Theoretical Framework for Modelling the Behaviour of Frictional Materials

A constitutive theory is proposed, which possesses the possibilities of modelling all the important features or the behaviour or frictional materials such as: influence of all three stress invariants, coupling between deviatoric and volumetric response, dilatancy, softening, and different behaviour in loading and unloading. The basic constitutive assumptions are relations between properly defined stress and strain rate invariants, from which the component equations are derived by means of a suitable reformulation. After the incremental stress-strain relations have been derived, they are augmented by consistent loading/unloading criteria. Emphasis is given to a fundamental discussion of the general properties of the theory proposed and it is shown to fulfil all the formal requirements (causality, determinism, admissibility, form-invariance, continuity) that a properly formulated constitutive theory must obey. Moreover, the theory contains a surprisingly large number of classical as well as nonclassical theories as special cases. In particular, it contains formulations ranging from nonassociated plasticity theory, associated plasticity theory, hypoelasticity to elasticfracturing theory

Behaviour of Viscoelastic-Viscoplastic Spheres and Cylinders-Partly Plastic Vessels walls

The material model consists of a viscoelastic Burgers element and an additional viscoplastic Bingham element when the effective stress exceeds the yield stress. For partly plastic vessel walls, expressions are derived for the stress and strain state in pressurised or relaxation loaded thick-walled cylinders in plane strain and spheres. For the spherical problem, the material compressibility is accounted for. The influence of the different material parameters on the behaviour of the vessels is evaluated. It is shown that the magnitude of the Maxwell viscosity is of major importance for the long-term behaviour of thick-walled partly plastic vessels

Relaxation of Thick-Walled Cylinders and Spheres

Using the nonlinear creep law proposed by Soderberg, closed-form solutions are derived for the relaxation of incompressible thick-walled spheres and cylinders in plane strain. These solutions involve series expressions which, however, converge very quickly. By simply ignoring these series expressions, extremely simple approximate solutions are obtained. Despite their simplicity these approximations possess an accuracy that is superior to approximations currently in use. Finally, several physical aspects related to the relaxation of cylinders and spheres are discussed

Viscoelastic-Viscoplastic Formulas for Analysis of Cavities in Rock Salt

The material model consists of a viscoelastic Burgers element and an additional viscoplastic element, which includes Bingham viscosity and a viscoplastic Kelvin element. For spherical and cylindrical cavities, expressions are derived for the stress and strain fields and volume convergence. Spherical and cylindrical cavities are treated in a unified formulation. The expressions for the transient phase require a numerical approach. A simple numerical scheme is proposed which solves these expressions efficiently. For constant pressurization stationary stresses, strain rates and convergence rate will eventually arise. Exact, closed-form solutions are derived for these quantities. The magnitude of the Maxwell viscosity is of vital importance for the stationary state. The material model compares favourably with experimental creep data

Thermodynamical Consequences of Strain Softening in Tension

The strain softening behavior of a tension bar loaded by an increasing elongation is analyzed. The constitutive model consists of linear elasticity in combination with associated plasticity theory using a maximum tensile stress criterion as yield surface. The resulting mechanical stability criterion is augmented by considerations of the use of the second law of thermodynamics. These thermodynamical considerations imply a significant reduction in the possible strain softening responses. Moreover, for very brittle material behavior, it is shown that the softening region cannot be considered to have a specific strain state, but rather is described by a strrss-elongation relation. This result provides strong physical support for a fictitious crack model. This crack model is then reevaluated in the spirit of a smeared crack approach and the resulting expressions turn out to be identical with those of a composite fracture model

Closure to "2-d Finite Element Analysis of Massive RC Structures"

Nonlinear analysis of concrete structures using finite elements is discussed. The applications include a thick-walled top-closure for a pressure vessel as well as the delicate problems of beams failing in shear. The top-closure analysis evaluates the effect of two different failure criteria and modeling of a realistic post-failure behavior is demonstrated to be mandatory for accurate structural predictions. For shear beams it is shown that the primary cause of failure is strain softening adjacent to the load point. This softening causes a strain localization which in turn results in a tendency toward diagonal cracking. Stirrups prevent this tendency and a shear-compression failure follows. Otherwise, a diagonal tension failure results. This again highlights modeling of strain softening. The influence of the shear retention factor is found to be relatively moderate. Variation of the uniaxial tensile strength influences the results insignificantly. Modeling of secondary cracks is found to be essential. Finally, it is shown that dowel action must be treated through the bending of the bars and not through their shear deformation

Nonlinear Analysis of Cavities in Rock Salt

The paper covers some material and computational aspects of the rock mechanics of leached cavities in salt. A material model is presented in which the instantaneous stiffness of the salt is obtained by interpolation between the unloaded state and a relevant failure state. The model enables prediction of short term triaxial behaviour from uniaxial stress-strain curves. Key results from a nonlinear finite element calculation of a gas-filled cavity are given, and the general features are related to a simple nonlinear method of stress evaluation