Dusan Krajcinovic

Damage tensors and the crack density distribution

Abstract The paper presents an algorithm for the derivation of damage tensors emphasizing its relationship with the actual and approximate crack density distributions. The proposed model is illustrated using scalar, second and fourth order continuous tensor approximations of some typical two and three dimensional crack distributions. It is also shown that the occurrence of regions with negative crack density (anticrack regions) is in many cases a common and as yet unexplored feature of the approximate solutions.

Statistical aspects of the continuous damage theory

Abstract The present study addresses several fundamental aspects of a link connecting the Continuous Damage Theory and the Statistical Strength Theories. The attention is focused on a simple but efficient way of devising rational damage laws based on the physical nature of the phenomenon. The computed results evidence the remarkable flexibility of the suggested model in its application for a wide range of different materials.

A micromechanical damage model for concrete

Abstract The present paper proposes a constitutive theory for concrete based on the geometry of its mesostructure and the actual kinetics of the microcrack evolution. The only material parameters used within the context of the proposed formulation are those associated with the elastic, macroscopic response and the critical stress intensity factors of the constituent phases. The model allows for a rational determination of the response in function of the volume fraction of the coarse aggregate, sieving curve, distribution and size of initial defects, relative strengths of the cement and aggregate, etc.

Damage model for brittle elastic solids with unequal tensile and compressive strengths

The paper presents a rate-type constitutive analysis of damage, applicable to brittle materials whose elastic properties degrade during a deformation process. Different tensile and compressive material responses are modeled incorporating positive and negative projections of the stress or strain tensors. Proposed evolution laws for the rate of compliance tensors are consistent with some of the prominent features of brittle material response. A new structure of the damage surface is introduced for a more accurate account of the effects of the hydrostatic states of stress on the overall response. Derived rate constitutive equations provide the explicit representation of the tangent compliance tensor. The proposed model is applied to uniaxial tension and compression to illustrate nonlinear relationships between stress and longitudinal, lateral, and volumetric strains. The proposed model is compared with some of the existing theories. DEGRADATION of elastic properties reflecting accumulating damage in brittle materials is primarily a consequence of the evolution of internal microcrack structure. Depending on the material microstructure and the current state of stress and strain and their rates, instantaneous material response and further evolution of damage may involve activation of different microcrack mechanisms. The tensile hoop stress generated at the surface of relatively large pores represents a preferential crack nucleation mechanism in very porous rocks. In low porosity, compact rocks frictional sliding of crack surfaces can destabilize original shear cracks, causing them to kink and develop wing cracks. Other mechanisms of microcracking are also possible. Some of these mechanisms were implemented in the failure analysis of brittle solids by Ashby and Sammis (I), and others. Progressive degradation of mechanical properties is an inherent feature of brittle material behavior. Several analytical models were developed to estimate the effective elastic properties of a solid weakened by a given distribution of microcracks or other defects. A comprehensive review of these models can be found in a recent treatise by Nemat-Nasser and Hori (2). An important issue in the formulation of continuum damage models is related to the appropriate choice of the mathematical form for the damage variable. This has been recently studied by Lubarda and Krajcinovic (3), who considered several frequently encountered two and three dimensional distri- butions of microcracks. Their analysis demonstrated the shortcomings of the scalar and second- order tensor damage variables, and the accuracy gained by using the fourth-order tensor variable. The mode and stability of crack growth and, therefore, behavior of brittle material strongly depends on the sign and magnitude of applied stresses. For instance? the response of brittle material subjected to a compressive loading is strongly dependent on the magnitude of lateral confinement. An unconfined specimen fails by axial splitting, attributed to unstable growth of a single crack, at relatively small microcrack density. As the confinement is increased, axial splitting is suppressed and at large levels of confinement homogeneous microcracking prevails throughout the sample, resulting in a quasi-ductile overall response (Horii and Nemat-Nasser (4)). The analysis presented in this paper addresses the important issue of modeling different tensile and compressive responses of brittle materials. The concept of positive and negative projections of stress and strain tensors is used to account approximately for two basic, tensile and compressive, damage evolution modes. This idea was independently introduced by Ladeveze and Lemaitre (5), Ortiz (6) and Mazars (7), and was subsequently utilized by Simo and Ju (8), Yazdani and Schreyer (9), Ju (IO), Stevens and Liu (l 11, Yazdani (12), and others. The positive parts of the stress

Damage mechanics: accomplishments, trends and needs

The objective of this study is to highlight the accomplishments, weaknesses and trends of damage mechanics and research needed for further development. The growing interest in damage mechanics is a proof that the accomplishments are significant. However, one of the messages is that the damage mechanics, in its focus on the dilute density of micro-defects and homogeneous solids, did not address the problems that are of primary interest in applications. The list of references in this paper is restricted to the current papers that list the older works.

A micromechanical model for concrete in compression

Abstract This paper develops a general three-dimensional micromechanical constitutive theory for plain concrete subjected to uniaxial and triaxial compressive loads. The overall nonlinear response of the material is attributed solely to the activation and growth of the randomly oriented microdefects present in the mesoscale prior to any loading. In addition, kinetic equations are developed that describe the microcrack evolution as a function of the applied loads. These equations are shown to pattern the actual damage evolution in the solid as confirmed by the acoustic emission tests. The results generated from this model are shown to compare favorably to the experimentally observed trends for both uniaxial and triaxial compression even though the formulation is not adorned with any additional fitting parameters.

Some fundamental issues in rate theory of damage-elastoplasticity

Abstract The paper elaborates on some fundamental constitutive issues in the rate theory of damage-elastoplasticity. The analysis combines the constitutive theories of elastoplastic and progressively damaged solids. After defining needed kinematic and kinetic preliminaries, the anisotropic elastic response is analyzed by introducing a set of damage tensors which represent material degradation and induced elastic anisotropy. Decomposition of the rate of stress and deformation tensors into their elastic and inelastic parts is then defined in a manner analogous to the corresponding decomposition used in large-deformation elastoplasdcity theory. The procedure is further developed to partition the inelastic stress and strain rates into the damage and plastic parts, which takes into account the physics of these deformation processes. The energy dissipation rate is derived and the thermodynamic forces conjugate to elastic stiffness and compliance tensors are identified, based on a thermodynamic analysis of isothermal deformation process. The damage potentials for the corresponding fluxes are introduced and the constitutive expressions for the damage stress and strain rates are established. The concept of a damage surface is used to define the onset and evolution of damage. A constitutive analysis for inelastic stress and strain rates is then presented. The inelastic potential function and the yield surface are introduced. A dual formulation is constructed in both the stress and strain spaces. The two limiting cases, one involving plasticity without damage, and the other involving damage without plasticity, are deduced from the developed and more general constitutive framework of damage-elastoplasticity.

A self-consistent model for microcrack-weakened solids

Abstract The paper focuses on the formulation of a self-consistent process model for a perfectly elastic solid weakened by an ensemble of microcracks. The derivation is restricted to the plane stress and strain, and monotonically increasing tensile loads. The proposed formulation does not require introduction of additional, physically unidentifiable, ‘material’ parameters.

Random Cantor set models for the elastic-perfectly plastic contact of rough surfaces

The objective of this study was to formulate discrete and continuous spatial models to describe the elastic-perfectly plastic deformation of two rough surfaces in contact. The two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate. The rough self-affine fractal structure of the effective surface is approximated by a random Cantor set representation embedded in two dimensions. Both of the proposed models admit analytical solutions whether the plastic deformation is volume conserving or not. Presented results illustrate the effects that volume conservation and initial surface structure have on the elastic-perfectly plastic deformation process. The results from the continuous model are compared with the results obtained from the discrete model, and existing experimental load displacement data for the deformation of a bead-blasted steel surface.

Some fundamental issues of damage mechanics

The present paper focuses on the discussion of a set of rational criteria for the selection of the damage parameter. The paper considers scalar, second-, fourth-, and six-order tensor representations of damage and evaluates the accuracy with which they approximate exact, micromechanical solutions. Considerations of geometrical, stiffness and failure criteria favor the selection of effective stiffness as being the most appropriate choice for the damage parameter.