Dieter Stolle

Deformation of strain softening materials Part II: Modelling of strain softening response

Abstract This paper is an extension of the research reported by the authors in ref. [1]. The emphasis is placed on the modelling of unstable strain softening response. The inception of softening is viewed as a bifurcation problem. Necessary conditions for bifurcation corresponding to strain localization are first reviewed, followed by the description of post bifurcation behaviour. The approach advocated herein regards strain softening as a local phenomenon occurring in a “smeared” sense at a material point. Two alternative techniques for incorporating strain softening response into phenomenological frameworks are discussed: a “smeared” shear band approach employing an internal variable (the thickness of the shear band), and a method based on direct incorporation of “size effect”.

DEFORMATION OF STRAIN SOFTENING MATERIALS. PART 1: OBJECTIVITY OF FINITE ELEMENT SOLUTIONS BASED ON CONVENTIONAL STRAIN SOFTENING FORMULATIONS

Abstract This paper is a continuation of the research initiated by the first author and Z. Mroz [1] during the 1980–1981 period. It is intended as a prelude to a series of articles which extend the concepts and ideas introduced at that time. In the present article, finite element analysis for conventional strain-softening concepts is provided. Sensitivity of the solution to the details of discretization (the type and number of elements) and to the strain-softening rate is discussed. The solutions obtained in this study, though unique in a mathematical sense, prove to be very sensitive to both factors. In order to avoid this sensitivity, the introduction of the geometrical strain-softening effect into the constitutive relation is recommended (after ref. [1]). An extended and generalized version of such a concept will be presented separately.

Modelling of dynamic response of pavements to impact loading

Abstract This contribution presents a discrete layer model for studying the elastostatic response of a pavement to falling weight deflectometer impact loading. The displacement field is represented by a Fourier-Bessel series expansion in the radial direction and piecewise linear variation in displacement in the vertical. Explicit time marching has been adopted to follow the history of a response. The results show that, although dynamic and static deflection bowls are different, little amplification in displacement due to inertia occurs directly under the load, even in the absence of damping. The results also suggest that measured displacements farther away from the load should not be used for backcalculation, if static analysis is used to interpret FWD generated data.

Parameter Estimates of Pavement Structure Layers and Uniqueness of the Solution

The question of uniqueness of backcalculated moduli of a pavement structure subjected to axisymmetric loading is addressed. Two simple examples are presented to demonstrate common difficulties associated with backcalculation, in particular problem conditioning. The sensitivity of the backcalculated solution to layer thickness, assumed Poissons ratios, and seed moduli is examined for a two-layered problem. It is shown that it may be possible to use adjusted measured falling weight deflectometer (FWD) data together with static analysis to effect backcalculated moduli for the subgrade. However, it is concluded that the calculation of the pavement moduli from surface displacement data may not yield representative in situ pseudoelastic moduli because of the nature of multilayered stress analysis and problem conditioning.

Stress-path dependency of resilient behaviour of granular materials

This paper describes an experimental study that was completed to investigate the resilient constitutive characteristics of a granular limestone, as well as to assess the applicability of conventional modelling within the framework of elasticity theory for the material that was studied. Test results corresponding to various stress paths are reported for a well-graded, sub-angular coarse sand. Noticeable differences are found with regard to the measured deformation responses when compared with those from linear elastic model predictions. On the basis of studying the stress–strain responses in terms of invariants, the authors conclude that the difference in the resilient responses of the material for various stress paths is largely due to the inherent nonlinear anisotropic nature of the material, and that stress-induced fabric associated with, for example, rearrangement of particles and particle connectivity should be taken into account for better interpretation of resilient behaviour of granular soil.

A comparison of Eulerian and updated Lagrangian finite element algorithms for simulating film casting

This paper describes and compares Eulerian (E) and Updated Lagrangian (UL) finite element algorithms for simulating film casting. It is found that the E algorithm is more accurate, faster and simpler to implement for one-dimensional film casting of a viscous fluid. However, the UL algorithm provides a natural and intuitive framework for accommodating viscoelasticity and for investigating the stability of the film.

On the Importance of Hysteresis in Numerical Modeling of Surfactant-Induced Unsaturated Flow

It is known that surfactants can induce flow in unsaturated porous media due to the dependence of capillary pressure on surface tension. A commonly observed feature in systems with surfactant-induced flow is a transient wetting/drying/wetting sequence associated with the propagation of a surfactant solute front under monotonic flow conditions. Previous efforts to model surfactant-induced flow in relatively complex (e.g., two-dimensional systems) have not successfully incorporated hysteretic moisture retention properties. In this research, hysteretic, two-dimensional simulations of surfactant-induced flow were performed to assess the potential importance of considering hysteresis in such simulations. Hysteretic simulation results were compared to experimental data and to non-hysteretic simulations. The results suggest that the inclusion of hysteresis in numerical simulations can improve the match between simulated and experimental results in systems with surfactant-induced unsaturated flow. Furthermore, the inclusion of hysteresis in numerical simulations played a significant role in predicting the distribution of the contaminant and correct pressure head/moisture condition at the end of the experiment.

Lower and upper limits of layered-soil strength

This paper presents an approach to determine the lower and upper limits for failure criteria of layered soils that have periodic structure. Particular functional forms are proposed for multilayered soil samples consisting of two periodic constituents. It was found that the upper limit of failure criterion is uniquely determined by volume fraction and strength characteristics of each constituent, whereas the lower limit is affected by the interaction between constituent layers, which in turn depends on the deformation characteristics. An important observation is that an upper limit can only be reached for certain stress paths. The directional dependency of layered soil strength was examined within the context of the proposed approach.

Draw Resonance in Film Casting as a Response Problem Using a Material Description of Motion

A new numerical algorithm was developed for simulating one-dimensional, isothermal film casting of a viscoelastic polymer. The algorithm incorporates a material description of motion and allows the observation of draw resonance as a response problem. Simulation results for velocity, thickness, stress and stability for a low relaxation time agreed with the closed-form solutions for a viscous fluid. When the elastic contribution was increased the observed effects were as follows: the velocity decreased; the thickness gradient at the die increased; the thickness at the roll increased; the axial stress decreased; and the stability of the film decreased.

Application of Stochastic Finite-Element Method to Deflection Analysis of Pavement Structures

The effect of random variations in layer properties of a pavement-subgrade system on surface deflections is investigated. This is done by using a stochastic finite-element framework based on the perturbation method. The Taylors expansion scheme is used. The variations of the surface deflections are related to the variations of layer moduli via a coefficient matrix, thereby allowing an investigation of the sensitivity of measured deflections to the variation of pavement and subgrade moduli. The analyses confirm that surface deflections are not very sensitive to variations of modulus within the pavement structure. Using the Boussinesq-Odemark approximation, it is concluded that, for the sample problem analyzed, the effect of higher-order terms on variation estimates of displacement is negligible when the coefficient of variation of subgrade modulus is less than 15 percent. The effect of inertia on the coefficient of variation of displacement due to variations in layer moduli is also briefly addressed. It i...