Abstract

This work presents a procedure to simulate the growth and propagation of localized tensile cracks on quasi-brittle materials. The so-called smeared damage approach, which consists in standard finite elements and local nonlinear constitutive laws, is recovered and improved in order to represent crack localization and avoid spurious mesh-bias dependence in the discrete problem. This is achieved by means of the implementation of a local crack-tracking algorithm which can reproduce individual (discrete) cracks and ensure objectivity of the finite element problem solution. The performance of the localized damage model is stressed by means of the analyses of structural case-studies. Compared to the Smeared Crack Approach in its original form, the presented procedure shows clearly a better capacity to predict realistic collapse mechanisms. The proposed tracking technique is relatively inexpensive.

Abstract

This paper extends the use of crack-tracking techniques within the smeared crack approach for the numerical simulation of cohesive–frictional damage on quasi-brittle materials. The mechanical behaviour is described by an isotropic damage model with a Mohr–Coulomb failure surface. The correct crack propagation among the two alternative fracture planes proposed by the Mohr–Coulomb theory is selected with the use of an energy criterion based on the total elastic strain energy. The simulation of three benchmark problems of mixed-mode fracture in concrete demonstrates that the proposed methodology can reproduce the material’s frictional characteristics, showing robustness, as well as mesh-size and mesh-bias independence.

Abstract

We identify in this paper a general framework for the development of continuum damage models in their fully coupled plastic damage form. The focus of this paper is directed to the general formulation of infinitesimal models defined by yield and damage surfaces in stress space. The main feature of the proposed formulation is the direct and independent consideration of the damage mechanisms (isotropic damage, cracking, etc.) degrading the stiffness of the material, thus allowing for a complete physical characterization of these effects. This modular structure is accomplished by a kinematic decomposition of the strains in an elastic, plastic and multiple damage parts, as belonging to each activated damage mechanism. An additive decomposition in the infinitesimal range of interest is considered. Based on this decomposition, the constitutive characterization alluded to above for each damage mechanism is carried out in a complete thermodynamically consistent framework. One of the virtues of the considered framework is the fact that it includes many of the diverse damage models existing in the literature as particular cases. In this way, the developments presented herein furnish a unified framework for the formulation of continuum damage models, including isotropic damage, compliance based formulations, effective stress anisotropic models, smeared crack models and the related formulations of cracking and damage based on strong discontinuities. Besides the clear physical significance added to these existing formulations, the proposed framework also defines a very convenient context for the efficient numerical integration of the resulting models. This aspect is explored in Part II of this work, as it is the application of the framework proposed herein to the numerical simulation of porous metals.