Advances in the Stochastic Modeling of Constitutive Laws at Small and Finite Strains

2021 ◽  
pp. 53-77
Author(s):  
Brian Staber ◽  
Johann Guilleminot
Keyword(s):  
Computational Models ◽  
Structural Response ◽  
Stochastic Simulations ◽  
Mathematical Treatment ◽  
Complex Materials ◽  
Design Procedures ◽  
Damage Propagation ◽  
Highly Nonlinear ◽  
Mechanical Models ◽  
Measure Of Uncertainty

The characterization and identification of uncertainties in the physical properties of complex materials have been the subjects of longstanding interest in both research and engineering. These efforts were supported by the growing interest in Uncertainty Quantification (UQ) where predominating system-parameter and model-form uncertainties are integrated in a unified mathematical treatment to endow predictions with some statistical measure of uncertainty (fidelity) [7] (see also [23, 30]). Once properly modeled and calibrated, these uncertainties can then be propagated to the structural response, following for instance the spectral approach introduced in the celebrated monograph by Ghanem and Spanos [8] (see also [13]). Such stochastic simulations are then purposely used in order to increase the robustness of the computational models and design procedures, especially when the mechanical models are highly nonlinear (in which case small variations in the inputs can have dramatic effects on the predicted outputs and thus, on design procedures). They also enable a deeper understanding of the critical mechanisms governing the physics (associated with damage propagation, for instance) at relevant scales.

scholarly journals Using Dissipative Particle Dynamics to Model Effects of Chemical Reactions Occurring within Hydrogels

Nanomaterials ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 2764
Author(s):  
Ya Liu ◽  
Joanna Aizenberg ◽  
Anna C. Balazs
Keyword(s):  
Computational Models ◽  
Structural Changes ◽  
Dissipative Particle Dynamics ◽  
Chemical Species ◽  
Structural Response ◽  
Particle Dynamics ◽  
Multi Stage ◽  
Chemical Stimuli ◽  
Chemical Events ◽  
Collapsed States

Computational models that reveal the structural response of polymer gels to changing, dissolved reactive chemical species would provide useful information about dynamically evolving environments. However, it remains challenging to devise one computational approach that can capture all the interconnected chemical events and responsive structural changes involved in this multi-stage, multi-component process. Here, we augment the dissipative particle dynamics (DPD) method to simulate the reaction of a gel with diffusing, dissolved chemicals to form kinetically stable complexes, which in turn cause concentration-dependent deformation of the gel. Using this model, we also examine how the addition of new chemical stimuli and subsequent reactions cause the gel to exhibit additional concentration-dependent structural changes. Through these DPD simulations, we show that the gel forms multiple latent states (not just the “on/off”) that indicate changes in the chemical composition of the fluidic environment. Hence, the gel can actuate a range of motion within the system, not just movements corresponding to the equilibrated swollen or collapsed states. Moreover, the system can be used as a sensor, since the structure of the layer effectively indicates the presence of chemical stimuli.

scholarly journals Numerical Optimization of an Open-Ended Coaxial Slot Applicator for the Detection and Microwave Ablation of Tumors

Biology ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 914
Author(s):  
Carolin Hessinger ◽  
Martin Schüßler ◽  
Sabrina Klos ◽  
Markus Kochanek ◽  
Rolf Jakoby
Keyword(s):  
Liver Tissue ◽  
Numerical Optimization ◽  
Microwave Ablation ◽  
Computational Models ◽  
Simulation Models ◽  
Optimization Method ◽  
Dual Mode ◽  
Design Procedures ◽  
Sensitivity Evaluation ◽  
Microwave Applicator

A multiobjective optimization method for a dual-mode microwave applicator is proposed. Dual-modality means that microwaves are used apart from the treatment, and also for the monitoring of the microwave ablation intervention. (1) The use of computational models to develop and improve microwave ablation applicator geometries is essential for further advances in this field. (2) Numerical electromagnetic–thermal coupled simulation models are used to analyze the performance of the dual-mode applicator in liver tissue; the sensitivity evaluation of the dual-mode applicator’s sensing mode constrains the set of optimal solutions. (3) Three Pareto-optimal design parameter sets are derived that are optimal in terms of applicator efficiency as well as volume and sphericity of the ablation zone. The resulting designs of the dual-mode applicator provide a suitable sensitivity to distinguish between healthy and tumorous liver tissue. (4) The optimized designs are presented and numerically characterized. An improvement on the performance of previously proposed dual-mode applicator designs is achieved. The multiphysical simulation model of electromagnetic and thermal properties of the applicator is applicable for future comprehensive design procedures.

scholarly journals Predicting cortical bone adaptation to axial loading in the mouse tibia

2015 ◽  
Vol 12 (110) ◽  
pp. 20150590 ◽  
Author(s):  
A. F. Pereira ◽  
B. Javaheri ◽  
A. A. Pitsillides ◽  
S. J. Shefelbine
Keyword(s):  
Cortical Bone ◽  
Computational Models ◽  
Mechanical Load ◽  
Fluid Velocity ◽  
Structural Response ◽  
Axial Loading ◽  
Mechanical Stimulus ◽  
Bone Adaptation ◽  
Mouse Tibia ◽  
Efficient Loading

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on–off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms.

On the Biaxial Mechanical Response of Porcine Tricuspid Valve Leaflets

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Keyvan Amini Khoiy ◽  
Rouzbeh Amini
Keyword(s):  
Tricuspid Valve ◽  
Computational Models ◽  
Mechanical Response ◽  
Ex Vivo ◽  
Biaxial Stress ◽  
Strain Behavior ◽  
Highly Nonlinear ◽  
Rapid Transition ◽  
Biaxial Tensile Testing ◽  
The Right

Located on the right side of the heart, the tricuspid valve (TV) prevents blood backflow from the right ventricle to the right atrium. Similar to other cardiac valves, quantification of TV biaxial mechanical properties is essential in developing accurate computational models. In the current study, for the first time, the biaxial stress–strain behavior of porcine TV was measured ex vivo under different loading protocols using biaxial tensile testing equipment. The results showed a highly nonlinear response including a compliant region followed by a rapid transition to a stiff region for all of the TV leaflets both in the circumferential and in the radial directions. Based on the data analysis, all three leaflets were found to be anisotropic, and they were stiffer in the circumferential direction in comparison to the radial direction. It was also concluded that the posterior leaflet was the most anisotropic leaflet.

scholarly journals Predicting cortical bone adaptation to axial loading in the mouse tibia

2015 ◽  
Author(s):  
Andre F Pereira ◽  
Behzad Javaheri ◽  
Andrew Pitsillides ◽  
Sandra Shefelbine
Keyword(s):  
Cortical Bone ◽  
Computational Models ◽  
Mechanical Load ◽  
Fluid Velocity ◽  
Structural Response ◽  
Axial Loading ◽  
Mechanical Stimulus ◽  
Bone Adaptation ◽  
Mouse Tibia ◽  
Efficient Loading

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on-off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's tau rank coefficient \(\tau = 0.51\), \(p<0.001\)). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to time variant stimulus. Such models could be used in the design of more efficient loading protocols and drugs therapies that target the relevant physiological mechanisms.

Stiffness Comparisons Between Adventitia, Media and Full Thickness Specimens From Human Atherosclerotic Carotid Arteries

2009 ◽  
Author(s):  
Allen H. Hoffman ◽  
Zhongzhao Teng ◽  
Calvin Mui ◽  
Jie Zheng ◽  
Pamela K. Woodard ◽  
...  
Keyword(s):  
Material Properties ◽  
Computational Models ◽  
Carotid Arteries ◽  
Layered Composite ◽  
Material Behavior ◽  
Full Thickness ◽  
Paired Samples ◽  
Highly Nonlinear ◽  
Deductive Method ◽  
The Media

Arteries display highly nonlinear, anisotropic material behavior and can be considered to be a layered composite of fiber oriented materials composed of three layers: intima, media and adventitia. The intima does not affect the material properties of the artery. Thus, the mechanical properties of an artery result from the combined interaction of the media and adventitia with each layer displaying different material properties. It has been widely accepted that atherosclerosis changes the material properties of the arterial wall. However, little experimental data exists relating the properties of the media and adventitia of atherosclerotic vessels to the overall properties of the artery. Knowledge of the properties of human atherosclerotic tissues is essential for an improved understanding the effects of atherosclerosis and also for creating more accurate computational models for predicting the effects of the disease [1]. A prior study of bovine carotid arteries determined the properties of the adventitia and media using a deductive method [2]. This paper focuses on directly measuring and comparing the stiffness of paired samples of adventitia, media and full thickness specimens from human atherosclerotic carotid arteries.

Multi-scale finite element modeling of 3D printed structures subjected to mechanical loads

2018 ◽  
Vol 24 (1) ◽  
pp. 177-187 ◽  
Author(s):  
Dalia Calneryte ◽  
Rimantas Barauskas ◽  
Daiva Milasiene ◽  
Rytis Maskeliunas ◽  
Audrius Neciunas ◽  
...  
Keyword(s):  
Finite Element ◽  
Composite Structures ◽  
Computational Models ◽  
Three Dimensional ◽  
Structural Response ◽  
Content Type ◽  
Multi Scale ◽  
Macro Scale ◽  
Internal Constitution ◽  
3D Printed

Purpose The purpose of this paper is to investigate the influence of geometrical microstructure of items obtained by applying a three-dimensional (3D) printing technology on their mechanical strength. Design/methodology/approach Three-dimensional printed items (3DPI) are composite structures of complex internal constitution. The buildup of the finite element (FE) computational models of 3DPI is based on a multi-scale approach. At the micro-scale, the FE models of representative volume elements corresponding to different additive layer heights and different thicknesses of extruded fibers are investigated to obtain the equivalent non-linear nominal stress–strain curves. The obtained results are used for the creation of macro-scale FE models, which enable to simulate the overall structural response of 3D printed samples subjected to tensile and bending loads. Findings The validation of the models was performed by comparing the computed results against the experimental ones, where satisfactory agreement has been demonstrated within a marked range of thicknesses of additive layers. Certain inadequacies between computed against experimental results were observed in cases of thinnest and thickest additive layers. The principle explanation of the reasons of inadequacies takes into account the poorer quality of mutual adhesion in case of very thin extruded fibers and too-early solidification effect. Originality/value Flexural and tensile experiments are simulated by FE models that are created with consideration to microstructure of 3D printed samples.

A Constitutive Law for Mitral Valve Tissue

1998 ◽  
Vol 120 (1) ◽  
pp. 38-47 ◽  
Author(s):  
K. May-Newman ◽  
F. C. P. Yin
Keyword(s):  
Mitral Valve ◽  
Transversely Isotropic ◽  
Quantitative Information ◽  
Substantial Improvement ◽  
Material Behavior ◽  
Constitutive Law ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Mechanical Models ◽  
Biaxial Mechanical Testing

Biaxial mechanical testing and theoretical continuum mechanics analysis are employed to formulate a constitutive law for cardiac mitral valve anterior and posterior leaflets. A strain energy description is formulated based on the fibrous architecture of the tissue, accurately describing the large deformation, highly nonlinear transversely isotropic material behavior. The results show that a simple three-coefficient exponential constitutive law provides an accurate prediction of stress–stretch behavior over a wide range of deformations. Regional heterogeneity may be accommodated by spatially varying a single coefficient and incorporating collagen fiber angle. The application of this quantitative information to mechanical models and bioprosthetic development could provide substantial improvement in the evaluation and treatment of valvular disease, surgery, and replacement.

scholarly journals A computational approach to studying ageing at the individual level

2016 ◽  
Vol 283 (1824) ◽  
pp. 20152346 ◽  
Author(s):  
Zachary M. Harvanek ◽  
Márcio A. Mourão ◽  
Santiago Schnell ◽  
Scott D. Pletcher
Keyword(s):  
Computational Models ◽  
Mortality Rates ◽  
Stochastic Simulations ◽  
Individual Level ◽  
Opposite Sex ◽  
Population Mortality ◽  
The Individual ◽  
Rate Of Ageing ◽  
Key Aspects

The ageing process is actively regulated throughout an organism's life, but studying the rate of ageing in individuals is difficult with conventional methods. Consequently, ageing studies typically make biological inference based on population mortality rates, which often do not accurately reflect the probabilities of death at the individual level. To study the relationship between individual and population mortality rates, we integrated in vivo switch experiments with in silico stochastic simulations to elucidate how carefully designed experiments allow key aspects of individual ageing to be deduced from group mortality measurements. As our case study, we used the recent report demonstrating that pheromones of the opposite sex decrease lifespan in Drosophila melanogaster by reversibly increasing population mortality rates. We showed that the population mortality reversal following pheromone removal was almost surely occurring in individuals, albeit more slowly than suggested by population measures. Furthermore, heterogeneity among individuals due to the inherent stochasticity of behavioural interactions skewed population mortality rates in middle-age away from the individual-level trajectories of which they are comprised. This article exemplifies how computational models function as important predictive tools for designing wet-laboratory experiments to use population mortality rates to understand how genetic and environmental manipulations affect ageing in the individual.

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