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Somnath Ghosh - One of the best experts on this subject based on the ideXlab platform.
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parametrically homogenized continuum Damage mechanics phcdm models for unidirectional composites with nonuniform microstructural distributions
Journal of Computational Physics, 2021Co-Authors: Xiaofan Zhang, Daniel J Obrien, Somnath GhoshAbstract:Abstract This paper develops a parametrically homogenized continuum Damage mechanics (PHCDM) model for multiscale analysis of Damage and failure in composite structures with nonuniform microstructures. Unidirectional glass fibers are nonuniformly dispersed in the microstructures of these epoxy matrix composites. The PHCDM models are thermodynamically consistent, reduced order constitutive models with coefficients that are explicit functions of microstructural descriptors and evolving material variables. Damage anisotropy is represented through a second order Damage Tensor that contributes to the evolution of a Damage surface in the space of Damage work conjugate, which characterizes the initiation and evolution of Damage. The nonuniform microstructural morphology descriptors are optimally expressed in terms of representative aggregated microstructural parameters or RAMPs for incorporation in the PHCDM coefficients. Optimal expressions for RAMPs are determined through principal component analysis of the two-point correlation functions. The functional forms of RAMPs in PHCDM coefficients are determined using machine learning tools operating on data generated by micromechanical analysis. It is shown that PHCDM models accounting for the fiber distribution information yield a much higher accuracy than those only accounting for fiber volume fractions. The developed PHCDM model is incorporated in a commercial finite element code and structural analysis of structural composites is executed for understanding concurrent Damage and failure at multiple scales. The paper successfully demonstrates the accuracy and significant efficiency of the resulting PHCDM model in analyzing deformation and Damage in nonuniform composites across length scales for various loading conditions.
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parametrically homogenized continuum Damage mechanics phcdm models for composites from micromechanical analysis
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Xiaofan Zhang, Daniel J Obrien, Somnath GhoshAbstract:This paper develops a parametrically homogenized continuum Damage mechanics (PHCDM) model for unidirectional fiber-reinforced composites undergoing progressive Damage. The PHCDM models are designed to overcome limitations of prohibitive computational overhead associated with many homogenization methods. They are thermodynamically consistent, reduced-order continuum models with explicit representation of microstructural morphology. The PHCDM model is derived from detailed micromechanics of representative volume element (RVE) using energy equivalence principles. Micromechanical failure is due to fiber–matrix interface debonding and matrix cracking. The macroscopic PHCDM models represent Damage anisotropy through a second-order Damage Tensor that contributes to the evolution of a Damage surface in the space of Damage work conjugate. The Damage surface characterizes the initiation and evolution of Damage. The constitutive relation between Damage and its work conjugate is represented by an anisotropic fourth-order Damage surface Tensor \(P_{ijkl}\), whose components are expressed as functions of current Damage state and composite morphology. These are calibrated and validated from homogenized micromechanical (HMM) responses. The PHCDM model is incorporated in a commercial finite element code, and analysis of macroscopic composite components is executed for understanding concurrent Damage at multiple material length scales.
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Damage Evolution in Composites with a Homogenization-based Continuum Damage Mechanics Model
2014Co-Authors: Jayesh R. Jain, Somnath GhoshAbstract:ABSTRACT: This paper develops a 3D homogenization-based continuum Damage mechanics (HCDM) model for fiber reinforced composites undergoing micro-mechanical Damage. Micromechanical Damage in the representative volume element (RVE) is explicitly incorporated in the form of fiber–matrix interfacial debonding. The model uses the evolving principal Damage coordinate system as its reference in order to represent the anisotropic coefficients. This is necessary for retaining accuracy with nonproportional loading. The material constitutive law involves a fourth order orthotropic Tensor with stiffness characterized as macroscopic internal variable. Damage in 3D composites is accounted for through functional forms of the fourth order Damage Tensor in terms of macroscopic strain components. The HCDM model parameters are calibrated by using homogenized micromechanical (HMM) solutions for the RVE for a few strain histories. The proposed model is validated by comparing the CDM results with HMM response of single and multiple fiber RVEs subjected to arbitrary loading history. Finally the HCDM model is incorporated in a macroscopic finite element code to conduct Damage analysis in a structure. The effec
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a continuum Damage mechanics model for unidirectional composites undergoing interfacial debonding
Mechanics of Materials, 2005Co-Authors: Prasanna Raghavan, Somnath GhoshAbstract:Abstract A continuum Damage mechanics (CDM) model is developed in this paper for fiber reinforced composites with interfacial debonding. The model is constructed from rigorous micromechanical analysis of the Representative Volume Element (RVE) using the Voronoi cell FEM (VCFEM) that is followed by homogenizing microscopic variables using asymptotic homogenization. The microstructural Damage mode considered in this paper is fiber–matrix interfacial debonding that is simulated using cohesive zone models in VCFEM. Following a systematic consideration of various order Damage Tensors, an anisotropic CDM model using fourth order Damage Tensor with stiffness characterized as an internal variable, is found to perform most accurately for this class of materials. The comparison of this CDM results with those obtained by homogenization of micromechanical analysis show excellent agreement between the two. Hence the CDM model is deemed suitable for implementing in macroscopic finite element codes to represent Damage evolution in composites with significant efficiency.
George Z Voyiadjis - One of the best experts on this subject based on the ideXlab platform.
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a comparative study of Damage variables in continuum Damage mechanics
International Journal of Damage Mechanics, 2009Co-Authors: George Z Voyiadjis, Peter I. KattanAbstract: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 � ¼ � " ¼ " ‘ ¼ �
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Damage mechanics with fabric Tensors
Mechanics of Advanced Materials and Structures, 2006Co-Authors: George Z Voyiadjis, Pete I KattaAbstract:A new formulation is presented to link continuum Damage mechanics with the concept of fabric Tensors within the framework of classical elasticity theory. A fourth-rank Damage Tensor is used and its exact relationship to the fabric Tensors is illustrated. A model of Damage mechanics for directional data is formulated using fabric Tensors. The applications of the new formulation to micro-crack distributions are well illustrated in two solved examples. In the first example, a micro-crack distribution is considered with its data represented by a circular histogram. The values of the fabric Tensors and Damage Tensor are calculated in this case. In the second example, two sets of parallel micro-crack distributions with two different orientations are investigated. In addition, a general hypothesis for Damage mechanics is postulated. It is seen that the two available hypotheses of elastic strain equivalence and elastic energy equivalence may be obtained as special cases of the postulated general hypothesis. This ...
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a new fabric based Damage Tensor
Journal of the mechanical behavior of materials, 2006Co-Authors: George Z Voyiadjis, Pete I KattaAbstract:The exact mathematical relations between the Damage Tensor and fabric Tensors are presented. These relations provide the missing link between the subjects of Damage Mechanics and Fabric Tensors. In this regard, a new fabricbased Damage Tensor is formulated. These Tensors play an important role in the mechanical characterization of the micro-structure of materials. Thus solids with micro-cracks may be studied using the relations provided here within the framework of Damage Mechanics. However, the theory is limited to linear elastic solids.
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thermodynamic modeling of creep Damage in materials with different properties in tension and compression
International Journal of Solids and Structures, 2000Co-Authors: George Z Voyiadjis, A. ZolochevskyAbstract:A constitutive model is developed to describe the creep response of polycrystalline metals and alloys with different behavior in tension and compression. A second-order Damage Tensor is introduced in order to describe the creep Damage under nonproportional loading in nonisothermal processes. The thermodynamic formulation of the creep equation and the Damage evolution equation is used to study the creep behavior and creep Damage in the initially isotropic materials. The determination of the material parameters in the proposed equations is demonstrated from a series of basic experiments outlined in this paper. The results generated from the model are compared with those obtained from experiments under uniaxial nonproportional and multiaxial nonproportional loading for both isothermal and nonisothermal processes.
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a coupled anisotropic Damage model for the inelastic response of composite materials
Computer Methods in Applied Mechanics and Engineering, 2000Co-Authors: George Z Voyiadjis, Babur DeliktasAbstract:A coupled incremental Damage and plasticity theory for rate-independent and rate-dependent composite materials is introduced here. This allows Damage to be path-dependent either on the stress history or thermodynamic force conjugate to Damage. This is achieved through the use of an incremental Damage Tensor. Damage and inelastic deformations are incorporated in the proposed model that is used for the analysis of fiber-reinforced metal‐matrix composite materials. The Damage is described kinematically in both the elastic and inelastic domains using the fourth-order Damage eAect Tensor which is a function of the second-order Damage Tensor. A physical interpretation of the second-order Damage Tensor is given in this work which relates to the microcrack porosity within the unit cell. The inelastic deformation behavior with Damage is viewed here within the framework of thermodynamics with internal state variables. Computational aspects of both the rate-independent and rate-dependent models are discussed in this work. The Newton‐Rapson iterative scheme is used for the overall laminate system. The constitute equations of both the rate-independent and the rate-dependent plasticity coupled with Damage models are additively decomposed into the elastic, inelastic and Damage deformations by using the three-step split operator algorithm [J.W. Ju, Internat. J. Solids Struc. 25 (1989) 803‐833]. The main framework return maping algorithm [M. Ortiz, C. Simo, Internat. J. Numer. Meth. Eng. 23 (1986) 353‐366] is used for the correction of the elasto-plastic and viscoplastic states. However, for the case of the Damage model these algorithms are redefined according to the governed Damage constitutive relations. In order to test the validity of the model, a series of laminated systemsO0O8sUU; O90O8sUU; O0=90U O4sU ; Oˇ45=45U O2sU are investigated at both room and elevated temperatures of 538∞C and 649∞C. The results obtained from the special purpose developed computer program, DVP-CALSET (Damage and Viscoplastic Coupled Analysis of Laminate Systems at Elevated Temperatures), are then compared with the available experimental results and other existing theoretical material models obtained from the work of B.S. Majumdar,
Xiaofan Zhang - One of the best experts on this subject based on the ideXlab platform.
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parametrically homogenized continuum Damage mechanics phcdm models for unidirectional composites with nonuniform microstructural distributions
Journal of Computational Physics, 2021Co-Authors: Xiaofan Zhang, Daniel J Obrien, Somnath GhoshAbstract:Abstract This paper develops a parametrically homogenized continuum Damage mechanics (PHCDM) model for multiscale analysis of Damage and failure in composite structures with nonuniform microstructures. Unidirectional glass fibers are nonuniformly dispersed in the microstructures of these epoxy matrix composites. The PHCDM models are thermodynamically consistent, reduced order constitutive models with coefficients that are explicit functions of microstructural descriptors and evolving material variables. Damage anisotropy is represented through a second order Damage Tensor that contributes to the evolution of a Damage surface in the space of Damage work conjugate, which characterizes the initiation and evolution of Damage. The nonuniform microstructural morphology descriptors are optimally expressed in terms of representative aggregated microstructural parameters or RAMPs for incorporation in the PHCDM coefficients. Optimal expressions for RAMPs are determined through principal component analysis of the two-point correlation functions. The functional forms of RAMPs in PHCDM coefficients are determined using machine learning tools operating on data generated by micromechanical analysis. It is shown that PHCDM models accounting for the fiber distribution information yield a much higher accuracy than those only accounting for fiber volume fractions. The developed PHCDM model is incorporated in a commercial finite element code and structural analysis of structural composites is executed for understanding concurrent Damage and failure at multiple scales. The paper successfully demonstrates the accuracy and significant efficiency of the resulting PHCDM model in analyzing deformation and Damage in nonuniform composites across length scales for various loading conditions.
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parametrically homogenized continuum Damage mechanics phcdm models for composites from micromechanical analysis
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Xiaofan Zhang, Daniel J Obrien, Somnath GhoshAbstract:This paper develops a parametrically homogenized continuum Damage mechanics (PHCDM) model for unidirectional fiber-reinforced composites undergoing progressive Damage. The PHCDM models are designed to overcome limitations of prohibitive computational overhead associated with many homogenization methods. They are thermodynamically consistent, reduced-order continuum models with explicit representation of microstructural morphology. The PHCDM model is derived from detailed micromechanics of representative volume element (RVE) using energy equivalence principles. Micromechanical failure is due to fiber–matrix interface debonding and matrix cracking. The macroscopic PHCDM models represent Damage anisotropy through a second-order Damage Tensor that contributes to the evolution of a Damage surface in the space of Damage work conjugate. The Damage surface characterizes the initiation and evolution of Damage. The constitutive relation between Damage and its work conjugate is represented by an anisotropic fourth-order Damage surface Tensor \(P_{ijkl}\), whose components are expressed as functions of current Damage state and composite morphology. These are calibrated and validated from homogenized micromechanical (HMM) responses. The PHCDM model is incorporated in a commercial finite element code, and analysis of macroscopic composite components is executed for understanding concurrent Damage at multiple material length scales.
A. Zolochevsky - One of the best experts on this subject based on the ideXlab platform.
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thermodynamic modeling of creep Damage in materials with different properties in tension and compression
International Journal of Solids and Structures, 2000Co-Authors: George Z Voyiadjis, A. ZolochevskyAbstract:A constitutive model is developed to describe the creep response of polycrystalline metals and alloys with different behavior in tension and compression. A second-order Damage Tensor is introduced in order to describe the creep Damage under nonproportional loading in nonisothermal processes. The thermodynamic formulation of the creep equation and the Damage evolution equation is used to study the creep behavior and creep Damage in the initially isotropic materials. The determination of the material parameters in the proposed equations is demonstrated from a series of basic experiments outlined in this paper. The results generated from the model are compared with those obtained from experiments under uniaxial nonproportional and multiaxial nonproportional loading for both isothermal and nonisothermal processes.
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A creep Damage model for initially isotropic materials with different properties in tension and compression
Engineering Fracture Mechanics, 1998Co-Authors: Josef Betten, S. Sklepus, A. ZolochevskyAbstract:Abstract A continuum Damage mechanics model for the dislocation creep response associated with the growth of parallel planar mesocracks in initially isotropic materials is presented. The model describes simultaneously different Damage development in tension, compression and torsion, Damage-induced anisotropy, as well as different creep properties in tension, compression and torsion. The proposed constitutive equation for creep and the Damage growth equation contain joint invariants of the stress Tensor and the second-order Damage Tensor. The determination of the material parameters required in the proposed equations, from a series of basic experiments, is shown. Theoretical predictions are compared with experimental data for a multiaxial stress state of various materials in the primary, secondary and tertiary creep state under proportional and non-proportional loading.
Namas Chandra - One of the best experts on this subject based on the ideXlab platform.
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effect of fiber fracture and interfacial debonding on the evolution of Damage in metal matrix composites
Composites Part A-applied Science and Manufacturing, 1998Co-Authors: C R Ananth, S R Voleti, Namas ChandraAbstract:Abstract A new approach for modeling the behavior of laminated composite structures using computational methods is presented, considering Damage evolution at the micromechanical level. Micromechanical models are developed to predict the stress–strain response of a composite lamina explicitly accounting for the local Damage mechanisms such as fiber fracture and interfacial bonding. The model is applied to metal matrix composites and hence the inelastic constitutive behavior of the matrix phase is included. The stochastic variation of the fiber properties is incorporated in this simulation using the two-parameter Weibull model. The effect of fiber volume fraction and the properties of the fiber, matrix and interface on the Damage evolution is studied using this approach. A constitutive Damage Tensor for the composite lamina is developed from the micromechanical models which can be input into laminate structural analysis codes.
