The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Mark F. Horstemeyer - One of the best experts on this subject based on the ideXlab platform.
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A historical review of the traditional methods and the Internal State Variable theory for modeling composite materials
Mechanics of Advanced Materials and Structures, 2021Co-Authors: Yucheng Liu, Thomas E. Lacy, Mark F. HorstemeyerAbstract:A review of the development and the usages of traditional non-Internal State Variable (ISV) models and ISV theory for modeling behaviors of composite materials are presented in this paper. The hist...
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On the thermo-mechanical coupling of the Bammann plasticity-damage Internal State Variable model
Acta Mechanica, 2019Co-Authors: Nikolay Dimitrov, Yucheng Liu, Mark F. HorstemeyerAbstract:In this study, thermodynamic incompatibility issues of the thermo-mechanical coupling of the Bammann-temperature-dependent plasticity-damage Internal State Variable (ISV) model are investigated. The exclusion of the thermal expansion phenomena from the Helmholtz free energy, as assumed in the model, is proven to contradict the First and Second Law of Thermodynamics, as well as the omnipresence principle. Four different approaches are discussed to address those issues, and the inclusion of the thermal expansion as a dependent Variable in the Helmholtz free energy is considered the most appropriate and efficient. Based on these findings, a multiphysics ISV theory that couples the elasto-visco-plasticity-damage model of Bammann with thermal expansion is presented in which the kinematics, thermodynamics, and kinetics are Internally consistent. Other material models may benefit from the findings of this study and apply similar modifications with their thermo-mechanical couplings.
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A unified static and dynamic recrystallization Internal State Variable (ISV) constitutive model coupled with grain size evolution for metals and mineral aggregates
International Journal of Plasticity, 2019Co-Authors: H. E. Cho, Youssef Hammi, A.l. Bowman, Shun-ichiro Karato, John Baumgardner, Mark F. HorstemeyerAbstract:Abstract A history dependent and physically-motivated Internal State Variable (ISV) constitutive model is presented that simultaneously accounts for the effects of static recrystallization, dynamic recrystallization, and grain size with respect to the mechanical behavior under different strain rates, temperatures, and pressures. A unique aspect of our ISV constitutive model is that grain size and recrystallized volume fraction can be directly included along with its associated rate of change under deformation and time in a coupled manner. The present ISV constitutive model was calibrated to several metals (oxygen-free high conductivity copper, AZ31 magnesium alloy, pure nickel, and 1010 low carbon steel) and geological materials (olivine and clinopyroxene). The model calibration shows good agreement with the experimental stress-strain behavior and average grain size data. Validation of the ISV constitutive model was accomplished by applying complex and history sensitive thermomechanical problems once the model was calibrated: i) sequential transitions of different loading conditions and ii) a multistage tubing process. The history dependence naturally provided by ISVs enabled the present model to effectively capture the complex boundary value problems with changing boundary conditions.
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A Thermo-Electro-Elasto-Viscoplastic Damage Internal State Variable (ISV) Model for Ductile Metals
Volume 12: Materials: Genetics to Structures, 2018Co-Authors: Nikolay Dimitrov, Yucheng Liu, Mark F. HorstemeyerAbstract:A multiphysics Internal State Variable (ISV) theory that couples the thermoelastoviscoplastic damage model of Bammann-Horstemeyer with electricity-related electromagnetic phenomena is presented in which the kinematics, thermodynamics, and kinetics are Internally consistent. An extended multiplicative decomposition of the deformation gradient that accounts for elasticity, plasticity, damage, thermal expansion, electricity, and magnetism is introduced. The different geometrically-affected rate equations are given for each phenomenon after the ISV formalism and have a thermodynamic force pair that acts as an Internal stress-like quantity. Guidelines for practical implementation, recommendations for simplifying assumptions, and suggestions for future work supplement the theoretical model. The abstraction of the model can capture the full multi-physics described above; however, the robustness of the model is realized when any of the listed phenomena are not included in the boundary value problem, the model reduces to the previous form — the model will revert to the Bammann-Horstemeyer plasticity-damage ISV model.
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A Multiphase Internal State Variable Model With Rate Equations for Predicting Elastothermoviscoplasticity and Damage of Fiber Reinforced Polymer Composites
Volume 9: Mechanics of Solids Structures and Fluids; NDE Structural Health Monitoring and Prognosis, 2017Co-Authors: Yucheng Liu, Douglas J. Bammann, Mark F. HorstemeyerAbstract:This paper agglomerates an Internal State Variable (ISV) model for polymers (Bouvard et al., 2010, 2013) with damage evolution (Horstemeyer and Gokhale, 1999: Horstemeyer et al., 2000; Francis et al., 2014) into a multiphase ISV framework (Rajagopal and Tao, 1995; Bammann et al., 1996) that features a finite strain theoretical framework for Fiber Reinforced Polymer (FRP) composites under various stress States, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage Variable is employed to capture the damage history of such material, which is a result of three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber-matrix interface, and each damage model was well calibrated to the experimental data from Rolland et al., (2016). The constitutive model developed herein arises employing standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being Internally consistent.
Douglas J. Bammann - One of the best experts on this subject based on the ideXlab platform.
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a multiphase Internal State Variable model with rate equations for predicting elastothermoviscoplasticity and damage of fiber reinforced polymer composites
Acta Mechanica, 2019Co-Authors: Yucheng Liu, Douglas J. Bammann, David Francis, Mei Q Chandler, M F HorstemeyerAbstract:This paper explores the integration of an Internal State Variable (ISV) model for polymers (Bouvard et al. in Acta Mech 213(1):77–96, 2010; Int J Plast 42:168–193, 2013) with damage evolution (Horstemeyer and Gokhale in Int J Solids Struct 36:5029–5055, 1999; Horstemeyer et al. in Theor Appl Fract Mech 33(1):31–47, 2000; Francis et al. in Int J Solids Struct 51:2765–2776, 2014) into a multiphase ISV framework (Rajagopal and Tao in Advances in mathematics for the applied sciences, World Scientific, Singapore, 1995; Bammann in Proceedings of 2nd international conference on quenching and the control of distortion, vols 4–7, 1996) that features a finite strain theoretical framework for fiber-reinforced polymer (FRP) composites under various stress States, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage Variable is employed to capture the damage history of the FRP, which comprises three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber–matrix interface. The constitutive model developed herein employs standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being Internally consistent, whose ISVs can be either calculated from molecular dynamics simulations or calibrated through microstructural characterizations for specific FRPs. The developed elastothermoviscoplasticity and damage modeling framework is then employed to model the Internal damage evolution of a glass fiber-reinforced polyamide 66 (Rolland et al. in Compos Part B Eng 90:65–377, 2016) in terms of above three damage mechanisms. A detailed description of the model parameter identification process is given by using the example of a unidirectional glass fiber-reinforced epoxy, and the mechanical behaviors and properties of the composites at varying temperature and fiber volume fraction are predicted by the model, which are in good agreement with the experimental result.
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A Multiphase Internal State Variable Model With Rate Equations for Predicting Elastothermoviscoplasticity and Damage of Fiber Reinforced Polymer Composites
Volume 9: Mechanics of Solids Structures and Fluids; NDE Structural Health Monitoring and Prognosis, 2017Co-Authors: Yucheng Liu, Douglas J. Bammann, Mark F. HorstemeyerAbstract:This paper agglomerates an Internal State Variable (ISV) model for polymers (Bouvard et al., 2010, 2013) with damage evolution (Horstemeyer and Gokhale, 1999: Horstemeyer et al., 2000; Francis et al., 2014) into a multiphase ISV framework (Rajagopal and Tao, 1995; Bammann et al., 1996) that features a finite strain theoretical framework for Fiber Reinforced Polymer (FRP) composites under various stress States, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage Variable is employed to capture the damage history of such material, which is a result of three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber-matrix interface, and each damage model was well calibrated to the experimental data from Rolland et al., (2016). The constitutive model developed herein arises employing standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being Internally consistent.
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modeling the dynamic failure of railroad tank cars using a physically motivated Internal State Variable plasticity damage nonlocal model
Modelling and Simulation in Engineering, 2013Co-Authors: Fazle R. Ahad, Yustianto Tjiptowidjojo, Koffi Enakoutsa, Kiran Solanki, Douglas J. BammannAbstract:We used a physically motivated Internal State Variable plasticity/damage model containing a mathematical length scale to idealize the material response in finite element simulations of a large-scale boundary value problem. The problem consists of a moving striker colliding against a stationary hazmat tank car. The motivations are (1) to reproduce with high fidelity finite deformation and temperature histories, damage, and high rate phenomena that may arise during the impact accident and (2) to address the material postbifurcation regime pathological mesh size issues. We introduce the mathematical length scale in the model by adopting a nonlocal evolution equation for the damage, as suggested by Pijaudier-Cabot and Bazant in the context of concrete. We implement this evolution equation into existing finite element subroutines of the plasticity/failure model. The results of the simulations, carried out with the aid of Abaqus/Explicit finite element code, show that the material model, accounting for temperature histories and nonlocal damage effects, satisfactorily predicts the damage progression during the tank car impact accident and significantly reduces the pathological mesh size effects.
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Modeling the Dynamic Failure of Railroad Tank Cars Using a Physically Motivated Internal State Variable Plasticity/Damage Nonlocal Model
Modelling and Simulation in Engineering, 2013Co-Authors: Fazle R. Ahad, Yustianto Tjiptowidjojo, Koffi Enakoutsa, Kiran Solanki, Douglas J. BammannAbstract:We used a physically motivated Internal State Variable plasticity/damage model containing a mathematical length scale to idealize the material response in finite element simulations of a large-scale boundary value problem. The problem consists of a moving striker colliding against a stationary hazmat tank car. The motivations are (1) to reproduce with high fidelity finite deformation and temperature histories, damage, and high rate phenomena that may arise during the impact accident and (2) to address the material postbifurcation regime pathological mesh size issues. We introduce the mathematical length scale in the model by adopting a nonlocal evolution equation for the damage, as suggested by Pijaudier-Cabot and Bazant in the context of concrete. We implement this evolution equation into existing finite element subroutines of the plasticity/failure model. The results of the simulations, carried out with the aid of Abaqus/Explicit finite element code, show that the material model, accounting for temperature histories and nonlocal damage effects, satisfactorily predicts the damage progression during the tank car impact accident and significantly reduces the pathological mesh size effects.
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An Internal State Variable material model for predicting the time, thermomechanical, and stress State dependence of amorphous glassy polymers under large deformation
International Journal of Plasticity, 2013Co-Authors: Jean-luc Bouvard, Douglas J. Bammann, E B Marin, David Francis, Mark A. Tschopp, Mark F. HorstemeyerAbstract:International audienceThis paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress State dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based Internal State Variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress State dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress States. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions
David L. Mcdowell - One of the best experts on this subject based on the ideXlab platform.
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microstructure sensitive notch root analysis for dwell fatigue in ni base superalloys
International Journal of Fatigue, 2009Co-Authors: Yustianto Tjiptowidjojo, M M Shenoy, Craig Przybyla, David L. McdowellAbstract:Abstract Macroscopic viscoplastic constitutive models for γ – γ ′ Ni-base superalloys typically do not contain an explicit dependence on the underlying microstructure. Microstructure-sensitive models are of interest in many applications since microstructure can vary in components, whether intentional or not. In such cases, the use of experiments from one microstructure condition to fit macroscopic models may be too limiting. The principal microstructure attributes that can significantly affect the cyclic stress–strain response of γ – γ ′ Ni-base superalloys are the grain size and γ ′ precipitate volume fraction and size distributions. An artificial neural network (ANN) is used to correlate the material parameters of a macroscale Internal State Variable cyclic viscoplasticity model with these microstructure attributes using a combination of limited experiments augmented by polycrystal plasticity calculations performed on other (virtual) microstructures within the range characterized experimentally. The trained model is applied to an example of a component fatigue notch root analysis with dwell periods at peak load to demonstrate the methodology and explore the potential impact of microstructure-sensitive constitutive models on life prediction for notched structures subjected to realistic load histories.
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An extended multiscale principle of virtual velocities approach for evolving microstructure
Procedia Engineering, 2009Co-Authors: Darby J. Luscher, David L. McdowellAbstract:AbstractA hierarchical multiscale approach is presented for modeling microstructure evolution in heterogeneous materials. Preservation of momentum across each scale transition is incorporated through the application of the principle of virtual velocities at the fine scale giving rise to the appropriate continuum momentum balance equations at the coarse scale. In addition to satisfying momentum balance and invariance of momentum among scales, invariance of elastic free energy, stored free energy, and dissipation between two scales of observation is regarded as crucial to the physics of each scale transition. The preservation of this energy partitioning scheme is obtained through construction of constitutive relations within the framework of Internal State Variable theory. Internal State Variables that are directly computed from the fine scale response are introduced to augment the State equations and describe the inelastic energy storage and dissipation within the fine scale. By virtue of a second gradient kinematic decomposition, the framework naturally gives rise to couple stresses
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microstructure sensitive notch root analysis for ni base superalloys preprint
2007Co-Authors: Yustianto Tjiptowidjojo, M M Shenoy, Craig Przybyla, David L. McdowellAbstract:Abstract : Macroscopic viscoplastic constitutive models for y-y Ni-base superalloys typically do not contain an explicit dependence on the underlying microstructure. Microstructure dependent models are of interest since the sizes, volume fractions, and morphologies of primary, secondary, and tertiary precipitates can substantially affect the stress-strain response. The principle microstructural features that can significantly affect the stress-strain response of y-y Ni-base superalloys are the grain size and precipitate volume fraction and size distributions. An Artificial Neural Network (ANN) is used to correlate the material parameters in an Internal State Variable cyclic viscoplasticity model with these microstructure plasticity calculations performed on other microstructures within the range characterized experimentally. The trained model is applied to an example of component notch root analyses to explore the potential impact of microstructure-sensitive constitutive models in fatigue design of structures.
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Internal State Variable theory
Handbook of Materials Modeling, 2005Co-Authors: David L. McdowellAbstract:Many practical problems of interest deal with irreversible, path dependent aspects of material behavior, such as hysteresis due to plastic deformation or phase transition, fatigue and fracture, or diffusive rearrangement. Some of these processes occur so slowly and so near equilibrium that attendant models forego description of nonequilibrium aspects of dissipation (e.g., grain growth). On the other hand, some irreversible behaviors such as thermally activated dislocation glide can occur farther from equilibrium with a spectrum of relaxation times. The fact that quasi-stable, nonequilibrium configurations of defects can exist in lattices at multiple length scales, combined with the long range nature of interaction forces, presents an enormous challenge to the utility of high fidelity, high degree of freedom (DoF) dynamical models that employ atomistic or molecular modeling methods. For example, analyses of simple crystal structures using molecular dynamics have now reached scales on the order of microns, but are limited to rather idealized systems such as pure metals and to small time durations of the order of nanoseconds. High fidelity analyses of generation, motion and interaction of line defects in lattices based on discrete dislocation dynamics, making use of interactions based on linear elastic solutions, cover somewhat higher length scales and longer time scales, but are also limited in considering realistic multiphase, hierarchical microstructures. Crystal plasticity as well cannot be used for large scale finite element simulations, for example, crash simulations of a vehicle into a barrier.
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Thermal stress and fatigue analysis of plated-through holes using an Internal State Variable constitutive model
Finite Elements in Analysis and Design, 1998Co-Authors: I. Charles Ume, David L. McdowellAbstract:Abstract Previous related research on plated-through hole (PTH) fatigue investigations has been based on the so-called effective stress/strain methods, which did not account for the fact that fatigue crack nucleation and growth is observed to occur on planes of specific orientation. Moreover, previous related thermal stress/strain analyses were at most based on bilinear constitutive relations for modeling copper plating along with a linear kinematic hardening assumption, and this cannot capture many aspects of cyclic stress/strain behavior during thermal excursions. In this paper, thermal stress analyses using Internal State Variable (ISV) models of metallic constituents of PTHs are conducted using the finite element code ABAQUS (1996). Two thermal history profiles having two repeated cycles were applied for the PTHs of a double layered printed wiring board (PWB) uniformly: (1) MIL-T-CYC (between −65°C and 125°C), and (2) IEC OIL-T-SHOCK (between 25°C and 260°C). A critical plane theory was used for purposes of multiaxial fatigue life prediction. The stress/strain results were reported and compared at the PTH corner and barrel. For both cases, the thermomechanical mismatch between the FR4 and copper constituents of the PWB generates nonproportional stress/strain responses. This complicates PTH thermal fatigue investigation.
M F Horstemeyer - One of the best experts on this subject based on the ideXlab platform.
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an electroplastic Internal State Variable isv model for nonferromagnetic ductile metals
Mechanics of Advanced Materials and Structures, 2020Co-Authors: Nikolay Dimitrov, Yucheng Liu, M F HorstemeyerAbstract:This study presents a multiphysics Internal State Variable (ISV) theory that couples the thermo-elasto-viscoplastic-damage model of Bammann with electroplasticity and other electricity-related elec...
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a multiphase Internal State Variable model with rate equations for predicting elastothermoviscoplasticity and damage of fiber reinforced polymer composites
Acta Mechanica, 2019Co-Authors: Yucheng Liu, Douglas J. Bammann, David Francis, Mei Q Chandler, M F HorstemeyerAbstract:This paper explores the integration of an Internal State Variable (ISV) model for polymers (Bouvard et al. in Acta Mech 213(1):77–96, 2010; Int J Plast 42:168–193, 2013) with damage evolution (Horstemeyer and Gokhale in Int J Solids Struct 36:5029–5055, 1999; Horstemeyer et al. in Theor Appl Fract Mech 33(1):31–47, 2000; Francis et al. in Int J Solids Struct 51:2765–2776, 2014) into a multiphase ISV framework (Rajagopal and Tao in Advances in mathematics for the applied sciences, World Scientific, Singapore, 1995; Bammann in Proceedings of 2nd international conference on quenching and the control of distortion, vols 4–7, 1996) that features a finite strain theoretical framework for fiber-reinforced polymer (FRP) composites under various stress States, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage Variable is employed to capture the damage history of the FRP, which comprises three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber–matrix interface. The constitutive model developed herein employs standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being Internally consistent, whose ISVs can be either calculated from molecular dynamics simulations or calibrated through microstructural characterizations for specific FRPs. The developed elastothermoviscoplasticity and damage modeling framework is then employed to model the Internal damage evolution of a glass fiber-reinforced polyamide 66 (Rolland et al. in Compos Part B Eng 90:65–377, 2016) in terms of above three damage mechanisms. A detailed description of the model parameter identification process is given by using the example of a unidirectional glass fiber-reinforced epoxy, and the mechanical behaviors and properties of the composites at varying temperature and fiber volume fraction are predicted by the model, which are in good agreement with the experimental result.
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application of the bammann inelasticity Internal State Variable constitutive model to geological materials
Geophysical Journal International, 2011Co-Authors: Jesse A. Sherburn, Douglas J. Bammann, M F Horstemeyer, J. R. BaumgardnerAbstract:SUMMARY We describe how the Bammann Internal State Variable (ISV) constitutive approach, which has proven highly successful in modelling deformation processes in metals, can be applied with great benefit to silicate rocks and other geological materials in modelling their deformation dynamics. In its essence, ISV theory provides a constitutive framework to account for changing history States that arise from inelastic dissipative microstructural evolution of a polycrystalline solid. In this paper, we restrict our attention to a Bammann ISV elastic-viscoplastic model with temperature and strain rate dependence and use isotropic hardening and anisotropic hardening as our two ISVs. We show the Bammann model captures the inelastic behaviour of olivine aggregates (with and without water), lherzolite (with and without water), Carrara marble and rock salt using some experimental data found in the literature. These examples illustrate that when more experimental stress–strain data are gathered on other rock materials, much more realistic numerical simulation of rock behaviour becomes feasible. Though not available in the literature, we outline a set of experiments to obtain unique Bammann ISV model constants.
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Internal State Variable plasticity damage modeling of the copper tee shaped tube hydroforming process
Journal of Materials Processing Technology, 2010Co-Authors: Justin M Crapps, M F Horstemeyer, E B Marin, Reza S Yassar, P T WangAbstract:Abstract This paper presents a parametric finite element analysis using a history-dependent Internal State Variable model for a hydroforming process. Experiments were performed for the Internal State Variable model correlation and for validating a 2-in. copper tee hydroforming process simulation. The material model constants were determined from uniaxial stress–strain responses obtained from tensile tests on the tube's material. In the finite element simulations, the mesh and boundary conditions were integrated with the geometry and process parameters currently used in industry. The study provides insights for the variation of different process parameters (velocity and pressure profiles, and bucking system characteristics) related to the finished product.
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an Internal State Variable damage model in crystal plasticity
Mechanics of Materials, 2007Co-Authors: G P Potirniche, M F Horstemeyer, Xianwu LingAbstract:Abstract This paper presents a polycrystalline plasticity theory including damage evolution in FCC materials. The formulation is thermodynamically-based and involves a multiplicative decomposition of the deformation gradient into its elastic, plastic and volumetric components. Plastic deformation at the grain level is assumed to occur by rate-dependent crystallographic slip. As a result of accumulated plastic strain and stress triaxiality, damage evolution leading to volumetric deformation is considered to occur within a single crystal by void nucleation, growth and coalescence. The overall stress–strain response of the polycrystalline material is obtained by Taylor averaging on the stress response of each grain. In the model, damage progression arises naturally from averaging each single crystal’s damage evolution. A parametric study is performed to evaluate the amount of damage and strains at fracture on both single and polycrystals in order to understand crystal orientation effects. For validation purposes, model predictions of uniaxial stress–strain data are compared with experimental results for some aluminum alloys, and the comparison is shown to agree very well.
E B Marin - One of the best experts on this subject based on the ideXlab platform.
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An Internal State Variable material model for predicting the time, thermomechanical, and stress State dependence of amorphous glassy polymers under large deformation
International Journal of Plasticity, 2013Co-Authors: Jean-luc Bouvard, D.k. Francis, E B Marin, Mark A. Tschopp, Mark F. HorstemeyerAbstract:This paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress State dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based Internal State Variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress State dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress States. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions.
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An Internal State Variable material model for predicting the time, thermomechanical, and stress State dependence of amorphous glassy polymers under large deformation
International Journal of Plasticity, 2013Co-Authors: Jean-luc Bouvard, Douglas J. Bammann, E B Marin, David Francis, Mark A. Tschopp, Mark F. HorstemeyerAbstract:International audienceThis paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress State dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based Internal State Variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress State dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress States. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions
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a new approach for determination of material constants of Internal State Variable based plasticity models and their uncertainty quantification
Computational Materials Science, 2012Co-Authors: S Salehghaffari, E B Marin, Masoud Raisrohani, Douglas J. BammannAbstract:Physically-based plasticity models such as the BCJ model include Internal State Variables that represent the current State of the material and allow capturing strain rate and temperature history effects as well as the coupling of rate- and temperature-dependence with material hardening. However, the inclusion of Internal State Variables increases significantly the number of unknown material constants that need to be found through fitting of the model to experimental stress–strain data at different strain rates and temperatures. This makes the fitting process extremely challenging and increases the uncertainty in the material constants. The paper presents a physics-guided numerical fitting approach that reduces the associated difficulties and uncertainties involved in determining the material constants of the BCJ plasticity model. The approach uses experimental data from monotonic and reverse loading stress–strain curves at different temperatures and strain rates to determine the 18 material constants of the model. An evidential uncertainty quantification approach is used to determine uncertainties rooted in experimental data, selection of stress–strain curves at different loading conditions, variability of material properties, numerical aspects of the fitting method and mathematical formulations of the BCJ model. The represented uncertainty of the BCJ material constants based on mathematical tools of evidence theory is propagated through Taylor impact simulations of a 7075-T651 aluminum alloy cylinder. Uncertainty quantification results verify the presented numerical fitting approach for the BCJ model and its potential applicability to other similar material models.
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Development of an Internal State Variable model to describe the mechanical behavior of amorphous polymer and its application to impact testing
Time Dependent Constitutive Behavior and Fracture Failure Processes Volume 3, 2011Co-Authors: Jean-luc Bouvard, Donald K. Ward, Douglas J. Bammann, E B Marin, Mark F. HorstemeyerAbstract:The use of lighter and impact resistant materials, such as polymers, in vehicular systems is an important motivation for the automotive industry as these materials would make vehicles more fuel-efficient without compromising safety standards. In general, polymers exhibit a rich variety of material behavior originating from their particular microstructural (long molecular chains) behavior that is strongly temperature, pressure, and time dependent. To capture such intricate behavior, a number of polymer constitutive models have been proposed and implemented into finite element codes in an effort to solve complex engineering problems (see [1] for a review of these models). However, developing improved constitutive models for polymers that are physically-based is always a challenging area that has important implications for the design of polymeric structural components.
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Internal State Variable plasticity damage modeling of the copper tee shaped tube hydroforming process
Journal of Materials Processing Technology, 2010Co-Authors: Justin M Crapps, M F Horstemeyer, E B Marin, Reza S Yassar, P T WangAbstract:Abstract This paper presents a parametric finite element analysis using a history-dependent Internal State Variable model for a hydroforming process. Experiments were performed for the Internal State Variable model correlation and for validating a 2-in. copper tee hydroforming process simulation. The material model constants were determined from uniaxial stress–strain responses obtained from tensile tests on the tube's material. In the finite element simulations, the mesh and boundary conditions were integrated with the geometry and process parameters currently used in industry. The study provides insights for the variation of different process parameters (velocity and pressure profiles, and bucking system characteristics) related to the finished product.