scholarly journals An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

2019 ◽  
Vol 19 (2) ◽  
pp. 633-659 ◽  
Author(s):  
Adrienne Propp ◽  
Alessio Gizzi ◽  
Francesc Levrero-Florencio ◽  
Ricardo Ruiz-Baier
Keyword(s):  
Cardiac Tissue ◽  
Viscoelastic Model ◽  
Constitutive Law ◽  
Governing Equations ◽  
Finite Element Scheme ◽  
Additional Degree ◽  
Active Strain ◽  
New Class ◽  
Calcium Interaction ◽  
Coupling Mechanisms

Abstract We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law, for both active stress and active strain formulations of active mechanics, coupled with a four-variable phenomenological model for human cardiac cell electrophysiology, which produces an accurate description of the action potential. The conductivities in the model of electric propagation are modified according to stress, inducing an additional degree of nonlinearity and anisotropy in the coupling mechanisms, and the activation model assumes a simplified stretch–calcium interaction generating active tension or active strain. The influence of the new terms in the electromechanical model is evaluated through a sensitivity analysis, and we provide numerical validation through a set of computational tests using a novel mixed-primal finite element scheme.

Three-Dimensional Dynamic Stress and Vibration Analyses of Thick Singular-Kernel Fractional-Order Viscoelastic Annular Rotating Discs Under Nonuniform Loads

2019 ◽  
Vol 20 (01) ◽  
pp. 2050007 ◽  
Author(s):  
M. Shariyat ◽  
R. Mohammadjani
Keyword(s):  
Fractional Order ◽  
Dynamic Stress ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Theory Of Elasticity ◽  
Constitutive Law ◽  
Sensitivity Analyses ◽  
Governing Equations

In this paper, the dynamic stress and radial/lateral vibration of circular/annular discs made of fractional-order viscoelastic materials under nonuniform mechanical loads are investigated for the first time, utilizing the exact 3D theory of elasticity, rather than the plate theories. The governing equations of motion of the disc are derived based on the Kelvin–Voigt fractional viscoelastic model. To solve these equations, the spatial partial and the time ordinary derivatives are replaced by adequate central, backward or forward finite difference expressions. Then the resulting Caputo-type time-dependent system of the coupled integro-differential governing equations of the fractional-order is solved by a novel numerical procedure. Namely, a time-marching procedure is employed to extract the time histories of the responses, in the space-time domain for various time and spatial distributions. Finally, comprehensive sensitivity analyses and various 3D plots are presented and discussed. In this regard, effects of the fractional-order of the constitutive law, viscoelastic parameters, material rigidity, distribution and time variation patterns of the nonuniform distributed transverse loads, and boundary conditions on the distributions of the displacement and stress components are investigated.

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

scholarly journals A new class of discontinuous solar wind solutions

2020 ◽  
Vol 496 (2) ◽  
pp. 1023-1034
Author(s):  
Bidzina M Shergelashvili ◽  
Velentin N Melnik ◽  
Grigol Dididze ◽  
Horst Fichtner ◽  
Günter Brenn ◽  
...  
Keyword(s):  
Solar Wind ◽  
External Source ◽  
Analytic Solutions ◽  
Governing Equations ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
Heating Source ◽  
New Class ◽  
Localized Heating ◽  
Physical Quantities

ABSTRACT A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point that supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast winds.

scholarly journals Sperm Cell Driven Microrobots—Emerging Opportunities and Challenges for Biologically Inspired Robotic Design

Micromachines ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 448 ◽  
Author(s):  
Ajay Singh ◽  
Mohammad Ansari ◽  
Mihir Mahajan ◽  
Shubhangi Srivastava ◽  
Shubham Kashyap ◽  
...  
Keyword(s):  
Targeted Drug Delivery ◽  
State Of The Art ◽  
Cell Manipulation ◽  
Small Scale ◽  
Sperm Cells ◽  
Biologically Inspired ◽  
New Class ◽  
Targeted Drug ◽  
New Applications ◽  
Coupling Mechanisms

With the advent of small-scale robotics, several exciting new applications like Targeted Drug Delivery, single cell manipulation and so forth, are being discussed. However, some challenges remain to be overcome before any such technology becomes medically usable; among which propulsion and biocompatibility are the main challenges. Propulsion at micro-scale where the Reynolds number is very low is difficult. To overcome this, nature has developed flagella which have evolved over millions of years to work as a micromotor. Among the microscopic cells that exhibit this mode of propulsion, sperm cells are considered to be fast paced. Here, we give a brief review of the state-of-the-art of Spermbots—a new class of microrobots created by coupling sperm cells to mechanical loads. Spermbots utilize the flagellar movement of the sperm cells for propulsion and as such do not require any toxic fuel in their environment. They are also naturally biocompatible and show considerable speed of motion thereby giving us an option to overcome the two challenges of propulsion and biocompatibility. The coupling mechanisms of physical load to the sperm cells are discussed along with the advantages and challenges associated with the spermbot. A few most promising applications of spermbots are also discussed in detail. A brief discussion of the future outlook of this extremely promising category of microrobots is given at the end.

Viscoelastic Characterization of Fiber-Reinforced Elastomeric Composites at Finite Strain

2010 ◽  
Vol 123-125 ◽  
pp. 603-606
Author(s):  
Mohammad Tahaye Abadi
Keyword(s):  
Constitutive Model ◽  
Large Deformation ◽  
Finite Strain ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Constitutive Law ◽  
Micromechanical Modeling ◽  
Fiber Reinforced ◽  
Material Parameters ◽  
Elastomeric Composites

A viscoelastic model is developed to describe the mechanical response of fiber-reinforced elastomeric composites at large deformation. A continuum approach is used to model the macroscopic mechanical behavior of elastomeric materials reinforced with unidirectional fibers, in which the resin and fibers are regarded as a single homogenized anisotropic material. The anisotropic viscoelastic constitutive model is developed considering transient reversible network theory. An efficient computational algorithm based on micromechanical modeling is proposed to relate the material parameters of constitutive model to the mechanical properties of composite constituents at finite strain. The microstructure is identified by a representative volume element (RVE) and it is subjected to large deformation with considering the conformity of opposite boundaries. The material parameters of the viscoelastic constitutive law are determined based on the response of heterogeneous microstructure which is examined under different loading conditions.

Numerical analysis of history-dependent variational–hemivariational inequalities with applications to contact problems

2015 ◽  
Vol 26 (4) ◽  
pp. 427-452 ◽  
Author(s):  
MIRCEA SOFONEA ◽  
WEIMIN HAN ◽  
STANISŁAW MIGÓRSKI
Keyword(s):  
Numerical Analysis ◽  
Real World ◽  
Viscoelastic Body ◽  
Contact Problems ◽  
Uniqueness Result ◽  
Constitutive Law ◽  
Hemivariational Inequalities ◽  
New Class ◽  
Nonlinear Anal ◽  
Dependence Result

A new class of history-dependent variational–hemivariational inequalities was recently studied in Migórski et al. (2015Nonlinear Anal. Ser. B: Real World Appl.22, 604–618). There, an existence and uniqueness result was proved and used in the study of a mathematical model which describes the contact between a viscoelastic body and an obstacle. The aim of this paper is to continue the analysis of the inequalities introduced in Migórski et al. (2015Nonlinear Anal. Ser. B: Real World Appl.22, 604–618) and to provide their numerical analysis. We start with a continuous dependence result. Then we introduce numerical schemes to solve the inequalities and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modelled with a viscoelastic constitutive law, the contact is given in the form of normal compliance, and friction is described with a total slip-dependent version of Coulomb's law.

Relaxation and Creep Quasilinear Viscoelastic Models for Normal Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 159-164 ◽  
Author(s):  
B. R. Simon ◽  
R. S. Coats ◽  
S. L.-Y. Woo
Keyword(s):  
Articular Cartilage ◽  
Soft Tissues ◽  
Least Squares Method ◽  
Viscoelastic Model ◽  
Generalized Least Squares ◽  
Constitutive Law ◽  
Analytical Models ◽  
Creep Data ◽  
Bovine Articular Cartilage ◽  
Generalized Least Squares Method

A quasilinear viscoelastic model was used to develop relaxation and creep forms for a constitutive law for soft tissues. Combined relaxation and cyclic test data as well as preconditioned and nonpreconditioned creep data were used to demonstrate the approach for normal bovine articular cartilage. Values for mechanical parameters in the analytical models were determined using a generalized least squares method.

Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part II: Three Dimensional Formulation for Thick Ventricular Wall Segments

1988 ◽  
Vol 110 (1) ◽  
pp. 62-68 ◽  
Author(s):  
A. Horowitz ◽  
I. Sheinman ◽  
Y. Lanir
Keyword(s):  
Finite Element ◽  
Cardiac Tissue ◽  
Large Deformations ◽  
Three Dimensional ◽  
Shear Stiffness ◽  
Cardiac Mechanics ◽  
Nonlinear Finite Element ◽  
Constitutive Law ◽  
Ventricular Wall ◽  
Collagenous Matrix

A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness, and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.

On the Development of Creep Laws for Rubber in the Parallel Rheological Framework

2019 ◽  
Vol 47 (1) ◽  
pp. 2-30 ◽  
Author(s):  
Gautam Sagar ◽  
Dong Zheng ◽  
Anuwat Suwannachit ◽  
Maik Brinkmeier ◽  
Kristin Fietz ◽  
...  
Keyword(s):  
Complex Modulus ◽  
Dynamic Stiffness ◽  
Viscoelastic Model ◽  
American Chemical Society ◽  
Small Strain ◽  
Chemical Society ◽  
Material Behavior ◽  
Constitutive Law ◽  
Rate Dependency ◽  
Linear Viscoelastic

ABSTRACT It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.

Sliding Resistance on a Constrained Rubber Layer Due to Rubber Hysteresis

2000 ◽  
Vol 73 (2) ◽  
pp. 217-224
Author(s):  
C. G. Li ◽  
P. S. Steif
Keyword(s):  
Universal Design ◽  
Rolling Resistance ◽  
Design Tool ◽  
Constitutive Law ◽  
Rubber Layer ◽  
New Class ◽  
Dependent Behavior ◽  
Theoretical Predictions ◽  
Filled Rubbers ◽  
Sliding Resistance

Abstract Sliding resistance of a rigid cylinder over a thin rubber layer due to rubber hysteresis is investigated. This problem underlies a model being developed for quantitatively accurate predictions of the performance of a new class of damping devices. As a full multiaxial constitutive law reflecting the amplitude-dependent behavior of filled rubbers is not available, this paper sets forth an approximate method of analysis which indirectly accounts for the material nonlinearity. Results of extensive finite element calculations are then reduced to compact material-independent forms which can be used as a universal design tool. Measurements of rolling resistance are also compared with theoretical predictions.

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