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In this work several new and fundamental concepts are proposed within the framework of continuum damage mechanics. These concepts deal primarily with the nature of the two processes of damage and healing along with introducing a... more
In this work several new and fundamental concepts are proposed within the framework of continuum damage mechanics. These concepts deal primarily with the nature of the two processes of damage and healing along with introducing a consistent and systematic definition for the concepts of damageability and integrity of materials. Toward this end, seven sections are presented as follows: “The logarithmic damage variable” section introduces the logarithmic and exponential damage variables and makes comparisons with the classical damage variable. In “Integrity and damageability of materials” section a new formulation for damage mechanics is presented in which the two angles of damage–integrity and healing–damageability are introduced. It is shown that both the damage variable and the integrity variable can be derived from the damage–integrity angle while the healing variable and damageability variable are derived from the healing–damageability angle. “The integrity field” section introduces the new concept of the integrity field while “The healing field” section introduces the new concept of the healing field. These two fields are introduced as a generalization of the classical concepts of damage and integrity. “Unhealable damage and nondamageable integrity” section introduces the new and necessary concept of unrecoverable damage or unhealable damage. In this section the concept of permanent integrity or nondamageable integrity is also presented. In “Generalized nonlinear healing” section generalized healing is presented where a distinction is clearly made between linear healing and nonlinear healing. As an example of nonlinear healing the equations of quadratic healing are derived. Finally in “Dissection of the healing process” section a complete and logical/mathematical dissection is made of the healing process. It is hoped that these new and fundamental concepts will pave the way for new, consistent, and holistic avenues in research in damage mechanics and characterization of materials.
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Research Interests: Materials Engineering, Mechanical Engineering, Civil Engineering, Materials Science, Mechanics, and 15 moreContinuum Mechanics, Finite element method, Finite Element, Damage Mechanics, High strain rate testing, Dissipation, Length scale, Impact damage, Constitutive model, Dynamic Loading, Internal Structure, Differential equation, Finite Strain, Constitutive Equation, and Higher order
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Thermodynamic Consistent Formulations of Viscoplastic Deformations in FCC Metals. [Journal of Engineering Mechanics 133, 76 (2007)]. Farid H. Abed, George Z. Voyiadjis. Abstract. A general consistent thermodynamic framework ...
Research Interests: Mechanical Engineering, Civil Engineering, Materials Science, Thermodynamics, Engineering Mechanics, and 12 moreMicrostructure, Viscoplasticity, Modeling, Finite element method, Strain Rate, Viscosity, Deformation, Dislocation, Free Energy, Constitutive Equation, Von Mises Yield Criterion, and Helmholtz Free Energy
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In this work, the principles of damage/healing mechanics are first reviewed. This is followed by introducing the concept of super healing of materials in the framework of continuum damage mechanics. Once a damaged material is healed and... more
In this work, the principles of damage/healing mechanics are first reviewed. This is followed by introducing the concept of super healing of materials in the framework of continuum damage mechanics. Once a damaged material is healed and the damage is recovered, further healing results in a strengthened material. This process of added healing beyond what is necessary to recover damage is termed here super healing. In super healing, the material gains stiffness and the end and final objective of the super healing process is to reach what is called the Super Material. The second part of this work generalizes these concepts to anisotropic damage and healing of materials. The concept of anisotropic super healing is also introduced. An example is presented for the case of plane stress where the mechanics of damage/healing and super healing are demonstrated. Finally, the characteristics of the elusive Super Material are postulated.
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Publisher Summary The aim of this chapter is to demonstrate under similar assumptions that both the local and overall approaches give similar results when applied to fiber-reinforced metal–matrix composites. Consistently derived... more
Publisher Summary The aim of this chapter is to demonstrate under similar assumptions that both the local and overall approaches give similar results when applied to fiber-reinforced metal–matrix composites. Consistently derived overall–local relations are used to prove the equivalence of the two approaches. This equivalence allows one to use the less complex overall approach for the numerical analysis of boundary value problems, yet obtain the same level of accuracy as that of the local damage approach. Both elastic and inelastic composites are considered. The fibers are assumed to be continuous and perfectly aligned. In addition, a perfect bond is assumed to exist at the matrix–fiber interface. This chapter uses a consistent mathematical formulation to show the equivalence of the two approaches. The elastic and plastic stiffness matrices are derived using both approaches, and each is shown to be identical in both cases.
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ABSTRACT This chapter introduces a new study in the field of continuum damage mechanics and includes two main topics. In the first topic, both the concepts of Voyiadjis-Kattan materials and undamageable materials are introduced. The... more
ABSTRACT This chapter introduces a new study in the field of continuum damage mechanics and includes two main topics. In the first topic, both the concepts of Voyiadjis-Kattan materials and undamageable materials are introduced. The Voyiadjis-Kattan material of order n is defined as a nonlinear elastic material that has a higher-order strain energy form in terms of n. The undamageable material is obtained as the limit of the Voyiadjis-Kattan material of order n as n goes to infinity. The relations of these types of materials to other nonlinear elastic materials from the literature are outlined. Also, comparisons of these types of materials with rubber materials are presented. 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. The second topic lays special emphasis on the order and sequence of damage processes occurring in materials. These processes can occur in series or in parallel. For example, in a metallic material, the evolution of micro-cracks and the evolution of micro-voids are considered as two separate damage processes. These two different evolutions can occur simultaneously or they can occur following each other. Another example would be matrix cracking and debonding in a composite material. These two different damage processes can occur simultaneously in parallel or sequentially in series. Three-dimensional states of deformation and damage are also presented using the concepts discussed in this work.
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In this work, the authors discuss a systematic method of characterizing the damage process in graphene. The mathematical formulation is limited to the elastic range. In the elastic constitutive equation for graphene, both the second-order... more
In this work, the authors discuss a systematic method of characterizing the damage process in graphene. The mathematical formulation is limited to the elastic range. In the elastic constitutive equation for graphene, both the second-order and third-order elastic stiffnesses are considered. The formulation is performed within the framework of Continuum Damage Mechanics. Thus, both the hypotheses of elastic strain equivalence and elastic energy equivalence are utilized. In addition to the classical damage variable that is defined in terms of the cross-sectional area, a new damage variable is introduced and defined in terms of the surface area. This particular damage variable is suited for general nanomaterials, especially graphene. Both the scalar and tensorial formulations are presented. The special case of plane stress in graphene is illustrated as an example using the derived general equations and some interesting results are obtained.
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The purpose of this study is to apply continuum damage mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of damage mechanics... more
The purpose of this study is to apply continuum damage mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of damage mechanics for composite materials will be developed using fabric tensors. The introduction of fabric tensors into the analysis of damage of composite materials will allow for an enhanced and better understood physical meaning of damage. The micromechanical approach will be used here to relate the damage effect through fabric tensors to the behavior of composite materials. In this approach, damage mechanics is introduced separately to the constituents of the composite material through different constituents’ damage effect tensors. The damaged properties of the composite system as a whole can then be obtained by proper homogenization of the damaged properties of the constituents.The derivation of a generalized formulation of damage evolution will be shown here in a mathematically consistent manner that is based on sound thermodynamic principles. Numerical examples will be presented to show applicability. In addition, damage evolution for the one-dimensional tension case is also illustrated.
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ABSTRACT Finite elasto-plastic deformation is analyzed using a Eulerian constitutive model which employs both isotropic and kinematic hardening laws. Corotational stress rates are discussed and numerical results are obtained for the... more
ABSTRACT Finite elasto-plastic deformation is analyzed using a Eulerian constitutive model which employs both isotropic and kinematic hardening laws. Corotational stress rates are discussed and numerical results are obtained for the problem of finite simple shear.
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Modeling of the evolution of distributed damage and plasticity such as micro-cracking, void formation, dislocation densities, and shear bands necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as... more
Modeling of the evolution of distributed damage and plasticity such as micro-cracking, void formation, dislocation densities, and shear bands necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means for regularizing the (initial) boundary value problems with strain softening, capturing the size effects observed in experiments, capturing small-scale deviations from local continuum models caused by material heterogeneity, and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations. This book discusses the integral and gradient formulations of nonlocality, computational aspects, and comparison of approaches and emphasizes recent developments in the bridging of material length scales.
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Publisher Summary This chapter presents the application of continuum damage mechanics to composite materials within the framework of the theory of elasticity, and presents a directional data model of damage mechanics for composite... more
Publisher Summary This chapter presents the application of continuum damage mechanics to composite materials within the framework of the theory of elasticity, and presents a directional data model of damage mechanics for composite materials using fabric tensors. The introduction of fabric tensors into the analysis of damage of composite materials allows for an enhanced and better understood physical meaning of damage. The micromechanical approach is used here to relate the damage effect through fabric tensors to the behavior of composite materials. In this approach, damage mechanics is introduced separately to the constituents of the composite material through different constituents' damage effect tensors. The damaged properties of the composite system as a whole can then be obtained by proper homogenization of the damaged properties of the constituents. The derivation of a generalized formulation of damage evolution is shown in a mathematically consistent manner that is based on sound thermodynamic principles and numerical examples are presented to show the applicability. Additionally, the chapter illustrates damage evolution for the one dimensional tension case.
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It is well-known by now through intensive experimental studies that have been performed at the micron and nano length scales that the material mechanical properties strongly depend on the size of specimen and the microstructural features.... more
It is well-known by now through intensive experimental studies that have been performed at the micron and nano length scales that the material mechanical properties strongly depend on the size of specimen and the microstructural features. The classical continuum mechanics fails to address this problem since no material length scale exists in its constitutive description. On the other hand, nonlocal continuum theories of integral-type or gradient-type have been to a good extent successful in predicting this type of size effect. However, they fail to predict size effects when strain gradients are minimal such as the Hall-Petch effect. This problem is the main focus of this work. The effect of the material microstructural interfaces increase as the surface-to-volume ratio increases. It is shown in this work that interfacial effects have a profound impact on the scale-dependent plasticity encountered in micro/nano-systems. This is achieved by developing a higher-order gradient-dependent plasticity theory that enforces microscopic boundary conditions at interfaces and free surfaces. These nonstandard boundary conditions relate the microtraction stress at the interface to the interfacial energy. Application of the proposed framework to size effects in shear loading of a thin-film on an elastic substrate is presented. Three film-interface conditions are modeled: soft, intermediate, and hard interfaces.
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AbstractSelf-healing materials have recently become more popular due to their capability of self-repairing cracks and rehabilitation of structures. Recent research has revealed that self-healing pr...