A thermodynamic framework for a gradient theory of continuum damage (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.
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.
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.
International Journal of Fracture, 2016
For a wide variety of quasi-brittle materials, the constitutive microplane models of damage are capable of describing the anisotropic development and growth of microcracks when materials exhibit inelastic response. Damage development in solids leads to the degradation of the macroscopic material stiffness and results in different response in loading and unloading. On the other hand, the constitutive microplane models of plasticity describe the anisotropic plastic sliding that originates macroscopic permanent deformation and remains upon unloading. For realistic modeling of these materials, in which both damage and plasticity mechanisms can evolve simultaneously, the microplane
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.
A two-scale model for dynamic damage evolution
Journal of the Mechanics and Physics of Solids, 2014
This paper presents a new micro-mechanical damage model accounting for inertial effect. The two-scale damage model is fully deduced from small-scale descriptions of dynamic micro-crack propagation under tensile loading (mode I). An appropriate micromechanical energy analysis is combined with homogenization based on asymptotic developments in order to obtain the macroscopic evolution law for damage. Numerical simulations are presented in order to illustrate the ability of the model to describe known behaviors like size effects for the structural response, strain-rate sensitivity, brittle-ductile transition and wave dispersion. Please cite this article as: Keita, O., et al., A two-scale model for dynamic damage evolution. J. Mech. Phys. Solids (2013), http://dx.Please cite this article as: Keita, O., et al., A two-scale model for dynamic damage evolution. J. Mech. Phys. Solids (2013), http://dx.
An approach for incorporating classical continuum damage models in state-based peridynamics
Computer Methods in Applied Mechanics and Engineering, 2013
Peridynamics has gained significant attention as an alternative formulation for problems in solid mechanics. Recent contributions have included initial attempts to include material damage and failure. In this paper, we propose an approach to incorporate classical continuum damage models in the state-based theory of peridynamics. This has the advantage of enabling the description of the damage evolution process in peridynamics according to well-established models. The approach is based on modifying the peridynamic influence function according to the state of accumulated damage. As a result, peridynamic bonds between nonlocal material points are severed in accordance with the damage law. The peridynamic damage formulation proposed is implemented for the particular case of a well established ductile damage model for metals. The model is applied to the simulation of ballistic impact of extruded corrugated aluminum panels and compared with experiments.
A Macroscopic Approach to Continuous Damage and Viscoelasticity Analysis
A 3D model for continuous damage is formulated within the framework of a thermodynamic reasoning. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is then proposed and a hardening law associated with the damage process is identified from available experiment results. For completeness, the rate-type constitutive equations are derived. The previous model is implemented within a finite element procedure. The code is first verified by comparison with closed-form solutions in simplified configurations, and then validated by comparison with experimental creep tests.
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.
A thermodynamically consistent peridynamics model for visco-plasticity and damage
Computer Methods in Applied Mechanics and Engineering, 2019
This article presents a unified visco-plastic-damage model in the peridynamics setup which may be applied across different regime of strain rates and temperatures. In the model, we introduce two internal variables, one describing plastic flow and other the damage in the material. Exploiting the idea of master balance, in addition to the conventional momentum balances, we postulate micro-force balances for both plastic flow and damage evolution in terms of additional peridynamic force states. The equations of motion are in the form of integro-differential equations and do not require continuity of field variables. Using the idea of energy equivalence and entropy equivalence, constitutive relations for the peridynamic force states are determined. The proposed peridynamic visco-plastic-damage model may be thought as a non-trivial extension of the recently developed peridynamic visco-plasticity model [69]. The current scheme couples the visco-plasticity and damage in a thermo-dynamically consistent manner and provides temperature evolution which reflects contribution from both plasticity and damage. The efficacy of the model is demonstrated through simulations of the adiabatic shear band propagation as observed in Kalthoff-Winkler experiment and the shear plugging failure of Weldox 460 E steel plates along with the determination of the ballistic limit.