Use Of Continuum Damage Mechanics Research Articles

A combined XFEM–damage mechanics approach for concrete crack propagation

This paper presents a crack model that couples the benefits of the damage mechanics approach and the extended finite element method (XFEM). A crack-tracking technique is developed to propagate the crack path along a single row of finite elements as a function of the stress-based nonlocal method. The level sets are computed to predict the crack path, and the path is corrected with the use of continuum damage mechanics. Once a certain level of damage is reached inside an element, the previously-computed level sets are used to apply the XFEM formulation. A cohesive XFEM formulation is used to transfer energy dissipation from the damage mechanics approach to the XFEM model. Using numerous test cases, it is shown that the model is mesh independent and that it removes the spurious stress transfer exhibited by continuum damage models. Various transition damage criteria are compared, and the optimal one is determined.

Determining Damage Development in Hot-Mix Asphalt with Use of Continuum Damage Mechanics and Small-Scale Accelerated Pavement Test

The modeling of asphalt concrete based on continuum damage mechanics (CDM) is an attractive and useful method of determining damage development in hot-mix asphalt (HMA). However, the CDM approach requires the calculation of the convolution integral over the loading duration and creates problems when large amounts of fatigue test data generated from accelerated pavement tests are handled. This study presents an approach to facilitating the calculation of the convolution integral for large amounts of data. Therefore, the approach can be used for pavement performance monitoring. Several asphalt concrete slabs were constructed in a laboratory with a vibratory roller compactor and instrumented with strain gauges and thermocouples. These slabs were tested under the small-scale accelerated loading device called the Model Mobile Load Simulator3. A frequency domain approach was used to analyze the continuous strain data. The constitutive equation in time domain was transformed to a frequency domain with the use of the Fourier transform technique; the pseudostrain and the complex modulus values were determined continuously during the loading. Results indicated that both the pseudostrain and the complex modulus were influenced by the combined effect of loading and temperature. A general trend of reduction of the pseudostiffness and the complex modulus because of these factors was observed in the study. Analysis results indicated that the frequency domain analysis approach was an efficient, better way to handle large amounts of data generated in long-term pavement studies and could be used to determine damage development in HMA as a result of loading.

On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers

The present paper reports and rationalizes the use of Continuum Damage Mechanics (CDM) to describe the Mullins effect in elastomers. Thermodynamics of rubber-like hyperelastic materials with isotropic damage is considered. Since it is demonstrated that stress-softening is not strictly speaking a damage phenomenon, the limitations of the CDM approach are highlighted. Moreover, connections with two-network-based constitutive models proposed by other authors are exhibited through the choice of both the damage criterion and the measure of deformation. Experimental data are used to establish the evolution equation of the stress-softening variable, and the choice of the maximum deformation endured previously by the material as the damage criterion is revealed as questionable. Nevertheless, the present model agrees qualitatively well with experiments except to reproduce the strain-hardening phenomenon that takes place as reloading paths rejoin the primary loading path. Finally, the numerical implementation highlights the influence of loading paths on material response and thereby demonstrates the importance of considering the Mullins effect in industrial design.

Modeling of metallic materials at high strain rates with continuum damage mechanics

Abstract Damage modeling of metallic materials under high strain rate loading conditions is reviewed. The emphasis is on the modeling efforts based on continuum damage mechanics, although many important references dealing with general aspects of dynamic behavior of materials are also discussed. Relevant issues on the use of continuum damage mechanics and on the damage modeling of composites are addressed as well. This review article deals with 134 references

A continuous low cycle fatigue damage model and its application in engineering materials

In this study, the low cycle fatigue (LCF) damage evolution of the engineering materials is studied by use of continuum damage mechanics (CDM) theory. Based on thermodynamics, on a continuum damage variable, D, and on the effective stress concept, a continuum damage model of isotropic LCF is derived and is used to analyze the strain-controlled LCF damage evolution of steam turbine blade material 2Cr13 steel. The damage variable D = 1 − Δσ/ Δσ 0 is selected and measured during strain-controlled LCF tests to verify the model, which is in good agreement with the results. The parameters in the model have clear physical meaning and can easily be determined. The evolution of microstructure during fatigue is observed by transmission electron microscopy, which gives the microscopic explanation for LCF damage evolution law of 2Cr13 steel.

Experimental and theoretical quantification of the development of damage in fatigue tests of bone and antler

This study concerns the development of damage (as measured by a reduction in elastic modulus) in two kinds of bones differing considerably in their degrees of mineralisation: laminar bone from bovine femur and osteonal bone from red deer antler. Antler bone is much tougher than ‘ordinary’ bone and its failure properties have been investigated in: (i) monotonic tensile tests and (ii) creep rupture experiments. Tensile fatigue is another way of examining how damage develops in bone. The development of damage in the present fatigue tests was non-linear with the cycle number, the degree of non-linearity was dependent on the level of stress and followed a clearly different course for bone and antler. Antler was a more damage-tolerant material, being able to achieve a reduction in the final modulus of elasticity, just prior to failure, three tkmes greater than ‘ordinary’ bone. The evolution of damage is quantified by an empirical and a graphical method and by the use of Continuum Damage Mechanics (CDM) expressions. The CDM method shows important conditions, found in antler, but not in bone, that seem necessary for achieving stable fractures and consequently producing very tough materials.

The use of continuum damage mechanics in creep analysis for design

The common theme of this paper is the use of Creep Continuum Damage Mechanics (CDM) in design analysis. It is shown how this approach has the capability to model the deformation and rupture behaviour of components which includes simple ligament situations, notched components, cracked members, and butt-welded steam pipes. The following three principal materials requirments are highlighted: (I) deformation behaviour including damage synergisms; (II) damage kinetics and their relation to physical mechanisms; and (III) stress state, stress level, and temperature dependence of the deformation, damage, and material failure. New methods are discussed for the determination of multi-axial stress rupture criteria. The use of CDM with mechanisms-based constitutive equations to analyse component behaviour in design is design is demonstrated.

Micro- and macroscopic damage and fracture behaviour of welding coarse grained heat affected zone of a low alloy steel: Mechanisms and modelling

Micro- and macroscopic damage and fracture behaviour of the simulated coarse grained heat affected zone (CGHAZ) of a high strength low alloy steel weld are studied through experimental and continuum damage mechanics (CDM) approaches. In order to study the damage and fracture behaviour of the CGHAZ carefully, weld thermal simulation technique is used to enlarge and to generate the region. The dynamic microprocesses of damage and fracture in the CGHAZ are observed through in situ techniques in conjunction with a scanning electron microscope (SEM) equipped with a tensile platform. Several mechanisms of void initiation and crack propagation are observed. A criterion for void initiation by cracking of the inclusion itself and/or debonding at the inclusion-matrix interface is derived. The macroscopic damage evolution law in the CGHAZ is measured through a new a.c. potential system and modelled by use of CDM. A damage evolution equation for the CGHAZ is presented. Comparison of experimental and modelling results is presented and good agreement is found. The effects of stress triaxiality on void initiation, damage evolution and failure in the CGHAZ are also discussed in the framework of CDM.

A continuum damage model for ductile fracture of weld heat affected zone

In this paper, the ductile plastic damage behaviour of weld heat affected zone (HAZ) is studied by use of continuum damage mechanics (CDM). Based on a continuum damage variable, D, the effective stress concept and the thermodynamics, a general continuum damage model for Isotropie ductile fracture is derived from a new dissipation potential chosen by the author herein. A comparison between the damage model and experimental results is presented and a good agreement is found. The model is also used to analyse the ductile plastic damage evolution in thermally simulated welding coarse-grained HAZ of a low alloy steel. The effects of stress triaxiality on plastic damage evolution and on ductile fracture of the coarse-grained HAZ are discussed.

A continuum damage model for weld heat affected zone under low cycle fatigue loading

In this paper, the Low Cycle Fatigue (LCF) damage evolution of weld Heat Affected Zone (HAZ) is studied by use of Continuum Damage Mechanics. Based on a continuum damage variable, D, on the effective stress concept and on thermodynamics, a continuum damage model of isotropic LCF is derived, and is used to analyse the LCF damage evolution of thermally simulated HAZ. A comparison between model and the experimental results is presented and a good agreement is found.

Continuum damage mechanics: Present state and future trends

Continuum Damage Mechanics (CDM) has developed since the initial works of Kachanov and Rabotnov. The paper gives a review of its main features, of the present possibilities and of further developments. Several aspects are considered successively: • - damage definitions and measures, • - damage growth equations and anisotropy effects, • - use of CDM for local approaches of fracture. Various materials, loading conditions and damaging processes are incorporated in the same general framework. Particular attention is given to the possible connections between different definitions of damage, especially between the CDM definition and the information obtained from material science.

Analysis of tests on impact strength of concrete armor blocks

This paper summarizes a series of tests on the impact strength of large concrete breakwater cubes. A simple, design-oriented, analytical model was established on the basis of the continuum damage theory in order to interpret the data collected during a rather ambitious and expensive experimental program involving a large number of cubes of different sizes subjected to impacts of varying intensity. The suggested model involves only one additional material parameter related to the static strength of the concrete specimen in uniaxial compression. A rather surprising accuracy of this fairly crude model is further encouragement for the use of continuum damage mechanics for concrete.