An Irreversible Thermodynamics Theory for Damage Mechanics of Solids (original) (raw)
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Acta Mechanica, 2008
We formulate a macroscopic description of the mechanics of damaged materials. To represent the microstructure, the distribution of crack sizes is captured by way of the Minkowski functionals, or so-called quermass integrals, while a second-rank tensor is used to describe the average orientation of the cracks. A two phase-type approach is adopted to distinguish elastically strained material from unstrained regions in the wake of the cracks. Using nonequilibrium thermodynamic techniques, the driving force for the growth of the microcracks is naturally identified. In particular, Griffith's law is generalized to assemblies of polydisperse crack sizes. Due to the detailed characterization of the microstructure, we are also able to account for the plastic zones at the rims of the cracks that are known to hamper the crack growth, and to discuss possible forms of the damage parameter. The presented approach separates in a transparent fashion the incorporation of fundamental thermodynamic and mechanic principles on one hand, from the specification of the material and details of the crack formation and growth on the other hand.
Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems
Entropy, 2016
Mechanics from its side and thermodynamics from its side consider evolution of complex systems, including the Universe. Created classical thermodynamic theory of evolution has one important drawback since it predicts an inevitable heat death of the Universe which is unlikely to take place according to the modern perceptions. The attempts to create a generalized theory of evolution in mechanics were unsuccessful since mechanical equations do not discriminate between future and past. It is natural that the union of mechanics and thermodynamics was difficult to realize since they are based on different methodology. We make an attempt to propose a generalized theory of evolution which is based on the concept of tribo-fatigue entropy. Essence of the proposed approach is that tribo-fatigue entropy is determined by the processes of damageability conditioned by thermodynamic and mechanical effects causing to the change of states of any systems. Law of entropy increase is formulated analytically in the general form. Mechanothermodynamical function is constructed for specific case of fatigue damage of materials due to variation of temperature from 3 K to 0.8 of melting temperature basing on the analysis of 136 experimental results.
Survey of modern trends in analysis of continuum damage mechanics
A brief review of the damage mechanics literature is given. As this area of scientific research is very modern, the authors have restricted themselves to about 100 most important books and papers. Basic equations to introduce the isotropic model in the framework of thermodynamics are given in a form easily applicable in numerical symulations.
A thermodynamic framework for a gradient theory of continuum damage
Acta Mechanica, 2010
In this paper, we present a formulation of state variable based gradient theory to model damage evolution and alleviate numerical instability associated within the post-bifurcation regime. This proposed theory is developed using basic microforce balance laws and appropriate state variables within a consistent thermodynamic framework. The proposed theory provides a strong coupling and consistent framework to prescribe energy storage and dissipation associated with internal damage. Moreover, the temporal evolution equation derived here naturally shows the effect of damage-nucleation, growth and coalescence. In addition, the theoretical framework presented here is easily extendable to the addition of other defects (not shown here), and can be generalized to the development of consistent coupled transport equations for species, such as hydrogen (Bammann et al. in JMPS, 2009, submitted), as well as providing a consistent structure for modeling events at diverse length scales. K. N. Solanki (B) Center for Advanced Vehicular Systems, 200 Research Blvd.,
A new thermodynamically consistent continuum model for hardening plasticity coupled with damage
International Journal of Solids and Structures, 2002
A phenomenological model for hardening-softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional.
On kinematic, thermodynamic, and kinetic coupling of a damage theory for polycrystalline material
International Journal of Plasticity, 2010
The paper proposes a new consistent formulation of polycrystalline finite-strain elastoplasticity coupling kinematics and thermodynamics with damage using an extended multiplicative decomposition of the deformation gradient that accounts for temperature effects. The macroscopic deformation gradient comprises four terms: thermal deformation associated with the thermal expansion, the deviatoric plastic deformation attributed to the history of dislocation glide/movement, the volumetric deformation gradient associated with dissipative volume change of the material, and the elastic or recoverable deformation associated with the lattice rotation/stretch. Such a macroscopic decomposition of the deformation gradient is physically motivated by the mechanisms underlying lattice deformation, plastic flow, and evolution of damage in polycrystalline materials. It is shown that prescribing plasticity and damage evolution equations in their physical intermediate configurations leads to physically justified evolution equations in the current configuration. In the past, these equations have been modified in order to represent experimentally observed behavior with regard to damage evolution, whereas in this paper, these modifications appear naturally through mappings by the multiplicative decomposition of the deformation gradient. The prescribed kinematics captures precisely the damage deformation (of any rank) and does not require introducing a fictitious undamaged configuration or mechanically equivalent of the real damaged configuration as used in the past.
Engineering Structures, 2017
In this study, a generic formulation for constitutive modelling of engineering materials is developed, employing theories of plasticity and continuum damage mechanics. The development of the proposed formulation is carried out within the framework of thermodynamics with internal variables. In this regard, the complete constitutive relations are determined by explicitly defining a free energy potential and a dissipation potential. The focus is put on the rigour and consistency of the proposed formulation in accommodating the coupling between damage and plasticity, while keeping its structure sufficiently generic to be applicable to a wide range of engineering materials. In particular, by specifying the coupling between damage and plasticity in the dissipation function, a single generalised loading function that controls the simultaneous evolution of these dissipative mechanisms is obtained. The proposed formulation can be readily used for either enriching existing plasticity models with damage, or for the developments of new coupled damage-plasticity models. The promising features and the applications of the proposed formulation for describing the behaviour of different engineering materials are discussed in details.
Continuum Damage Mechanics: Part I—General Concepts
Continuum Damage Mechanics (C.D.M.) has developed continuously since the early works of Kachanov and Rabotnov. It constitutes a practical tool to take into account the various damaging processes in materials and structures at a macroscopic continuum level. The main basic features of C.D.M. are considered in the first part together with its present capabilities, including damage definitions and measures, and its incorporation into a thermodynamic general framework. Practical damage growth equations will be reviewed in the second part of the paper.
A comparative study of damage variables in continuum damage mechanics
International Journal of Damage …, 2009
In this work, various definitions of the damage variables are examined and compared. In particular, special emphasis is given to a new damage variable that is defined in terms of the elastic stiffness of the material. Both the scalar and tensorial cases are investigated. The scalar definition of the new damage variable was used recently by many researchers. However, the generalization to tensors and general states of deformation and damage is new and appears here for the first time. In addition, transformation laws for various elastic constants are derived. Finally, the cases of plane stress, plane strain, and isotropic elasticity are examined in detail. In these cases it is shown that only two independent damage parameters are needed to describe the complete state of damage in the material. In this work, a physical basis is sought for the damage tensor [M ] that is used to link the damage state of the material with effective undamaged configuration. The authors and numerous other researchers have used different paths including fabric tensors to connect the two configurations. However, the approach presented here provides for a strong physical basis for this missing link.
On certain fundamental issues in continuum damage mechanics
Journal of the Mechanical Behaviour of Materials
In this article, we discuss three fundamental issues in continuum damage mechanics. First, we investigate the nature of the damage process. For this purpose, we dissect the expression of the effective stress into an infinite geometric series and introduce several stages of damage that we call primary damage, secondary damage, tertiary damage, etc. The second issue to be discussed is the problem of small damage. In this regard, we introduce a new definition of the damage variable that is suitable for small-damage cases. Finally, we discuss the new concept of undamageable materials. These are currently hypothetical materials that maintain a zero value of the damage variable throughout the deformation process. It is hoped that these proposed new types of materials will open the way to new areas of research in both damage mechanics and materials science.