Anisotropic Elastic-Brittle-Damage and Fracture Models Based on Irreversible Thermodynamics
01 Jan 2003-pp 143-184
TL;DR: In this paper, an incremental formulation of the stress-strain equations is developed by the use of the tangent elastic-damage stiffness, and the unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds.
Abstract: Anisotropic damage evolution and crack propagation in elastic-brittle materials is analyzed by the concepts of Continuum Damage Mechanics (CDM) and Finite Element Method FEM (ABAQUS). The original total formulation of the Murakami-Kamiya (MK) model of elastic-damage material is extended and used for damage anisotropy and fracture prediction in concrete. The incremental formulation of the stress-strain equations is developed by the use of the tangent elastic-damage stiffness. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The Local Approach to Fracture (LAF) by FEM is applied to both the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modeled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress-strain curves are reached. Another way to model crack consists in releasing of the kinematic constrains in the nodes. The developed constitutive model is capable of capturing anisotropic damage evolution and crack growth in 2D structure subjected to the quasistatic or cyclic mechanical or thermal loadings. Different damage evolution in tension or compression, as well as the corresponding fracture modes may be analysed.
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20 Apr 2007
TL;DR: In this paper, a wing crack damage model was developed for the analysis of brittle failure of transversely isotropic solids. And the model was implemented in ABAQUS/Standard FE software as a user subroutine.
Abstract: A new continuum damage model, the wing crack damage (WCD) model, was developed for the analysis of brittle failure of transversely isotropic solids. Special attention was paid to the analysis of axial splitting under compression and tensile cracking under tension. In addition to the WCD model a three-dimensional version of the damage model proposed by Murakami and Kamiya was enhanced and implemented in ABAQUS/Standard FE software. The proposed WCD model is based on the use of the damage vector. The vector represents both the normal direction of the surface of the plane crack and the size of the damaged area. Damaging induces anisotropy in an originally transversely isotropic material. The evolution equations for damage are motivated by the wing crack growth mechanism. The evolution is based on propagation of pre-existing damage. The proposed model enables modelling of pre-existing cracks. The feature can be exploited in studying the effect of orientation and size distribution of pre-existing cracks on the failure of materials. The model was implemented in ABAQUS/Standard FE software as a user subroutine. The unsymmetrical behaviour of cracked materials under tension and compression due to the opening and closure of cracks is taken into account in the proposed model. In the work it was shown that the widely used strain-based crack closure criteria cannot be reliably applied in a two- and three-dimensional stress state. To attain a deformation localisation zone of finite width, a damage rate-dependent damage surface was introduced. The validity of the proposed model was verified by testing it against five basic structures composed of known natural materials (ice, marble and concrete). The numerical simulations revealed the capability of the model in modelling brittle failure modes of transversely isotropic materials.%%%%Tutkimuksessa on esitetty kaksi vauriomekaniikkaan (Continuum damage mechanics) perustuvaa materiaalimallia: Murakami Kamiyan (MK) malli, seka uusi "wing crak damage" -malli (WCD). Molemmat mallit on liitetty ABAQUS-elementtimenetelmaohjelmistoon UMAT-aliohjelmana. Esitetty uusi WCD-malli on tarkoitettu transversaali-isotrooppisten materiaalien haurasmurtuman mallintamiseen. Erityista huomiota on kiinnitetty yksiaksiaalisessa puristuksessa tapahtuvan kuormituksen kanssa yhdensuuntaisen halkeamisen seka yksiaksiaalisessa vedossa tapahtuvan kuormitusta vastaan kohtisuorassa olevan saroytymisen mallintamiseen. Esitetty WCD-malli perustuu "vauriovektorin" kayttoon. Vauriovektori edustaa seka tasomaisen saron normaalin suuntaa etta vaurioituneen alueen kokoa. Vaurioitumisen vuoksi transversaali-isotrooppisesta materiaalista tulee anisotrooppista. Vaurion kasvumekanismi simuloi siipisaron (wing crack) kasvumekanismia. Uusi WCD-malli mahdollistaa materiaalissa ennen kuormitusta olevien alkusarojen mallintamisen. Piirretta voidaan hyodyntaa tutkittaessa alkusarojen suunnan ja suuruuden vaikutusta materiaalin vaurioitumiseen. Halkeilleen materiaalin epasymmetrinen kayttaytyminen vedossa ja puristuksessa…
58 citations
Cites methods from "Anisotropic Elastic-Brittle-Damage ..."
...The method is based on continuum damage mechanics (CDM) and has proved to be promising in axial splitting analysis as shown by Skrzypek and Kuna-Ciskal (2003)....
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TL;DR: In this article, anisotropic damage evolution and crack propagation in the elastic-brittle materials is analyzed by the concepts of continuum damage mechanics and finite element method (FEM).
45 citations
TL;DR: In this article, a continuum damage mechanics-based elasto-plastic damage theory, that extends the total form of Hayakawa and Murakami equations, is developed.
Abstract: The continuum damage mechanics-based elasto-plastic damage theory, that extends the total form of Hayakawa and Murakami equations, is developed. Weak elastic-plastic dissipation coupling is assumed by the use of two dissipation potentials, plastic and damage, where only isotropic plasticity and damage hardening is included, whereas kinematic hardening is not accounted for. Unilateral damage condition, based on the concept of generalized projection operators, accounts for a partial damage deactivation, which allows for an influence of negative principal components of the stress tensor on damage evolution. The incremental representation of the elastic-damage constitutive equations is derived. Both elastic-damage and plastic-damage compliance matrices are developed for plane stress condition, and implemented to ABAQUS finite element code by the user-supplied procedure for non-standard material properties. Effective computation algorithm for plastic and damage loading/unloading conditions based on the doubly ...
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TL;DR: In this paper, the analysis of the low cycle fatigue behavior of P91 steel is presented, and an appropriate constitutive model is developed within the framework of thermodynamics of irreversible processes with internal state variables.
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TL;DR: In this article, the authors study a mechanical modeling of complicated materials with damages such as voids, defects, and cracks within the framework of continuum mechanics, and represent the voids and defects, e.g.
Abstract: In this paper we study a mechanical modeling of complicated materials with damages such as voids, defects, and cracks within the framework of continuum mechanics. We represent the voids, defects, e...
25 citations
Cites methods from "Anisotropic Elastic-Brittle-Damage ..."
...Skrzypek and Kuna-Ciskal (2003) represented the crack closure effect by using the modified strain in the principal strain coordinate system and Murakami and Kamiya (1997) applied the above method to the expression of the Helmholtz free energy per unit mass....
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References
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TL;DR: In this paper, the authors proposed a nonlocal damage theory, which is based on the nonlocal treatment of damage from the local treatment of elastic behavior, and the only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of a material.
Abstract: In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh ...
1,672 citations
Book•
25 Aug 1988
TL;DR: In this article, the authors present a practical work that provides engineers and students in structural engineering or structural mechanics with the background needed to make the transition from fundamental theory to computer implementation and engineering practice.
Abstract: "Plasticity for Structural Engineers" is a practical work that provides engineers and students in structural engineering or structural mechanics with the background needed to make the transition from fundamental theory to computer implementation and engineering practice. It sets out initially to examine the stress-strain behaviors of materials under simple test conditions, goes on to show how these behaviors can be generalized under combined stresses, and finally outlines the finite element implementation of the generalized stress-strain relations for the solution of practical steel and concrete structural problems. "Plasticity" "for Structural Engineers" not only offers the reader an understanding of the fundamental principles and theory of plasticity in a form that does not require extensive mathematical experience, but also provides the reader with a compact and convenient summary of the modern development of concrete plasticity and limit analysis in structural engineering.
1,118 citations
TL;DR: In this paper, an energy-based coupled elastoplastic damage theory for ductile and brittle materials is presented, which employs irreversible thermodynamics and internal state variable theory for damage.
865 citations