Strain- and stress-based continuum damage models—I. Formulation
TL;DR: In this article, a dual framework for elastic cap damage was proposed, where a strain-and a stress-based approach was employed, and a viscous regularization of strain-based, rate-independent damage models was also developed.
About: This article is published in International Journal of Solids and Structures.The article was published on 1987-01-01. It has received 1158 citations till now. The article focuses on the topics: Infinitesimal strain theory & Strain energy density function.
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TL;DR: In this article, a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented, which uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects.
3,080 citations
TL;DR: In this paper, a new plastic-damage model for concrete subjected to cyclic loading is developed using the concepts of fracture-energy-based damage and stiffness degradation in continuum damage mechanics.
Abstract: A new plastic-damage model for concrete subjected to cyclic loading is developed using the concepts of fracture-energy-based damage and stiffness degradation in continuum damage mechanics. Two damage variables, one for tensile damage and the other for compressive damage, and a yield function with multiple-hardening variables are introduced to account for different damage states. The uniaxial strength functions are factored into two parts, corresponding to the effective stress and the degradation of elastic stiffness. The constitutive relations for elastoplastic responses are decoupled from the degradation damage response, which provides advantages in the numerical implementation. In the present model, the strength function for the effective stress is used to control the evolution of the yield surface, so that calibration with experimental results is convenient. A simple and thermodynamically consistent scalar degradation model is introduced to simulate the effect of damage on elastic stiffness and its recovery during crack opening and closing. The performance of the plastic-damage model is demonstrated with several numerical examples of simulating monotonically and cyclically loaded concrete specimens.
2,825 citations
TL;DR: In this article, a consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena, and the introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models.
Abstract: SUMMARY Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
1,207 citations
TL;DR: In this article, the authors provide an overview of the existing quasi-static and dynamic phase-field fracture formulations from the physics and the mechanics communities, and propose and test the so-called hybrid formulation, which leads within a staggered implementation to an incrementally linear problem.
Abstract: In this contribution we address the issue of efficient finite element treatment for phase-field modeling of brittle fracture. We start by providing an overview of the existing quasi-static and dynamic phase-field fracture formulations from the physics and the mechanics communities. Within the formulations stemming from Griffith's theory, we focus on quasi-static models featuring a tension-compression split, which prevent cracking in compression and interpenetration of the crack faces upon closure, and on the staggered algorithmic implementation due to its proved robustness. In this paper, we establish an appropriate stopping criterion for the staggered scheme. Moreover, we propose and test the so-called hybrid formulation, which leads within a staggered implementation to an incrementally linear problem. This enables a significant reduction of computational cost--about one order of magnitude--with respect to the available (non-linear) models. The conceptual and structural similarities of the hybrid formulation to gradient-enhanced continuum damage mechanics are outlined as well. Several benchmark problems are solved, including one with own experimental verification.
880 citations
Additional excerpts
...ε̃ := ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ √ 2Ψ0(ε), Simo and Ju [30], √√√ 3 ∑...
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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
References
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Book•
01 Jan 1950
TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.
Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy
7,810 citations
TL;DR: In this paper, a model of isotropic ductile plastic damage based on a continuum damage variable, on the effective stress concept and on thermodynamics is derived, showing a large influence of triaxiality by means of a damage equivalent stress.
Abstract: A model of isotropic ductile plastic damage based on a continuum damage variable, on the effective stress concept and on thermodynamics is derived. The damage is linear with equivalent strain and shows a large influence of triaxiality by means of a damage equivalent stress. Identification for several metals is made by means of elasticity modulus change induced by damage. A comparison with the McClintock and Rice-Tracey models and with some experiments is presented for the influence of triaxiality on the strain to rupture.
2,327 citations
Book•
01 Nov 1982TL;DR: In this article, the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis are discussed. But the authors do not discuss the application of functional analysis to the problem of elasticity.
Abstract: [Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to see this classical subject in a modern setting and to see some examples of what newer mathematical tools have to contribute.
2,115 citations
TL;DR: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body as mentioned in this paper, which can be expressed as follows: a body is regarded as a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies.
Abstract: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body. In a formal rational development of the subject, one first tries to state precisely what mathematical entities represent these physical concepts: a body is regarded to be a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies1. Once these concepts are made precise one can proceed to the statement of general principles, such as the principle of objectivity or the law of balance of linear momentum, and to the statement of specific constitutive assumptions, such as the assertion that a force system can be resolved into body forces with a mass density and contact forces with a surface density, or the assertion that the contact forces at a material point depend on certain local properties of the configuration at the point. While the general principles are the same for all work in classical continuum mechanics, the constitutive assumptions vary with the application in mind and serve to define the material under consideration.
1,885 citations
Book•
01 Jan 1986TL;DR: In this article, the authors introduce the concept of applied mathematics and apply it to applied mathematics problems in the context of applied applications. [2]... ].. [3]
Abstract: Introduction to applied mathematics , Introduction to applied mathematics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
1,715 citations