Finite Element Investigation of Effective Moduli of Transversely Isotropic Thermoelastic Materials with Nanoscale Porosity

2020 ◽  
pp. 325-337
Author(s):  
Andrey Nasedkin ◽  
Anna Nasedkina ◽  
Amirtham Rajagopal
Keyword(s):  
Finite Element ◽  
Transversely Isotropic ◽  
Effective Moduli

Finite Element Contact Analysis of a Cartilage Layer Exhibiting Tension-Compression Nonlinearity

1999 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael A. Soltz
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Experimental Studies ◽  
Transversely Isotropic ◽  
Element Solution ◽  
Biphasic Model ◽  
Cartilage Mechanics ◽  
State Of Stress ◽  
Cartilage Layer ◽  
Diarthrodial Joints

Abstract Experimental studies have demonstrated that the moduli of articular cartilage in compression are one to two orders of magnitude smaller than in tension. However, only a few analyses of cartilage mechanics have been performed which account for this tension-compression nonlinearity (Soulhat et al., 1998; Ateshian and Soltz, 1999a,b). In order to understand the state of stress under loading conditions which simulate the physiologic environment of diarthrodial joints, and the possible implications for tissue failure and the pathomechanics of osteoarthritis, it is important to determine whether the tension-compression nonlinearity of cartilage significantly affects our current understanding of its response in contact mechanics. Most analyses of cartilage contact have employed linear isotropic or transversely isotropic models for cartilage, either within the context of elasticity theory or porous media theories. In this study, we present a finite element solution for the contact of a rigid spherical impermeable sphere against a cartilage layer supported on a rigid impermeable subchondral bone foundation, where cartilage is modeled using our recently proposed biphasic conewise linear elasticity model (Ateshian and Soltz, 1999a,b). A comparison is also provided with the more frequently used linear isotropic biphasic model, under similar conditions.

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

The Effect of Debonding Angle on the Reduction of Effective Moduli of Particle and Fiber-Reinforced Composites

2002 ◽  
Vol 69 (3) ◽  
pp. 292-302 ◽  
Author(s):  
Y. H. Zhao ◽  
G. J. Weng
Keyword(s):  
Transversely Isotropic ◽  
Fiber Composites ◽  
Fiber Reinforced Composites ◽  
Anisotropic Damage ◽  
Reinforced Composites ◽  
Effective Moduli ◽  
Loading Mode ◽  
Interfacial Cracks ◽  
The Matrix ◽  
Composite Stiffness

In an effort to uncover the effect of interfacial partial debonding on the reduction of composite stiffness, a reduced moduli approach is proposed for the fictitious inclusions which are used to replace the original partially debonded inclusions. The fictitious inclusions are now perfectly bonded to the matrix and any micromechanical theory can be called upon to estimate the moduli of the composite. Using the volume of the inclusion directly beneath the interfacial cracks under the considered loading mode as a measure of damage, a set of anisotropic damage parameters is established in terms of the debonding angle, providing the reduced moduli for the fictitious inclusions. Specific considerations include debonding on the top and bottom of spheres and prolate inclusions, debonding on the lateral surface of spheres and oblate inclusions, and debonding on the top and bottom of circular fibers and elliptic cylinders. The reductions of the five transversely isotropic moduli for the partially debonded particle composites and the nine orthotropic moduli for the partially debonded fiber composites are examined as the debonding angle increases. The theory is also compared with some finite element results, and it suggests that the concept proposed to estimate the reduced moduli of the fictitious inclusions is a viable one.

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