Nonlinear Thermohyperviscoelastic Constitutive Model for Soft Materials with Strain Rate and Temperature Dependency

2020 ◽  
Vol 12 (06) ◽  
pp. 2050059
Author(s):  
Zahra Matin Ghahfarokhi ◽  
Mehdi Salmani-Tehrani ◽  
Mahdi Moghimi Zand
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Soft Materials ◽  
Material Behavior ◽  
Temperature Dependent ◽  
Dependent Behavior ◽  
Temperature Dependent Behavior

Soft materials, such as polymeric materials and biological tissues, often exhibit strain rate and temperature-dependent behavior when subjected to external loads. To characterize the thermomechanical behavior of isotropic soft material, a thermohyperviscoelastic constitutive model has been developed through an additive decomposition of strain energy function into elastic and viscous parts. A three-term generalized Rivlin strain energy function is utilized to formulate the hyperelastic part of the model, while a new viscous potential function is proposed to describe the effect of strain rate and temperature on material behavior. Toward this end, a new procedure has been proposed to determine the viscous mechanical properties as a function of strain-rate and temperature. Comparing with the previously published experimental data for linear low-density polyethylene reveals that the proposed model can sufficiently capture the nonlinearity, rate- and temperature-dependent behavior of the soft materials.

Rate-Dependent Behavior and Constitutive Model of Polycarbonate at Strain Rate from 10-5 to 103 S-1

2011 ◽  
Vol 117-119 ◽  
pp. 434-437
Author(s):  
Wen Jun Hu ◽  
Xi Cheng Huang ◽  
Fang Ju Zhang ◽  
Cheng Jun Chen
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Mechanical Behavior ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Temperature Dependent ◽  
Static Tests ◽  
Rate Range ◽  
Rate Dependent ◽  
Dependent Behavior

Uni-axial quasi-static tests at strain rates 10-5, 10-4, 10-3,10-2 and 10-1 s-1 and dynamic compressive tests at strain rates 1679, 2769,5000 and 8200 s-1 have been carried out to study the mechanical behavior for polycarbonate used in the avigation industry. The stress–strain curves of polycarbonate in the strain-rate range from 10-5 to 8200 s-1 have been obtained. The effects of the strain rate on yield phenomenon and rate-dependent mechanical behavior are discussed. A plastic flow law based on the DSGZ rate-temperature-dependent constitutive model was used to describe the mechanical behavior of polycarbonate in the strain-rate range from 10-5 to 103 s-1. The results at the six strain rates are in excellent agreement with the experimental data, which illustrates that the constitutive model can describe the mechanical behavior for polycarbonate at low and high strain rates perfectly.

A Hyperelastic Constitutive Law for Aortic Valve Tissue

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Karen May-Newman ◽  
Charles Lam ◽  
Frank C. P. Yin
Keyword(s):  
Aortic Valve ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Behavior ◽  
Constitutive Law ◽  
Biaxial Testing ◽  
Strain Behavior ◽  
Wide Range ◽  
Strain Invariants

The objective of the present study was to perform biaxial testing and apply constitutive modeling to develop a strain energy function that accurately predicts the material behavior of the aortic valve leaflets. Ten leaflets from seven normal porcine aortic valves were biaxially stretched in a variety of protocols and the data combined to develop and fit a strain energy function to describe the material behavior. The results showed that the nonlinear anisotropic behavior of the aortic valve is well described by a strain energy function of two strain invariants, which uses only three coefficients to accurately predict the stress-strain behavior over a wide range of deformations. This structurally-motivated constitutive law has many applications, including computational modeling for clinical and engineering valve treatments.

A New Viscous Potential Function for Developing the Viscohyperelastic Constitutive Model for Bovine Liver Tissue: Continuum Formulation and Finite Element Implementation

2020 ◽  
Vol 12 (03) ◽  
pp. 2050029 ◽  
Author(s):  
Zahra Matin Ghahfarokhi ◽  
Mehdi Salmani-Tehrani ◽  
Mahdi Moghimi Zand ◽  
Sara Esmaeilian
Keyword(s):  
Constitutive Model ◽  
Strain Energy ◽  
Soft Tissues ◽  
Short Term Memory ◽  
Strain Energy Function ◽  
Bovine Liver ◽  
Material Behavior ◽  
Compression Tests ◽  
Continuum Formulation ◽  
Linear Viscoelastic

The mechanical behavior of very soft tissues, such as liver, brain, kidney, etc. is assumed to be viscohyperelastic. The conventional approaches like quasi-linear viscoelastic (QLV) are limited to low strain rates and are unable to capture the short-term memory effects. In this paper, a new viscohyperelastic constitutive model is presented in which the strain energy function is decomposed into an elastic and a viscous part. The elastic part of the strain energy is assumed as a Mooney–Rivlin model, while a new viscous potential, as a function of strain and its rate, is proposed. Unconfined uniaxial compression tests are conducted up to 10% compression at two loading velocities of 1.3 and 10.56[Formula: see text](mm/min), to determine the material constants. A numerical simulation is also used to investigate the model-predicted material behavior. It is shown that the model is more sensitive to the hyperelastic parameters than the viscous parameters. This model is also able to predict the stress relaxation and hysteresis; however, an instantaneous relaxation is observed.

A Microstructurally Based Orthotropic Hyperelastic Constitutive Law

2002 ◽  
Vol 69 (5) ◽  
pp. 570-579 ◽  
Author(s):  
J. E. Bischoff ◽  
E. A. Arruda ◽  
K. Grosh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Entropy Change ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
The Finite Element Method

A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.

An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus

2005 ◽  
Vol 73 (5) ◽  
pp. 815-824 ◽  
Author(s):  
X. Q. Peng ◽  
Z. Y. Guo ◽  
B. Moran
Keyword(s):  
Constitutive Model ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Parameters ◽  
The Matrix ◽  
Fiber Matrix ◽  
Matrix Shear ◽  
Fiber Interaction

Based on fiber reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model for the human annulus fibrosus is developed. A strain energy function representing the anisotropic elastic material behavior of the annulus fibrosus is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber-matrix shear interaction, respectively. Taking advantage of the laminated structure of the annulus fibrosus with one family of aligned fibers in each lamella, interlamellar fiber-fiber interaction is eliminated, which greatly simplifies the constitutive model. A simple geometric description for the shearing between the fiber and the matrix is developed and this quantity is used in the representation of the fiber-matrix shear interaction energy. Intralamellar fiber-fiber interaction is also encompassed by this interaction term. Experimental data from the literature are used to obtain the material parameters in the constitutive model and to provide model validation. Determination of the material parameters is greatly facilitated by the partition of the strain energy function into matrix, fiber and fiber-matrix shear interaction terms. A straightforward procedure for computation of the material parameters from simple experimental tests is proposed.

Extending Marlow’s general first-invariant constitutive model to compressible, isotropic hyperelastic materials

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Florian Hüter ◽  
Frank Rieg
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Test Data ◽  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Content Type ◽  
Hyperelastic Materials ◽  
Fitting Procedures

Purpose A general first-invariant constitutive model has been derived in literature for incompressible, isotropic hyperelastic materials, known as Marlow model, which reproduces test data exactly without the need of curve-fitting procedures. This paper aims to describe how to extend Marlow’s constitutive model to the more general case of compressible hyperelastic materials. Design/methodology/approach The isotropic constitutive model is based on a strain energy function, whose isochoric part is solely dependent on the first modified strain invariant. Based on Marlow’s idea, a principle of energetically equivalent deformation states is derived for the compressible case, which is used to determine the underlying strain energy function directly from measured test data. No particular functional of the strain energy function is assumed. It is shown how to calibrate the volumetric and isochoric strain energy functions uniquely with uniaxial or biaxial test data only. The constitutive model is implemented into a finite element program to demonstrate its applicability. Findings The model is well suited for use in finite element analysis. Only one set of test data is required for calibration without any need for curve-fitting procedures. These test data are reproduced exactly, and the model prediction is reasonable for other deformation modes. Originality/value Marlow’s basic concept is extended to the compressible case and applied to both the volumetric and isochoric part of the compressible strain energy function. Moreover, a novel approach is described on how both compressive and tensile test data can be used simultaneously to calibrate the model.

Sign in / Sign up

Export Citation Format

Share Document