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Papers by Abhimanyu Kumar

Research paper thumbnail of On the Dynamics of Non-linear, Coupled Structures with Primary - and Moving Secondary-Oscillating Systems

Earth & Space 2008, 2008

In past two decades, two intriguing classes of problems, having a wide range of applications in e... more In past two decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers:(i) coupled dynamics of distributed parameter system carrying one or more moving oscillators, and (ii) transient ...

Research paper thumbnail of On the Comprehensive Modeling of Response of Shape Memory (SMA) Materials

Earth & Space 2008, 2008

Despite, significant work over many years (utilizing either one of the micromechanics based or ph... more Despite, significant work over many years (utilizing either one of the micromechanics based or phenomenological approaches; see Lagoudas et al. 2006; Patoor et al. 2006), there are still prospects of much improvements to be made in constitutive modeling of Shape ...

Research paper thumbnail of The important roles of tissue anisotropy and tissue-to-tissue contact on the dynamical behavior of a symmetric tri-leaflet valve during multiple cardiac pressure cycles

Medical Engineering & Physics, 2013

Restricting our scope to the dynamical motion of the leaflets, we present a computational model f... more Restricting our scope to the dynamical motion of the leaflets, we present a computational model for a symmetric, tri-leaflet, bioprosthetic heart valve (BHV) at the end of five complete cardiac pressure cycles, reaching the steady state of deformation during both closing and opening phases. To this end, we utilized a highly anisotropic material model for the large deformation behavior of the tissue material, for which an experimental validation was provided. The important findings are: (1) material anisotropy has significant effect on the valve opening/closing; (2) the asymmetric deformations, especially in the fully closed configuration, justify the use of cyclic symmetry; (3) adopting the fully-open position as an initial/reference configuration has the advantage of completely bypassing any complications arising from the need to assume the size and shape of the contact area in the coaptation regions of the leaflets that is necessary when the alternative, commonly-used, approach of selecting the fully-closed position is used as a reference; and (4) with proper treatments for both material anisotropy and tissue-to-tissue contact, the overall BHV model provide realistic results in conformity with the ex vivo/in vitro experiments.

Research paper thumbnail of The cyclic and evolutionary response to approach the attraction loops under stress controlled isothermal conditions for a multi-mechanism based multi-axial SMA model

Mechanics of Materials, 2013

ABSTRACT The main focus in the present work has been on studying the evolutionary responses of Sh... more ABSTRACT The main focus in the present work has been on studying the evolutionary responses of Shape Memory Alloy (SMA) materials under isothermal, cyclic loading conditions. To this end, predictions of a recently-developed SMA material model by the authors is used here to carry out the qualitative comparisons to some of the available experimental results in the literature for SMA material responses under different uniaxial and multi-axial conditions of stress-control, both in the pseudoelastic and the pseudoplastic regimes. In the formulation of this model, the significant roles played by the internal state variables, underlying the inelastic mechanisms in the model to regulate the material’s evolutionary response under extended cycles, are emphasized. The results presented have led to a number of important conclusions. First, the evolutionary character for pseudoelasticity is markedly different from that occurring in the pseudoplastic regime. Second, the virgin material response under minor loop cycles is dramatically different from its pre-cycled counterpart for which a prior major loop was established. Third, the careful selection of the loading-control variable such as magnitudes of the mean stress and stress amplitude plays a major role in dictating the amount of strain and detailed shapes of the saturated stress–strain loop achieved, as well as the number of cycles required to reach the saturation. Lastly, multi-axial load cycling under conditions of combined tension/compression/shear leads to a faster approach to the saturated states compared to the uniaxial load condition.

Research paper thumbnail of Computer Modeling for the Complex Response Analysis of Nonstandard Structural Dynamics Problems

Journal of Aerospace Engineering, 2009

Over the past several decades, two intriguing classes of problems, having a wide range of applica... more Over the past several decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers:(1) coupled dynamics of a distributed parameter system traversed by one or more moving oscillators; ...

Research paper thumbnail of Comprehensive Modeling of Shape Memory Alloy Material Response Using a Multimechanism-Based Inelastic Model

Journal of Aerospace Engineering, 2009

Despite significant work over many years, using either one of the micromechanics based or phenome... more Despite significant work over many years, using either one of the micromechanics based or phenomenological approaches, there are still prospects of much improvement to be made in constitutive modeling of shape memory alloys ͑SMAs͒. This is especially true if we sufficiently target the general scope in the modeling, i.e., including such important attributes as ͑1͒ multiaxiality; ͑2͒ possible asymmetry in tension and compression; ͑3͒ accounting for pseudoelasticity and pseudoplasticity; ͑4͒ rate dependence; and ͑5͒ effects of shape memory training under cyclic loading. The desire for comprehensive modeling of SMA materials provides the primary motivation for the inelastic model described here. Its theoretical formulation employs two main ingredients: ͑1͒ multiplicity of hardening mechanisms and ͑2͒ the partition of the energy storage/dissipation that is so vital in capturing the extremes of pseudoelasticity and pseudoplasticity in SMAs. For the purpose of validation and assessment part of the model capabilities, we report the results of a large number of simulations that were inspired by recent experimental test results under both monotonic and cyclic as well as uniaxial and multiaxial stress conditions.

Research paper thumbnail of A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions

International Journal of Plasticity, 2011

Research paper thumbnail of Automated Finite Element Analysis of Complex Dynamics of Primary System Traversed by Oscillatory Subsystem

International Journal for Computational Methods in Engineering Science and Mechanics, 2011

The extensive literature on a particular dynamics problem, the bridge-vehicle-interaction, has pr... more The extensive literature on a particular dynamics problem, the bridge-vehicle-interaction, has provided insights and understanding of the many complex issues involved, but the mathematical and numerical work reported remained too highly specialized for practicing engineers. In particular, the use of standard FEA packages is virtually nonexistent. To this end, we propose an alternative approach by considering the primary and secondary systems as deformable solids, undergoing large, overall relative sliding motion. This will directly account for important convective accelerations, and the possible contact/separation. The versatility of the proposed strategy has been demonstrated by the solution of an extensive number of benchmark problems.

Research paper thumbnail of On the Dynamics of Non-linear, Coupled Structures with Primary - and Moving Secondary-Oscillating Systems

Earth & Space 2008, 2008

In past two decades, two intriguing classes of problems, having a wide range of applications in e... more In past two decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers:(i) coupled dynamics of distributed parameter system carrying one or more moving oscillators, and (ii) transient ...

Research paper thumbnail of On the Comprehensive Modeling of Response of Shape Memory (SMA) Materials

Earth & Space 2008, 2008

Despite, significant work over many years (utilizing either one of the micromechanics based or ph... more Despite, significant work over many years (utilizing either one of the micromechanics based or phenomenological approaches; see Lagoudas et al. 2006; Patoor et al. 2006), there are still prospects of much improvements to be made in constitutive modeling of Shape ...

Research paper thumbnail of The important roles of tissue anisotropy and tissue-to-tissue contact on the dynamical behavior of a symmetric tri-leaflet valve during multiple cardiac pressure cycles

Medical Engineering & Physics, 2013

Restricting our scope to the dynamical motion of the leaflets, we present a computational model f... more Restricting our scope to the dynamical motion of the leaflets, we present a computational model for a symmetric, tri-leaflet, bioprosthetic heart valve (BHV) at the end of five complete cardiac pressure cycles, reaching the steady state of deformation during both closing and opening phases. To this end, we utilized a highly anisotropic material model for the large deformation behavior of the tissue material, for which an experimental validation was provided. The important findings are: (1) material anisotropy has significant effect on the valve opening/closing; (2) the asymmetric deformations, especially in the fully closed configuration, justify the use of cyclic symmetry; (3) adopting the fully-open position as an initial/reference configuration has the advantage of completely bypassing any complications arising from the need to assume the size and shape of the contact area in the coaptation regions of the leaflets that is necessary when the alternative, commonly-used, approach of selecting the fully-closed position is used as a reference; and (4) with proper treatments for both material anisotropy and tissue-to-tissue contact, the overall BHV model provide realistic results in conformity with the ex vivo/in vitro experiments.

Research paper thumbnail of The cyclic and evolutionary response to approach the attraction loops under stress controlled isothermal conditions for a multi-mechanism based multi-axial SMA model

Mechanics of Materials, 2013

ABSTRACT The main focus in the present work has been on studying the evolutionary responses of Sh... more ABSTRACT The main focus in the present work has been on studying the evolutionary responses of Shape Memory Alloy (SMA) materials under isothermal, cyclic loading conditions. To this end, predictions of a recently-developed SMA material model by the authors is used here to carry out the qualitative comparisons to some of the available experimental results in the literature for SMA material responses under different uniaxial and multi-axial conditions of stress-control, both in the pseudoelastic and the pseudoplastic regimes. In the formulation of this model, the significant roles played by the internal state variables, underlying the inelastic mechanisms in the model to regulate the material’s evolutionary response under extended cycles, are emphasized. The results presented have led to a number of important conclusions. First, the evolutionary character for pseudoelasticity is markedly different from that occurring in the pseudoplastic regime. Second, the virgin material response under minor loop cycles is dramatically different from its pre-cycled counterpart for which a prior major loop was established. Third, the careful selection of the loading-control variable such as magnitudes of the mean stress and stress amplitude plays a major role in dictating the amount of strain and detailed shapes of the saturated stress–strain loop achieved, as well as the number of cycles required to reach the saturation. Lastly, multi-axial load cycling under conditions of combined tension/compression/shear leads to a faster approach to the saturated states compared to the uniaxial load condition.

Research paper thumbnail of Computer Modeling for the Complex Response Analysis of Nonstandard Structural Dynamics Problems

Journal of Aerospace Engineering, 2009

Over the past several decades, two intriguing classes of problems, having a wide range of applica... more Over the past several decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers:(1) coupled dynamics of a distributed parameter system traversed by one or more moving oscillators; ...

Research paper thumbnail of Comprehensive Modeling of Shape Memory Alloy Material Response Using a Multimechanism-Based Inelastic Model

Journal of Aerospace Engineering, 2009

Despite significant work over many years, using either one of the micromechanics based or phenome... more Despite significant work over many years, using either one of the micromechanics based or phenomenological approaches, there are still prospects of much improvement to be made in constitutive modeling of shape memory alloys ͑SMAs͒. This is especially true if we sufficiently target the general scope in the modeling, i.e., including such important attributes as ͑1͒ multiaxiality; ͑2͒ possible asymmetry in tension and compression; ͑3͒ accounting for pseudoelasticity and pseudoplasticity; ͑4͒ rate dependence; and ͑5͒ effects of shape memory training under cyclic loading. The desire for comprehensive modeling of SMA materials provides the primary motivation for the inelastic model described here. Its theoretical formulation employs two main ingredients: ͑1͒ multiplicity of hardening mechanisms and ͑2͒ the partition of the energy storage/dissipation that is so vital in capturing the extremes of pseudoelasticity and pseudoplasticity in SMAs. For the purpose of validation and assessment part of the model capabilities, we report the results of a large number of simulations that were inspired by recent experimental test results under both monotonic and cyclic as well as uniaxial and multiaxial stress conditions.

Research paper thumbnail of A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions

International Journal of Plasticity, 2011

Research paper thumbnail of Automated Finite Element Analysis of Complex Dynamics of Primary System Traversed by Oscillatory Subsystem

International Journal for Computational Methods in Engineering Science and Mechanics, 2011

The extensive literature on a particular dynamics problem, the bridge-vehicle-interaction, has pr... more The extensive literature on a particular dynamics problem, the bridge-vehicle-interaction, has provided insights and understanding of the many complex issues involved, but the mathematical and numerical work reported remained too highly specialized for practicing engineers. In particular, the use of standard FEA packages is virtually nonexistent. To this end, we propose an alternative approach by considering the primary and secondary systems as deformable solids, undergoing large, overall relative sliding motion. This will directly account for important convective accelerations, and the possible contact/separation. The versatility of the proposed strategy has been demonstrated by the solution of an extensive number of benchmark problems.