution procedures for consolidation problems abstract a systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented consistency convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made conclusions based also on numerical evidence are drawn the significance of the ratio of the time step length to the square of the finite element mesh length is shown

propagation characteristic of rayleigh waves in orthotropic fluid saturated porous media in this paper the influence of anisotropy of the solid skeleton on the propagation characteristic of rayleigh waves in orthotropic fluid saturated porous media is studied from a more general sense based on biot s theory firstly the governing equations for orthotropic fluid saturated porous media are derived then the three dimensional complex characteristic equations for rayleigh waves are deduced and their existence conditions are given based on the characteristic equations the rayleigh wave speeds along arbitrary directions and particle traces in arbitrary sagittal planes are numerically calculated the effects of anisotropy of the solid skeleton on the propagation characteristic of rayleigh waves are analyzed in detail the results show that the rayleigh waves display different characteristic in orthotropic fluid saturated porous media from that they have exhibited in isotropic or transversely isotropic fluid saturated porous media

dispersion of small amplitude solutions of the generalized korteweg de vries equation abstract we study the long time behavior of small solutions of the initial value problem for the generalized korteweg de vries equation t u x 3 u x f u 0 gkdv u x 0 g x for the case where f w w s with s 1 4 23 57 3 8625 our results imply that if g l11 g l22 is sufficiently small then sup r 1 t 1 3 u t l in particular the solution tends to zero in the supremum norm the proofs make use of duhamel s formula and dispersion estimates for the linear propagator as well as chain and leibniz rules for fractional derivatives of compositions d f u lp and products d fg lp 0

final state problem for korteweg de vries type equations we study the final state problem for the korteweg de vries type equations ut 1 x 1ux u2ux t x r r u t fs t l2 0 as t where r the function fs t we call a final state defined by the final data u we show that there does not exist a nontrivial solution of this equation in the case of fs t u t u where u t is the free evolution group of this equation we construct the modified wave operator for the korteweg de vries type equations under the conditions that the final data u arc real valued functions and the fourier transform u vanishes at the origin

characteristic analysis of wave propagation in anisotropic fluid saturated porous media in this investigation a characteristic analysis of stress wave propagation in anisotropic fluid saturated porous media is performed based on generalized characteristic theory this method enables us to carry out a complete basic analysis of wave propagation characteristic in fluid saturated porous media and immediately determine the wave fronts through the normal velocity surfaces first the characteristic differential equations and compatibility relations along bicharacteristics are deduced then the analytical expressions for the normal velocity surfaces and wave fronts are presented based on these equations the characteristic of the normal velocity surfaces and the wave fronts for all components of the stress waves in an orthotropic fluid saturated porous media as well as its special cases in three dimensional space is computed and discussed the results show that the wave fronts of fast and slow waves remain regular along with the increase of anisotropy of the media but great anisotropy may lead to more than one triple angle on the wave fronts of quasi transverse or transverse waves

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

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 new numerically stable sequential algorithm for coupled finite strain elastoplastic geomechanics and flow abstract we propose a new numerically stable sequential implicit method for coupled flow and finite strain multiplicative elastoplastic geomechanics we find from stability analysis that the sequential method that solves the flow problem first by fixing the first piola kirchhoff total stress solving the geomechanics solid deformation problem at the next step is unconditionally stable contractive and b stable in this sense this method named the fixed first piola kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics we also study the fixed second piola kirchhoff stress method comparing it with the fixed first piola kirchhoff stress method because the constitutive relations are formulated by the second piola kirchhoff total stress although fixing the second piola kirchhoff total stress field does not provide theoretical unconditional stability in space discretization we use the finite element method for the geomechanics problem with the total lagrangian approach while employing the finite volume method for the flow problem geometrical nonlinearity from the total lagrangian approach results in full tensor permeability even if the initial permeability is isotropic to consider the full tensor permeability accurately we employ the multipoint flux approximation in solving the flow problem in time discretization the backward euler method is used then we perform numerical experiments of the two fixed stress sequential methods with various scenarios and find superiority of their numerical stability specifically the two fixed stress sequential methods provide almost identical results for elasticity for j 2 plasticity the two sequential methods yield slightly different numerical results although the trends of the results are similar for the drucker prager plasticity we find that the results from the two methods are almost identical for all the test cases the two sequential methods are numerically stable

flow through fissured porous media with deformable matrix an approach which is based on the double porosity concept and takes into account pore deformation has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media this approach has resulted in a set of non linear variable coefficient differential equations various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters the finite element technique has been employed as the numerical tool for the solution of these equations the results based on the proposed non linear formulation have been compared with those of previously presented linear constant coefficient formulations it is found that in relatively rigid formations the linearity assumption is quite reasonable and can successfully model the behaviour of fissured porous media however in very deformable formations the linearity assumption could lead to a significant level of error in the numerical solutions

stability and convergence of sequential methods for coupled flow and geomechanics drained and undrained splits abstract we perform a stability and convergence analysis of sequential methods for coupled flow and geomechanics in which the mechanics sub problem is solved first we consider slow deformations so that inertia is negligible and the mechanical problem is governed by an elliptic equation we use biot s self consistent theory to obtain the classical parabolic type flow problem we use a generalized midpoint rule parameter between 0 and 1 time discretization and consider two classical sequential methods the drained and undrained splits the von neumann method provides sharp stability estimates for the linear poroelasticity problem the drained split with backward euler time discretization 1 is conditionally stable and its stability depends only on the coupling strength and it is independent of time step size the drained split with the midpoint rule 0 5 is unconditionally unstable the mixed time discretization with 1 0 for mechanics and 0 5 for flow has the same stability properties as the backward euler scheme the von neumann method indicates that the undrained split is unconditionally stable when 0 5 we extend the stability analysis to the nonlinear regime poro elastoplasticity via the energy method it is well known that the drained split does not inherit the contractivity property of the continuum problem thereby precluding unconditional stability for the undrained split we show that it is b stable therefore unconditionally stable at the algorithmic level when 0 5 we also analyze convergence of the drained and undrained splits and derive the a priori error estimates from matrix algebra and spectral analysis we show that the drained split with a fixed number of iterations is not convergent even when it is stable the undrained split with a fixed number of iterations is convergent for a compressible system i e finite biot modulus for a nearly incompressible system i e very large biot modulus the undrained split loses first order accuracy and becomes non convergent in time we also study the rate of convergence of both splits when they are used in a fully iterated sequential scheme when the medium permeability is high or the time step size is large which corresponds to a high diffusion of pressure the error amplification of the drained split is lower and therefore converges faster than the undrained split the situation is reversed in the case of low permeability and small time step size we provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits in the linear and nonlinear regimes we also show that our spatial discretization finite volumes for flow and finite elements for mechanics removes the well documented spurious instability in consolidation problems at early times

on the optimization of the fixed stress splitting for biot s equations in this work we are interested in efficiently solving the quasi static linear biot model for poroelasticity we consider the fixed stress splitting scheme which is a popular method for iterative

non linear b stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity a class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward euler return maps as a particular case more importantly it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary helmholz free energy function b stability since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm the requirement of b stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity the analysis that follows depends critically on the assumption of convexity in particular the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation the proposed algorithms obey the discrete counterpart of this classical principle

decay and scattering of small solutions of a generalized boussinesq equation abstract we study the long time behavior of small solutions of the initial value problem for a generalized boussinesq equation we obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations that is the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem under certain hypotheses we can construct a scattering operator for the boussinesq equation which carries a neighborhood of 0 in the energy space x into x

acoustic waves in a medium bounded by curved surfaces abstract a method for obtaining quasi analytic solutions to the three dimensional 3d helmholtz equation for the case of an acoustic medium bounded by two identical curved surfaces is presented the method can be extended to a semi infinite medium with a curved boundary for the study of rayleigh waves on a non planar surface albeit the solution procedure entails the numerical matrix method the formulation of the method is based on the differential geometry argument employing the curved coordinates u 1 u 2 u 3 where u 1 and u 2 are along the local tangent plane of one of the bounding surfaces z z x and u 3 is perpendicular to the local tangent plane this choice of coordinates allows the 3d helmholtz equation subject to boundary conditions specified on non planar surfaces to be solved with relative ease normal mode solutions are shown for the case of a fluid layer with two pressure release boundaries where the bounding surfaces are given by the ramp the gaussian and the sinusoidal functions respectively

error propagation of staggered solution procedures for transient problems abstract closed formulas for the error of staggered and simultaneous procedures are derived and compared conditions of global convergence are determined it is shown that in some cases a complicated condition for stability of the staggered scheme can be replaced by a simpler one the simultaneous stability condition for one iteration step a counterexample for global convergence of the staggered method with a constant number of iterations is presented

taylor series expansion for solutions of the korteweg devries equation with respect to their initial values abstract the initial value problem ivp for the korteweg devries kdv equation t u u x u 3 x u 0 u x 0 x for x r t r establishes a nonlinear map k from the space hs r to the space c t t hs r it has been known for many years that this map k is continuous bona and smith 1975 kato 1983 and it was proved recently that this map is lipschitz continuous kenig et al 1993 it is shown in this paper that the nonlinear map k is infinitely many times frechet differentiable from hs r to c t t hs r furthermore it is proved that k has a taylor series expansion at any given hs r i e formula where kn the nth derivative of k at is an n linear map from the n fold space of hs r to c t t hs r and the series converges in the space c t t hs r uniformly for h for some 0 each term yn kn hn in the series solves a linearized kdv equation thus any solutions of the ivp can be obtained by solving a series of linear problems by contrast the corresponding map kp established by the initial value problem for the periodic kdv equation t u u x u 3 x u 0 u x 0 x for x s t r where s is the unit length circle in the plane is known to be continuous only from hs s to c t t hs s this is due to the lack of smoothing effects for solutions of the periodic kdv equation in this paper it is shown that kp is lipschitz continuous from hs 1 s to c t t hs s and is n times frechet differentiable from hs n 1 s to c t t hs s for any n 1 the method developed in this paper applies to other nonlinear dispersive wave equations

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

large time asymptotics of solutions to the generalized korteweg de vries equation we study the asymptotic behavior for large time of solutions to the cauchy problem for the generalized korteweg de vries gkdv equationut u 1 u x 13uxxx 0 wherex t rwhen the initial data are small enough if the power of the nonlinearity is greater than 3 then the solution of the cauchy problem has a quasilinear asymptotic behavior for large time more precisely we show that the solutionu t satisfies the decay estimate u t l c 1 t 1 3 1 1 for 4 uux t l ct 2 3 1 t 1 3and using these estimates we prove the existence of the scattering stateu l2such that u t u t u l2 ct 3 3for any small initial data belonging to the weighted sobolev spaceh1 1 f l2 1 x 2 1 2 1 2x 1 2 f l2 whereu t is the airy free evolution group

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

global existence of small solutions to nonlinear evolution equations abstract we study the global existence and asymptotic behaviour of small solutions of a large class of nonlinear partial differential equations if the nonlinear terms are of high degree the solutions will be asymptotic to solutions of the linear equation

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework