Article

Limit load analysis of thick-walled concrete structures - a finite element approach to fracture

Institut fur Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, University of Stuttgart, Germany
Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.62). 01/1976; DOI: 10.1016/0045-7825(76)90046-3

ABSTRACT The paper illustrates the interaction of constitutive modelling and finite element solution techniques for limit load prediction of concrete structures.On the constitutive side, an engineering model of concrete fracture is developed in which the Mohr-Coulomb criterion is augmented by tension cut-off to describe incipient failure. Upon intersection with the stress path the failure surface collapses for brittle behaviour according to one of three softening rules — no-tension, no-cohesion, and no-friction. The stress transfer accompanying the energy dissipation during local failure is modeled by several fracture rules which are examined with regard to ultimate load prediction.On the numerical side the effect of finite element idealization is studied first as far as ultimate load convergence is concerned. Subsequently, incremental tangential and initial load techniques are compared together with the effect of step size.Limit load analyses of a thick-walled concrete ring and a lined concrete reactor closure conclude the paper along with engineering examples.

0 Bookmarks
 · 
44 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: Tensile failure of unreinforced concrete involves progressive micro-cracking, and the related strain-softening can coalesce into geometrical discontinuities, which separate the material. Advanced mechanical theories and numerical schemes are required to efficiently and adequately represent crack propagation in 3D. In this paper we use the concept of strong discontinuities to model concrete failure. We introduce a cohesive fracture process zone, which is characterized by a transversely isotropic traction–separation law. We combine the cohesive crack concept with the partition of unity finite element method, where the finite element space is enhanced by the Heaviside function. The concept is implemented for tetrahedral elements and the failure initialization is based on the simple (non-local) Rankine criterion. For each element we assume the embedded discontinuity to be flat in the reference configuration, which leads to a non-smooth crack surfaces approximation in 3D, in general; different concepts for tracking non-planar cracks in 3D are reviewed. In addition, we propose a two-step algorithm for tracking the crack path, where a predictor step defines discontinuities according to the (non-local) failure criterion and a corrector step draws in non-local information of the existing discontinuities in order to predict a ‘closed’ 3D crack surface; implementation details are provided. The proposed framework is used to analyze the predictability of concrete failure by two benchmark examples, i.e. the Nooru-Mohamed test, and the Brokenshire test. We compare our numerical results, which are mesh independent, with experimental data and numerical results adopted from the literature.
    Computer Methods in Applied Mechanics and Engineering 01/2006; · 2.62 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The failure behavior of isotropic non-linear elastic materials is macroscopically studied in terms of elastic strain energy density generalizing the Coulomb criterion. This generalization is based on a rigorous mathematical substrate developed on the principle of conservation of the total elastic strain energy. In the general case of loading the behavior of a material is described with regard to the secant elastic moduli depending on both first strain and second deviatoric strain invariants. This dependence enlightens, in physical terms, the different reaction of materials in normal and shear stresses. Besides, these two moduli establish two constitutive equations for the complete description of any material, instead of the usual one. A theoretical application is given and the failure surfaces which are obtained in stress space are being commented. Predictions obtained in tension of steel under pressure from Bridgman's experiments and some of his observations for the failure behavior of steels are explained on the existence of a universal criterion with the present approach.
    International Journal of Mechanical Sciences 01/2012; 54(1):241–248. · 1.61 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The application of finite element methods (FEM) is often restricted by the available computer capacity and the computing costs. The purpose of this paper, therefore, is, to present test results and to discuss possible ways of achieving a substantial reduction in computing times. Dividing the numerical analysis into the five levels–hardware, software, element-mesh and element-type, iteration technique (approximation of non-linearity) and constitutive model–one can show that the computing time can be reduced by about 20 per cent at every level. In particular, the use of the modified Newton-Raphson method for approximation of non-linearity and the constitutive model–apart from the theoretical concept (elastoplastic, hypoelastic etc.)—must be formulated in a manner which does not produce substantial changes in the coefficients of the material matrix caused by small stress changes. On the whole, computing time can be reduced to about 10 per cent of present computing costs. Thus, it would even be economically viable to solve three-dimensional non-linear problems by FEM.
    International Journal for Numerical and Analytical Methods in Geomechanics 07/2005; 9(3):261 - 275. · 1.56 Impact Factor