Jean H. Prevost

A simple plasticity theory for frictional cohesionless soils

Abstract A simple elastic-plastic constitutive model for cohesionless soils is proposed. The model retains the extreme versatility and accuracy of the simple multi-surface J 2 -theory in describing observed shear nonlinear hysteretic behaviour, shear stress-induced anisotropy; and reflects the strong dilatancy dependency on the effective stress ratio. The theory is applicable to general three-dimensional stress-strain conditions, but its parameters can be derived entirely from the results of conventional laboratory soil tests. A number of examples are presented including an analysis of seismically induced liquefaction behind a retaining structure.

Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples

Abstract Viscoplasticity is introduced as a procedure to regularize the elasto-plastic solid, especially for those situations in which the underlying inviscid material exhibits instabilities which preclude further analysis of initial-value problems. The procedure is general, and therefore has the advantage of allowing the regularization of any inviscid elastic-plastic material. Rate-dependency is shown to naturally introduce a length-scale into the dynamical initial-value problem. Furthermore, the width of the localized zones in which high strain gradients prevail and strain accumulations take place, is shown to be proportional to the characteristic length c η, which is the distance the elastic wave travels in the characteristic time η. Viscosity can thus be viewed either as a regularization parameter (computational point of view), or as a substructural/micromechanical parameter to be determined from observed shear-band widths (physical point of view). Finally, from a computational point of view, the proposed approach is shown to have striking advantages: (1) the wave speeds always remain real (even in the softening regime) and are set by the elastic moduli; (2) the elasto-(visco-)plastic constitutive equations are amenable to unconditionally stable integration; (3) the resulting well-posedness of the dynamical initial-value problem guarantees stable and convergent solutions with mesh refinements. The initial-value problems reported in this first part are essentially one-dimensional. They are used because they offer the simplest possible context to illustrate both the physical and computational significance of the proposed viscoplastic regularization procedure. The methods used in multi-dimensional analysis and examples will be reported in Part 2.

Inhomogeneous deformation in metallic glasses

The present study provides a theoretical framework for the inhomogeneous deformation in metallic glasses. The free volume concentration is adopted as the order parameter, which is a function of position and time. The three processes that can change the local free volume concentration are diffusion, annihilation, and stress-driven creation. The rate functions for free volume generation and plastic flow depend on the underlying microscopic model, but the framework is generally valid for different models. A simple shear problem is solved as an example. A linear stability analysis is performed on the basis of the homogeneous solution. An inhomogeneous solution is obtained with a finite amplitude disturbance to the initial free volume distribution. Numerical simulation shows the development of the inhomogeneous deformation and strain localization.

Mechanics of continuous porous media

Abstract Soils consist of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with water and air or gas. The word “soil”, therefore, implies a mixture of assorted mineral grains with various fluids. When free or no drainage conditions prevail, a single phase description of soil behavior is adequate. However, in intermediate cases in which some flow can take place, there is an interaction between the skeleton strains and the water flow. The solutions of these problems require that soil behavior be analyzed by incorporating the effects of the transient flow of the pore-fluids through the voids, and, therefore, requires that a multiphase formulation be available for porous media. Such a theory was first proposed by Biot, early in 1955, for a linear elastic and a linear visco-elastic porous medium. However, it is observed experimentally that the stress-strain-strength behavior of the soil skeleton is strongly non-linear, anisotropic, elastoplastic and path-dependent. An extension of Biots theory into the nonlinear anelastic range is, therefore, necessary in order to analyze the transient response of soil deposits. This extension has acquired considerable importance in recent years due to the increased concern with the dynamic behavior of saturated soil deposits and associated liquifaction of saturated sand deposits under seismic loading conditions. Such an extension of Biots formulation is proposed herein.

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 mixtures 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.

Finite element analysis of dynamic coupled thermoelasticity problems with relaxation times

A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Green and Lindsay’s dynamic thermoelasticity model is selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. Time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis. A number of examples are presented which demonstrate the accuracy and versatility of the proposed model, and the importance of finite thermal propagation speed effects.

Channel-cracking of thin films with the extended finite element method

The recently developed extended finite element method (XFEM) is applied to compute the steady-state energy release rate of channeling cracks in thin films. The method is demonstrated to be able to model arbitrary singularities by using appropriate enriching functions at selected nodes with a relatively coarse mesh. The dimensionless driving force for channeling cracks is obtained as a function of elastic mismatch, crack spacing, and the thickness ratio between the substrate and the film. The results are compared with those from several previous studies when available. Emphasis is placed on the cases with compliant substrates, for which much less information is available from previous studies. It is found that, while it is quite challenging to model the cases with very compliant substrates using regular finite element method because of the strong singularities, the present approach using XFEM is relatively simple and straightforward.

Simulation of homogeneous nonGaussian stochastic vector fields

A spectral representation-based simulation methodology is proposed to generate sample functions of a multi-variate, multi-dimensional, nonGaussian stochastic vector field, according to a prescribed cross-spectral density matrix and prescribed (nonGaussian) marginal probability distribution functions. The proposed methodology starts by generating a Gaussian vector field that is then transformed into the desired nonGaussian one using a memoryless nonlinear transformation in conjunction with an iterative scheme. The generation of the Gaussian vector field is performed taking advantage of the Fast Fourier Transform technique for great computational efficiency. The special case of simulation of nonGaussian vector fields modeling material properties is examined, mainly from the point of view of certain simplifying assumptions that can be made for such random media. Finally, a numerical example involving a tri-variate, two-dimensional, nonGaussian stochastic vector field is presented in order to demonstrate the capabilities and the efficiency of the proposed methodology.

Accurate numerical solutions for Drucker-Prager elastic-plastic models

Abstract An exact solution for the Drucker-Prager elastic-plastic equations with linear hardening and arbitrary degree of nonassociativity is presented. The accuracy of two approximate integration schemes, incremental tangent prediction with radial projection and one-step Euler (forward/backward) integration, is examined.

Wave propagation in fluid-saturated porous media: An efficient finite element procedure

Abstract An efficient finite element procedure to analyze wave propagation phenomena in fluid-saturated porous media is presented. The saturated porous medium is modelled as a two-phase system consisting of a solid and a fluid phase. Time integration of the resulting semi-discrete finite element equations is performed by using an implicit-explicit algorithm. In order to remove the time step size restriction associated with the presence of the stiff fluid in the mixture, the fluid contribution to the equations of motion is always treated implicitly. The procedure allows an optimal selection of the time step size independently of the fluid. Depending upon the particular intended applications (e.g., seismic, blast loading,...) the fluid may be assumed incompressible or compressible. Numerical results which demonstrate the accuracy and versatility of the proposed procedure are presented.