On Constitutive Relations and Finite Deformations of Passive Cardiac Tissue: I. A Pseudostrain-Energy Function

1987 ◽  
Vol 109 (4) ◽  
pp. 298-304 ◽  
Author(s):  
J. D. Humphrey ◽  
F. C. P. Yin
Keyword(s):  
Energy Function ◽  
Cardiac Tissue ◽  
Functional Form ◽  
Structural Information ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Limited Range ◽  
Material Parameters ◽  
Data Result

A three-dimensional constitutive relation for passive cardiac tissue is formulated in terms of a structurally motivated pseudostrain-energy function, W, while the mathematical simplicity of phenomenological approaches is preserved. A specific functional form of W is proposed on the basis of limited structural information and multiaxial experimental data. The material parameters are determined in a least-squared sense from both uniaxial and biaxial data. Our results suggest that (1) multiaxially-loaded cardiac tissue is nearly transversely-isotropic with respect to local muscle fiber directions, at least for a limited range of strain histories, (2) material parameters determined from uniaxial papillary muscle data result in gross underestimates of the stresses in multiaxially-loaded specimens, and (3) material parameters determined from equibiaxial tests predict the behavior of the tissue under various nonequibiaxial stretching protocols reasonably well.

Process modeling, joint-property characterization and construction of joint connectors for mechanical fastening by self-piercing riveting

2014 ◽  
Vol 10 (4) ◽  
pp. 631-658 ◽  
Author(s):  
Mica Grujicic ◽  
Jennifer Snipes ◽  
S. Ramaswami ◽  
Fadi Abu-Farha
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Large Scale ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Modeling And Simulations ◽  
Content Type ◽  
Material Parameters ◽  
Computational Analyses

Purpose – The purpose of this paper is to propose a computational approach in order to help establish the effect of various self-piercing rivet (SPR) process and material parameters on the quality and the mechanical performance of the resulting SPR joints. Design/methodology/approach – Toward that end, a sequence of three distinct computational analyses is developed. These analyses include: (a) finite-element modeling and simulations of the SPR process; (b) determination of the mechanical properties of the resulting SPR joints through the use of three-dimensional, continuum finite-element-based numerical simulations of various mechanical tests performed on the SPR joints; and (c) determination, parameterization and validation of the constitutive relations for the simplified SPR connectors, using the results obtained in (b) and the available experimental results. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, e.g. car-body electro-coat paint-baking process. In such simulations, explicit three-dimensional representation of all SPR joints is associated with a prohibitive computational cost. Findings – It is found that the approach developed in the present work can be used, within an engineering optimization procedure, to adjust the SPR process and material parameters (design variables) in order to obtain a desired combination of the SPR-joint mechanical properties (objective function). Originality/value – To the authors’ knowledge, the present work is the first public-domain report of the comprehensive modeling and simulations including: self-piercing process; virtual mechanical testing of the SPR joints; and derivation of the constitutive relations for the SPR connector elements.

Determination of a Constitutive Relation for Passive Myocardium: I. A New Functional Form

1990 ◽  
Vol 112 (3) ◽  
pp. 333-339 ◽  
Author(s):  
J. D. Humphrey ◽  
R. K. Strumpf ◽  
F. C. P. Yin
Keyword(s):  
Constitutive Relation ◽  
Invariant Measures ◽  
Functional Form ◽  
Transversely Isotropic ◽  
The Other ◽  
Material Symmetry ◽  
Material Parameters ◽  
Experimental Protocols ◽  
Theory And Experiment

The specific aim of this study is to determine a constitutive relation for non-contracting myocardium in terms of a pseudostrain-energy function W whose form is guided by both theory and experiment. We assume that the material symmetry of myocardium is initially and locally transversely-isotropic, and seek a W which depends upon only two coordinate invariant measures of the finite deformation. The specific functional form of such a W is inferred directly from experimental protocols in which one invariant is held constant while the other is varied, and vice versa. On the basis of data from families of these “constant invariant” tests on thin slabs of myocardium taken from the mid-walls of six canine left ventricles, we propose a new polynomial form of W containing only five material parameters.

scholarly journals PDE based determination of piezoelectric material tensors

2006 ◽  
Vol 17 (4) ◽  
pp. 383-416 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
TOM LAHMER ◽  
MARCUS MOHR ◽  
MANFRED KALTENBACHER
Keyword(s):  
Inverse Problem ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Forward Problem ◽  
System Of Equations ◽  
Material Tensor ◽  
Infinite Dimensional ◽  
Material Parameters ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The exact numerical simulation of piezoelectric transducers requires the knowledge of all material tensors that occur in the piezoelectric constitutive relations. To account for mechanical, dielectric and piezoelectric losses, the material parameters are assumed to be complex. The issue of material tensor identification is formulated as an inverse problem: As input measured impedance values for different frequency points are used, the searched-for output is the complete set of material parameters. Hence, the forward operator F mapping from the set of parameters to the set of measurements, involves solutions of the system of partial differential equations arising from application of Newton's and Gauss' law to the piezoelectric constitutive relations. This, via two or three dimensional finite element discretisation, leads to an indefinite system of equations for solving the forward problem. Well-posedness of the infinite dimensional forward problem is proven and efficient solution strategies for its discretized version are presented. Since unique solvability of the inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularisation strategies. Consequently, inversion of the (nonlinear) parameter-to-measurement map F is performed using regularised versions of Newton's method. Numerical results for different piezoelectric specimens conclude this paper.

Marine magnetotellurics for petroleum exploration, Part II: Numerical analysis of subsalt resolution

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 826-840 ◽  
Author(s):  
G. Michael Hoversten ◽  
H. Frank Morrison ◽  
Steven C. Constable
Keyword(s):  
Structural Information ◽  
Numerical Models ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Lateral Position ◽  
Petroleum Exploration ◽  
Vertical Position ◽  
Velocity Anisotropy ◽  
Position Errors ◽  
Marine Magnetotellurics

In areas where seismic imaging of the base of salt structures is difficult, seaborne electromagnetic techniques offer complementary as well as independent structural information. Numerical models of 2-D and 3-D salt structures demonstrate the capability of the marine magnetotelluric (MT) technique to map the base of the salt structures with an average depth accuracy of better than 10%. The mapping of the base of the salt with marine MT is virtually unaffected by internal variation within the salt. Three‐dimensional anticlinal structures with a horizontal aspect ratio greater than two can be interpreted adequately via two‐dimensional inversions. Marine MT can distinguish between salt structures which possess deep vertical roots and those which do not. One measure of the relative accuracy of MT and seismic methods can be made by considering the vertical and lateral position errors in the locations of interfaces caused by neglecting velocity anisotropy in migration. For the shallow part of the section where two‐way travel times are on the order of 1 s, the vertical and lateral position errors in the locations of salt‐sediment interfaces from 2-D MT inversion is more than twice the expected migration error in reflectors in transversely isotropic sediments, such as those in the Gulf of Mexico. Deeper in the section where two‐way times are on the order of 4 s, lateral position errors in migration become comparable to those of the MT inverse, whereas seismic vertical position errors remain more than a factor of two smaller than MT errors. This analysis shows that structural mapping accuracy would be improved using MT and seismic together.

Process modeling, joint virtual testing and construction of joint connectors for mechanical fastening by flow-drilling screws

2015 ◽  
Vol 231 (6) ◽  
pp. 1048-1061 ◽  
Author(s):  
Mica Grujicic ◽  
JS Snipes ◽  
S Ramaswami
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Large Scale ◽  
Mechanical Performance ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Material Parameters ◽  
Computational Analyses ◽  
Flow Drilling

In this work, a computational approach is proposed in order to help establish the effect of various flow-drilling screw process and material parameters on the quality and the mechanical performance of the resulting flow-drilling screw joints. Toward that end, a sequence of three distinct computational analyses is developed. These analyses include the following: (a) finite element modeling and simulations of the flow-drilling screw process; (b) determination of the mechanical properties of the resulting flow-drilling screw joints through the use of three-dimensional, continuum finite element–based numerical simulations of various mechanical tests performed on the flow-drilling screw joints and (c) determination, parameterization and validation of the constitutive relations for the simplified flow-drilling screw connectors, using the results obtained in (b) and the available experimental results. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, for example, car-body electro-coat paint-baking process. In such simulations, explicit three-dimensional representation of all flow-drilling screw joints is associated with a prohibitive computational cost. The approach developed in this work can be used, within an engineering-optimization procedure, to adjust the flow-drilling screw process and material parameters (design variables) in order to obtain a desired combination of the flow-drilling screw joint mechanical properties (objective function).

Process and product-performance modeling for mechanical fastening by flow drilling screws

2016 ◽  
Vol 7 (3) ◽  
pp. 370-396 ◽  
Author(s):  
Mica Grujicic ◽  
Jennifer Snipes ◽  
S Ramaswami
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Large Scale ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Content Type ◽  
Material Parameters ◽  
Computational Analyses ◽  
Flow Drilling

Purpose – The purpose of this paper is to propose a computational approach to establish the effect of various flow drilling screw (FS) process and material parameters on the quality and the mechanical performance of the resulting FS joints. Design/methodology/approach – Toward that end, a sequence of three distinct computational analyses is developed. These analyses include: (a) finite-element modeling and simulations of the FS process; (b) determination of the mechanical properties of the resulting FS joints through the use of three-dimensional, continuum finite-element-based numerical simulations of various mechanical tests performed on the FS joints; and (c) determination, parameterization and validation of the constitutive relations for the simplified FS connectors, using the results obtained in (b) and the available experimental results. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, e.g. car-body electro-coat paint-baking process. In such simulations, explicit three-dimensional representation of all FS joints is associated with a prohibitive computational cost. Findings – Virtual testing of the shell components fastened using the joint connectors validated the ability of these line elements to realistically account for the strength, ductility and toughness of the three-dimensional FS joints. Originality/value – The approach developed in the present work can be used, within an engineering-optimization procedure, to adjust the FS process and material parameters (design variables) in order to obtain a desired combination of the FS-joint mechanical properties (objective function).

Determination of a Constitutive Relation for Passive Myocardium: II.—Parameter Estimation

1990 ◽  
Vol 112 (3) ◽  
pp. 340-346 ◽  
Author(s):  
J. D. Humphrey ◽  
R. K. Strumpf ◽  
F. C. P. Yin
Keyword(s):  
Constitutive Relation ◽  
Functional Form ◽  
Nonlinear Least Squares ◽  
Transversely Isotropic ◽  
Least Squares Regression ◽  
Material Parameters ◽  
Biomechanical Behavior ◽  
Best Fit

In the first paper of this series, we proposed a new transversely isotropic pseudostrain-energy function W for describing the biomechanical behavior of excised noncontracting myocardium. The specific functional form of W was inferred directly from biaxial data to be a polynomial function of two coordinate invariant measures of the finite deformation and five material parameters. In this paper, best-fit values of the material parameters are determined from biaxial data using a nonlinear least-squares regression. These values of the parameters are shown to be well-determined, and the final constitutive relation is shown to have good predictive capabilities. Since the proposed constitutive relation describes much broader classes of in-vitro biaxial data than previously proposed relations, it may be better applicable to analyses of stress in the passive heart.

A Novel Constitutive Formulation for Rubberlike Materials in Thermoelasticity

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Zhu-Ping Huang
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Coupling Effect ◽  
Constitutive Relations ◽  
Strain Energy Function ◽  
Mechanical Coupling ◽  
Material Parameters ◽  
Incompressible Materials ◽  
Gent Model ◽  
Rubberlike Materials

The objective of this paper is to present a new framework to formulate thermoelastic constitutive relations for initially isotropic rubberlike materials undergoing finite deformations. The strain-energy function for incompressible materials is extended to include the effects of compressibility and temperature changes. The novelty of this framework is that only a few material functions and material parameters to be fitted with the experimental data are required, and these functions and parameters have clear physical meaning. In order to validate the proposed formulation, the Gent–Gent model for incompressible rubbers is chosen as an illustrative example. A new expression of the Helmholtz free energy of rubberlike materials, which takes into account the material compressibility and thermal effect, is then derived. In this generalized Gent–Gent model, only one material function and six material parameters are introduced. It is shown that the generalized Gent–Gent model can be used to predict the stress-strain behavior over the entire range of deformation. Even for incompressible materials, the strain-energy function in this paper is different from that given by Gent himself. The generalized Gent–Gent model can also adequately describe the thermal-mechanical coupling effect, in which thermoelastic inversion phenomena occur.

Two-Dimensional Crystallization of Tetanus Toxin

1985 ◽  
Vol 43 ◽  
pp. 528-529
Author(s):  
Jeffry A. Reidler ◽  
John P. Robinson
Keyword(s):  
Electron Microscopy ◽  
Tetanus Toxin ◽  
Structural Information ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Membrane Interface ◽  
3D Reconstructions ◽  
Cellular Receptors ◽  
Computer Reconstruction ◽  
2D Crystals

We have prepared two-dimensional (2D) crystals of tetanus toxin using procedures developed by Uzgiris and Kornberg for the directed production of 2D crystals of monoclonal antibodies at an antigen-phospholipid monolayer interface. The tetanus toxin crystals were formed using a small mole fraction of the natural receptor, GT1, incorporated into phosphatidyl choline monolayers. The crystals formed at low concentration overnight. Two dimensional crystals of this type are particularly useful for structure determination using electron microscopy and computer image refinement. Three dimensional (3D) structural information can be derived from these crystals by computer reconstruction of photographs of toxin crystals taken at different tilt angles. Such 3D reconstructions may help elucidate the mechanism of entry of the enzymatic subunit of toxins into cells, particularly since these crystals form directly on a membrane interface at similar concentrations of ganglioside GT1 to the natural cellular receptors.

EMCAT: An automatic image-processing system for electron-microscopic tomography

1994 ◽  
Vol 52 ◽  
pp. 418-419
Author(s):  
Weiping Liu ◽  
John W. Sedat ◽  
David A. Agard
Keyword(s):  
Image Processing ◽  
Structural Information ◽  
Imaging Technique ◽  
Three Dimensional ◽  
Processing System ◽  
Electron Microscopic ◽  
Data Set ◽  
Ordered Structures ◽  
Automatic Image Processing ◽  
Em Tomography

Any real world object is three-dimensional. The principle of tomography, which reconstructs the 3-D structure of an object from its 2-D projections of different view angles has found application in many disciplines. Electron Microscopic (EM) tomography on non-ordered structures (e.g., subcellular structures in biology and non-crystalline structures in material science) has been exercised sporadically in the last twenty years or so. As vital as is the 3-D structural information and with no existing alternative 3-D imaging technique to compete in its high resolution range, the technique to date remains the kingdom of a brave few. Its tedious tasks have been preventing it from being a routine tool. One keyword in promoting its popularity is automation: The data collection has been automated in our lab, which can routinely yield a data set of over 100 projections in the matter of a few hours. Now the image processing part is also automated. Such automations finish the job easier, faster and better.

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