X. Gary Tan | U.S. Naval Research Laboratory (original) (raw)

Papers by X. Gary Tan

Research paper thumbnail of Development of a lower extremity model for high strain rate impact loading

International Journal of Experimental and Computational Biomechanics, 2015

In recent military conflicts, the incidence of underbody blasts has led to severe injuries, speci... more In recent military conflicts, the incidence of underbody blasts has led to severe injuries, specifically in the lower extremities. The development of a lower extremity model may lead to a better understanding of injury patterns and mechanisms. A computational finite element model of the lower extremity was developed based on geometry made available in an anatomical repository. The portion of the extremity model below the knee was used in initial comparisons between simulations and experimental data. Impact was applied via a loading plate with a vertical velocity of 5 m/s, 10 m/s, and 12 m/s. Resultant axial force was compared to experimental data. Results of these simulations fall within the range of available experimental data, which gives confidence that this model represents advancement in lower extremity modelling capabilities. Bone fracture has also been modelled and shows consistency with injuries typical of underbody blast scenarios.

Research paper thumbnail of Geometrically exact sandwich shells: The dynamic case

Computer Methods in Applied Mechanics and Engineering, 2001

The present formulation oers a general method for analyzing the static response of geometrically-... more The present formulation oers a general method for analyzing the static response of geometrically-exact sandwich shells undergoing large deformation. The layer directors at a point in the reference surface are connected to each other by universal joints, and form a chain of rigid links. Finite rotations of the directors in every layer are allowed, with shear deformation independently accounted for in each layer. The thickness and the length of each layer can be arbitrary, thus allowing the modeling of an important class of multilayer structures having ply drop-os. The present formulation is thus suitable to model shell structures with patches of constrained viscoelastic materials or of piezoelectric materials. The nonlinear weak form of the governing equations of equilibrium is constructed here, and then the linearization of the weak form and the associated inextensible directors update are derived, leading to a symmetric tangent stiness matrix. A Galerkin ®nite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations, in which the interpolation accounts for the ®nite rotations of the directors. We present extensive numerical examples, including sandwich shells with three identical layers and ply drop-os, to illustrate the applicability and versatility of the proposed formulation.

Research paper thumbnail of Optimizing Helmet Pad Placement Using Computational Predicted Injury Pattern to Reduce Mild Traumatic Brain Injury

Military Medicine, 2021

ABSTRACTIntroductionThis effort, motivated and guided by prior simulated injury results of the un... more ABSTRACTIntroductionThis effort, motivated and guided by prior simulated injury results of the unprotected head, is to assess and compare helmet pad configurations on the head for the effective mitigation of blast pressure transmission in the brain in multiple blast exposure environments.Materials and MethodsA finite element model of blast loading on the head with six different helmet pad configurations was used to generate brain model biomechanical responses. The blast pressure attenuation performance of each pad configuration was evaluated by using the calculated pressure exposure fraction in the brain model. Monte Carlo simulations generated repetitive blast cumulative exposures.ResultsSignificant improvement of a 6-Pad Modified configuration compared to a 6-Pad Baseline configuration indicates the importance of providing protection against the side blast. Both 12-Pad configurations are very effective in mitigating pressure in the brain. Repetitive blast exposure statistics for o...

Research paper thumbnail of Coupled modeling for investigation of blast induced traumatic brain injury

Modeling of human body biomechanics resulting from blast exposure is very challenging because of ... more Modeling of human body biomechanics resulting from blast exposure is very challenging because of the complex geometry and the substantially different materials involved. We have developed anatomy based high-fidelity finite element model (FEM) of the human body and finite volume model (FVM) of air around the human. The FEM model was used to accurately simulate the stress wave propagation in the human body under blast loading. The blast loading was generated by simulating C4 explosions, via a combination of 1-D and 3-D computational fluid dynamics (CFD) formulations. By employing the coupled Eulerian-Lagrangian fluid structure interaction (FSI) approach we obtained the parametric response of the human brain by the blast wave impact. We also developed the methodology to solve the strong interaction between cerebrospinal fluids (CSF) and the surrounding tissue for the closed-head impact. We presented both the arbitrary Lagrangian Eulerian (ALE) method and a new unified approach based on...

Research paper thumbnail of Computational Modeling of Blast Induced Human Injury Biomechanics and Traumatic Brain Injury

Journal of Trauma & Treatment, 2017

The work aims to understand the blast induced injury mechanism and facilitate the development of ... more The work aims to understand the blast induced injury mechanism and facilitate the development of protection and treatment. Novel multi-scale and multi-physics computational models of coupled blast physics, whole body biodynamics and injury biomechanics are presented. Modeling components include blast wave threat characterization, anatomy-based high-fidelity human model, human body blast loading, biodynamics and body/brain biomechanics leading to primary injury, as well as the multi-physics solver suitable for high-performance computing. The coupled gas dynamics and biomechanics solutions were validated against shock tube test data. The parametric simulations of human body exposed to blasts were conducted to find biomechanical responses and brain injury mechanism.

Research paper thumbnail of On the Development of Interspecies Traumatic Brain Injury Correspondence Rules

Military Medicine, 2019

Traumatic brain injury analysis in human is exceedingly difficult due to the methods in which dat... more Traumatic brain injury analysis in human is exceedingly difficult due to the methods in which data can be collected, thus many researchers commonly implement animal surrogates. However, use of these surrogates is costly and restricted by ethical concerns and test logistics. Computational models and simulations do not have these constraints and can produce significant amounts of data in relatively short periods. This paper shows the development of a human head and neck model and a full body porcine model. Both models are developed from high-resolution CT and MRI scans and the latest low-to-high strain rate mechanical data available in the literature to represent tissue component material behaviors. Both models are validated against experiments from the literature and used to complete an initial interspecies correspondence rule development study for blast overpressure effects. The results indicate the similarities in the way injury develops in the pig brain and human brain but these s...

Research paper thumbnail of Biomechanics of Blast TBI With Time-Resolved Consecutive Primary, Secondary, and Tertiary Loads

Military Medicine, 2019

Blast-induced traumatic brain injury (bTBI) has become a signature casualty of recent military op... more Blast-induced traumatic brain injury (bTBI) has become a signature casualty of recent military operations. In spite of significant clinical and preclinical TBI research, current understanding of injury mechanisms and short- and long-term outcomes is limited. Mathematical models of bTBI biomechanics may help in better understanding of injury mechanisms and in the development of improved neuroprotective strategies. Until present, bTBI has been analyzed as a single event of a blast pressure wave propagating through the brain. In many bTBI events, the loads on the body and the head are spatially and temporarily distributed, involving the primary intracranial pressure wave, followed by the head rotation and then by head impact on the ground. In such cases, the brain microstructures may experience time/space distributed (consecutive) damage and recovery events. The paper presents a novel multiscale simulation framework that couples the body/brain scale biomechanics with micro-scale mechan...

Research paper thumbnail of Multiscale Modelling of Blast-Induced TBI Mechanobiology - From Body to Neuron to Molecule

Defence Life Science Journal, 2017

Blast induced Traumatic Brain Injury (bTBI) has become a signature wound of the recent military o... more Blast induced Traumatic Brain Injury (bTBI) has become a signature wound of the recent military operations and is becoming a significant factor of recent civilian blast explosion events. In spite of significant clinical and preclinical research on TBI, current understanding of injury mechanisms is limited and little is known about the short and long-term outcomes. Mathematical models of bTBI may provide capabilities to study brain injury mechanisms, perhaps accelerating the development of neuroprotective strategies and aiding in the development of improved personal protective equipment. The paper presents a novel multiscale simulation framework that couples the body/brain scale biomechanics with micro-scale mechanobiology to study the effects of “primary” micro-damage to neuro-axonal structures with the “secondary” injury and repair mechanisms. Our results show that oligodendrocyte myelinating processes distribute strains among neighbor axons and cause their off-axis deformations. S...

Research paper thumbnail of Optimal solid shells for non-linear analyses of multilayer composites. I. Statics

Computer Methods in Applied Mechanics and Engineering, 2003

We present in this paper a simple low-order solid-shell element formulation-having only displacem... more We present in this paper a simple low-order solid-shell element formulation-having only displacement degrees of freedom (dofs), i.e., without rotational dofs-that has an optimal number of parameters to pass the patch tests, and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio. The formulation of this element is based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle leading to a novel enhancing strain tensor (EAS method) that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. We also review the equivalence between various choices of the enhancing strains in tensor form, and point out the relative efficiency of these choices. We discuss the enhanced assumed strain (EAS) formulations based on both the Green-Lagrange strain and the displacement gradient (the companion paper), point out the pitfalls in each approach, e.g., not passing the patch test, and the possibility and the method to remedy the problem. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The element passes the patch tests (both membrane and out-ofplane bending). We provide an optimal combination of the ANS method and the minimal number of EAS parameters required to pass the out-of-plane bending patch test. Numerical examples involving static analyses of multilayer shell structures having a large range of element aspect ratios are presented. Finally, we note that the topic in this paper is a fitting dedication to Professor Ekkehard Ramm, who has made important pioneering contributions in this research direction.

Research paper thumbnail of Material characterization and simulation for soft gels subjected to impulsive loading

For impact and blast experiments of traumatic brain injury (TBI), soft gel materials are used as ... more For impact and blast experiments of traumatic brain injury (TBI), soft gel materials are used as surrogates to imitate the mechanical responses of brain tissue. To properly model a viscoelastic gel brain in a surrogate head using a finite element (FE) model, material parameters such as the shear moduli and relaxation time at high strain rates are required. However, such information is scarce in the literature and its applicability for a range of dynamic conditions is unclear. We used an integrated experiment and simulation approach to efficiently determine mechanical properties of soft gels at finite strains, as well as over a wide range of strain rates. A novel impact experiment using a gel block was developed to capture the high strain rate behavior by maximizing the inherent shear wave motion at different impact conditions. A corresponding computational model was used to simulate the gel dynamics of the impact. Parametric simulations utilizing optimization and correlation analyses were used to calibrate multiple material parameters in the nonlinear viscoelastic model to the experimental data. The optimal parameters for gels, including Sylgards 184, 3-6636, and 527, were found. We ascertained the initial shear stiffening effect in gels at high strain rate loadings experimentally and incorporated this effect in the simulation. We have verified the integrated approach by comparing the material properties of the gels with analytical results based on shear wave propagation. This study provides a new approach to calibrate the material behavior of soft gels under high strain rate loading conditions.

Research paper thumbnail of Computational modeling of blast wave interaction with a human body and assessment of traumatic brain injury

The modeling of human body biomechanics resulting from blast exposure poses great challenges beca... more The modeling of human body biomechanics resulting from blast exposure poses great challenges because of the complex geometry and the substantial material heterogeneity. We developed a detailed human body finite element model representing both the geometry and the materials realistically. The model includes the detailed head (face, skull, brain and spinal cord), the neck, the skeleton, air cavities (lungs) and the tissues. Hence, it can be used to properly model the stress wave propagation in the human body subjected to blast loading. The blast loading on the human was generated from a simulated C4 explosion. We used the highly scalable solvers in the multi-physics code CoBi for both the blast simulation and the human body biomechanics. The meshes generated for these simulations are of good quality so that relatively large time-step sizes can be used without resorting to artificial time scaling treatments. The coupled gas dynamics and biomechanics solutions were validated against the shock tube test data. The human body models were used to conduct parametric simulations to find the biomechanical response and the brain injury mechanism due to blasts impacting the human body. Under the same blast loading condition, we showed the importance of inclusion of the whole body.

Research paper thumbnail of Optimal solid shells for non-linear analyses of multilayer composites. I. Statics

We present in this paper a simple low-order solid-shell element formulation-having only displacem... more We present in this paper a simple low-order solid-shell element formulation-having only displacement degrees of freedom (dofs), i.e., without rotational dofs-that has an optimal number of parameters to pass the patch tests, and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio. The formulation of this element is based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle leading to a novel enhancing strain tensor (EAS method) that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. We also review the equivalence between various choices of the enhancing strains in tensor form, and point out the relative efficiency of these choices. We discuss the enhanced assumed strain (EAS) formulations based on both the Green-Lagrange strain and the displacement gradient (the companion paper), point out the pitfalls in each approach, e.g., not passing the patch test, and the possibility and the method to remedy the problem. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The element passes the patch tests (both membrane and out-ofplane bending). We provide an optimal combination of the ANS method and the minimal number of EAS parameters required to pass the out-of-plane bending patch test. Numerical examples involving static analyses of multilayer shell structures having a large range of element aspect ratios are presented. Finally, we note that the topic in this paper is a fitting dedication to Professor Ekkehard Ramm, who has made important pioneering contributions in this research direction.

Research paper thumbnail of Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics

Elsevier, 2003

We are presenting a simple low-order solid-shell element formulation––having only displacement de... more We are presenting a simple low-order solid-shell element formulation––having only displacement degrees of freedom
(dofs), i.e., without rotational dofs––that has an optimal number of parameters to pass the patch tests, and thus allows
for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high
aspect ratio. With the dynamics referred to a fixed inertial frame, the elements can be used to analyze multilayer shell
structures undergoing large overall motion. The formulation of this element is based on the mixed Hu-Washizu
variational principle leading to a novel enhancing strain tensor (enhanced assumed strain (EAS) method) that renders
the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness
locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. The
energy–momentum conserving algorithm in the context of current solid shell element is presented. We discuss the EAS
formulation based on the displacement gradient and its complexity compared to formulation on the Green–Lagrange
strain. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The
element has an optimal combination of the ANS method and the minimal number of EAS parameters required to pass
the plate bending patch test. Numerical examples involving dynamic analyses (with conservation of energy and momentum) of multilayer shell structures having a large range of element aspect ratios are presented. Several implicit direct
integration methods with/without numerical dissipation are used and compared in terms of the accuracy, stability
and cost in multilayer shell structure. Finally, we note that the topic in this paper is a fitting dedication to Professor
Ekkehard Ramm, who has made important pioneering contributions in this research direction.

Research paper thumbnail of Development of a lower extremity model for high strain rate impact loading

International Journal of Experimental and Computational Biomechanics, 2015

In recent military conflicts, the incidence of underbody blasts has led to severe injuries, speci... more In recent military conflicts, the incidence of underbody blasts has led to severe injuries, specifically in the lower extremities. The development of a lower extremity model may lead to a better understanding of injury patterns and mechanisms. A computational finite element model of the lower extremity was developed based on geometry made available in an anatomical repository. The portion of the extremity model below the knee was used in initial comparisons between simulations and experimental data. Impact was applied via a loading plate with a vertical velocity of 5 m/s, 10 m/s, and 12 m/s. Resultant axial force was compared to experimental data. Results of these simulations fall within the range of available experimental data, which gives confidence that this model represents advancement in lower extremity modelling capabilities. Bone fracture has also been modelled and shows consistency with injuries typical of underbody blast scenarios.

Research paper thumbnail of Geometrically exact sandwich shells: The dynamic case

Computer Methods in Applied Mechanics and Engineering, 2001

The present formulation oers a general method for analyzing the static response of geometrically-... more The present formulation oers a general method for analyzing the static response of geometrically-exact sandwich shells undergoing large deformation. The layer directors at a point in the reference surface are connected to each other by universal joints, and form a chain of rigid links. Finite rotations of the directors in every layer are allowed, with shear deformation independently accounted for in each layer. The thickness and the length of each layer can be arbitrary, thus allowing the modeling of an important class of multilayer structures having ply drop-os. The present formulation is thus suitable to model shell structures with patches of constrained viscoelastic materials or of piezoelectric materials. The nonlinear weak form of the governing equations of equilibrium is constructed here, and then the linearization of the weak form and the associated inextensible directors update are derived, leading to a symmetric tangent stiness matrix. A Galerkin ®nite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations, in which the interpolation accounts for the ®nite rotations of the directors. We present extensive numerical examples, including sandwich shells with three identical layers and ply drop-os, to illustrate the applicability and versatility of the proposed formulation.

Research paper thumbnail of Optimizing Helmet Pad Placement Using Computational Predicted Injury Pattern to Reduce Mild Traumatic Brain Injury

Military Medicine, 2021

ABSTRACTIntroductionThis effort, motivated and guided by prior simulated injury results of the un... more ABSTRACTIntroductionThis effort, motivated and guided by prior simulated injury results of the unprotected head, is to assess and compare helmet pad configurations on the head for the effective mitigation of blast pressure transmission in the brain in multiple blast exposure environments.Materials and MethodsA finite element model of blast loading on the head with six different helmet pad configurations was used to generate brain model biomechanical responses. The blast pressure attenuation performance of each pad configuration was evaluated by using the calculated pressure exposure fraction in the brain model. Monte Carlo simulations generated repetitive blast cumulative exposures.ResultsSignificant improvement of a 6-Pad Modified configuration compared to a 6-Pad Baseline configuration indicates the importance of providing protection against the side blast. Both 12-Pad configurations are very effective in mitigating pressure in the brain. Repetitive blast exposure statistics for o...

Research paper thumbnail of Coupled modeling for investigation of blast induced traumatic brain injury

Modeling of human body biomechanics resulting from blast exposure is very challenging because of ... more Modeling of human body biomechanics resulting from blast exposure is very challenging because of the complex geometry and the substantially different materials involved. We have developed anatomy based high-fidelity finite element model (FEM) of the human body and finite volume model (FVM) of air around the human. The FEM model was used to accurately simulate the stress wave propagation in the human body under blast loading. The blast loading was generated by simulating C4 explosions, via a combination of 1-D and 3-D computational fluid dynamics (CFD) formulations. By employing the coupled Eulerian-Lagrangian fluid structure interaction (FSI) approach we obtained the parametric response of the human brain by the blast wave impact. We also developed the methodology to solve the strong interaction between cerebrospinal fluids (CSF) and the surrounding tissue for the closed-head impact. We presented both the arbitrary Lagrangian Eulerian (ALE) method and a new unified approach based on...

Research paper thumbnail of Computational Modeling of Blast Induced Human Injury Biomechanics and Traumatic Brain Injury

Journal of Trauma & Treatment, 2017

The work aims to understand the blast induced injury mechanism and facilitate the development of ... more The work aims to understand the blast induced injury mechanism and facilitate the development of protection and treatment. Novel multi-scale and multi-physics computational models of coupled blast physics, whole body biodynamics and injury biomechanics are presented. Modeling components include blast wave threat characterization, anatomy-based high-fidelity human model, human body blast loading, biodynamics and body/brain biomechanics leading to primary injury, as well as the multi-physics solver suitable for high-performance computing. The coupled gas dynamics and biomechanics solutions were validated against shock tube test data. The parametric simulations of human body exposed to blasts were conducted to find biomechanical responses and brain injury mechanism.

Research paper thumbnail of On the Development of Interspecies Traumatic Brain Injury Correspondence Rules

Military Medicine, 2019

Traumatic brain injury analysis in human is exceedingly difficult due to the methods in which dat... more Traumatic brain injury analysis in human is exceedingly difficult due to the methods in which data can be collected, thus many researchers commonly implement animal surrogates. However, use of these surrogates is costly and restricted by ethical concerns and test logistics. Computational models and simulations do not have these constraints and can produce significant amounts of data in relatively short periods. This paper shows the development of a human head and neck model and a full body porcine model. Both models are developed from high-resolution CT and MRI scans and the latest low-to-high strain rate mechanical data available in the literature to represent tissue component material behaviors. Both models are validated against experiments from the literature and used to complete an initial interspecies correspondence rule development study for blast overpressure effects. The results indicate the similarities in the way injury develops in the pig brain and human brain but these s...

Research paper thumbnail of Biomechanics of Blast TBI With Time-Resolved Consecutive Primary, Secondary, and Tertiary Loads

Military Medicine, 2019

Blast-induced traumatic brain injury (bTBI) has become a signature casualty of recent military op... more Blast-induced traumatic brain injury (bTBI) has become a signature casualty of recent military operations. In spite of significant clinical and preclinical TBI research, current understanding of injury mechanisms and short- and long-term outcomes is limited. Mathematical models of bTBI biomechanics may help in better understanding of injury mechanisms and in the development of improved neuroprotective strategies. Until present, bTBI has been analyzed as a single event of a blast pressure wave propagating through the brain. In many bTBI events, the loads on the body and the head are spatially and temporarily distributed, involving the primary intracranial pressure wave, followed by the head rotation and then by head impact on the ground. In such cases, the brain microstructures may experience time/space distributed (consecutive) damage and recovery events. The paper presents a novel multiscale simulation framework that couples the body/brain scale biomechanics with micro-scale mechan...

Research paper thumbnail of Multiscale Modelling of Blast-Induced TBI Mechanobiology - From Body to Neuron to Molecule

Defence Life Science Journal, 2017

Blast induced Traumatic Brain Injury (bTBI) has become a signature wound of the recent military o... more Blast induced Traumatic Brain Injury (bTBI) has become a signature wound of the recent military operations and is becoming a significant factor of recent civilian blast explosion events. In spite of significant clinical and preclinical research on TBI, current understanding of injury mechanisms is limited and little is known about the short and long-term outcomes. Mathematical models of bTBI may provide capabilities to study brain injury mechanisms, perhaps accelerating the development of neuroprotective strategies and aiding in the development of improved personal protective equipment. The paper presents a novel multiscale simulation framework that couples the body/brain scale biomechanics with micro-scale mechanobiology to study the effects of “primary” micro-damage to neuro-axonal structures with the “secondary” injury and repair mechanisms. Our results show that oligodendrocyte myelinating processes distribute strains among neighbor axons and cause their off-axis deformations. S...

Research paper thumbnail of Optimal solid shells for non-linear analyses of multilayer composites. I. Statics

Computer Methods in Applied Mechanics and Engineering, 2003

We present in this paper a simple low-order solid-shell element formulation-having only displacem... more We present in this paper a simple low-order solid-shell element formulation-having only displacement degrees of freedom (dofs), i.e., without rotational dofs-that has an optimal number of parameters to pass the patch tests, and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio. The formulation of this element is based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle leading to a novel enhancing strain tensor (EAS method) that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. We also review the equivalence between various choices of the enhancing strains in tensor form, and point out the relative efficiency of these choices. We discuss the enhanced assumed strain (EAS) formulations based on both the Green-Lagrange strain and the displacement gradient (the companion paper), point out the pitfalls in each approach, e.g., not passing the patch test, and the possibility and the method to remedy the problem. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The element passes the patch tests (both membrane and out-ofplane bending). We provide an optimal combination of the ANS method and the minimal number of EAS parameters required to pass the out-of-plane bending patch test. Numerical examples involving static analyses of multilayer shell structures having a large range of element aspect ratios are presented. Finally, we note that the topic in this paper is a fitting dedication to Professor Ekkehard Ramm, who has made important pioneering contributions in this research direction.

Research paper thumbnail of Material characterization and simulation for soft gels subjected to impulsive loading

For impact and blast experiments of traumatic brain injury (TBI), soft gel materials are used as ... more For impact and blast experiments of traumatic brain injury (TBI), soft gel materials are used as surrogates to imitate the mechanical responses of brain tissue. To properly model a viscoelastic gel brain in a surrogate head using a finite element (FE) model, material parameters such as the shear moduli and relaxation time at high strain rates are required. However, such information is scarce in the literature and its applicability for a range of dynamic conditions is unclear. We used an integrated experiment and simulation approach to efficiently determine mechanical properties of soft gels at finite strains, as well as over a wide range of strain rates. A novel impact experiment using a gel block was developed to capture the high strain rate behavior by maximizing the inherent shear wave motion at different impact conditions. A corresponding computational model was used to simulate the gel dynamics of the impact. Parametric simulations utilizing optimization and correlation analyses were used to calibrate multiple material parameters in the nonlinear viscoelastic model to the experimental data. The optimal parameters for gels, including Sylgards 184, 3-6636, and 527, were found. We ascertained the initial shear stiffening effect in gels at high strain rate loadings experimentally and incorporated this effect in the simulation. We have verified the integrated approach by comparing the material properties of the gels with analytical results based on shear wave propagation. This study provides a new approach to calibrate the material behavior of soft gels under high strain rate loading conditions.

Research paper thumbnail of Computational modeling of blast wave interaction with a human body and assessment of traumatic brain injury

The modeling of human body biomechanics resulting from blast exposure poses great challenges beca... more The modeling of human body biomechanics resulting from blast exposure poses great challenges because of the complex geometry and the substantial material heterogeneity. We developed a detailed human body finite element model representing both the geometry and the materials realistically. The model includes the detailed head (face, skull, brain and spinal cord), the neck, the skeleton, air cavities (lungs) and the tissues. Hence, it can be used to properly model the stress wave propagation in the human body subjected to blast loading. The blast loading on the human was generated from a simulated C4 explosion. We used the highly scalable solvers in the multi-physics code CoBi for both the blast simulation and the human body biomechanics. The meshes generated for these simulations are of good quality so that relatively large time-step sizes can be used without resorting to artificial time scaling treatments. The coupled gas dynamics and biomechanics solutions were validated against the shock tube test data. The human body models were used to conduct parametric simulations to find the biomechanical response and the brain injury mechanism due to blasts impacting the human body. Under the same blast loading condition, we showed the importance of inclusion of the whole body.

Research paper thumbnail of Optimal solid shells for non-linear analyses of multilayer composites. I. Statics

We present in this paper a simple low-order solid-shell element formulation-having only displacem... more We present in this paper a simple low-order solid-shell element formulation-having only displacement degrees of freedom (dofs), i.e., without rotational dofs-that has an optimal number of parameters to pass the patch tests, and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio. The formulation of this element is based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle leading to a novel enhancing strain tensor (EAS method) that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. We also review the equivalence between various choices of the enhancing strains in tensor form, and point out the relative efficiency of these choices. We discuss the enhanced assumed strain (EAS) formulations based on both the Green-Lagrange strain and the displacement gradient (the companion paper), point out the pitfalls in each approach, e.g., not passing the patch test, and the possibility and the method to remedy the problem. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The element passes the patch tests (both membrane and out-ofplane bending). We provide an optimal combination of the ANS method and the minimal number of EAS parameters required to pass the out-of-plane bending patch test. Numerical examples involving static analyses of multilayer shell structures having a large range of element aspect ratios are presented. Finally, we note that the topic in this paper is a fitting dedication to Professor Ekkehard Ramm, who has made important pioneering contributions in this research direction.

Research paper thumbnail of Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics

Elsevier, 2003

We are presenting a simple low-order solid-shell element formulation––having only displacement de... more We are presenting a simple low-order solid-shell element formulation––having only displacement degrees of freedom
(dofs), i.e., without rotational dofs––that has an optimal number of parameters to pass the patch tests, and thus allows
for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high
aspect ratio. With the dynamics referred to a fixed inertial frame, the elements can be used to analyze multilayer shell
structures undergoing large overall motion. The formulation of this element is based on the mixed Hu-Washizu
variational principle leading to a novel enhancing strain tensor (enhanced assumed strain (EAS) method) that renders
the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness
locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. The
energy–momentum conserving algorithm in the context of current solid shell element is presented. We discuss the EAS
formulation based on the displacement gradient and its complexity compared to formulation on the Green–Lagrange
strain. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The
element has an optimal combination of the ANS method and the minimal number of EAS parameters required to pass
the plate bending patch test. Numerical examples involving dynamic analyses (with conservation of energy and momentum) of multilayer shell structures having a large range of element aspect ratios are presented. Several implicit direct
integration methods with/without numerical dissipation are used and compared in terms of the accuracy, stability
and cost in multilayer shell structure. Finally, we note that the topic in this paper is a fitting dedication to Professor
Ekkehard Ramm, who has made important pioneering contributions in this research direction.