scholarly journals Constitutive Relation for Large Deformations of Fiber-Reinforced Rubberlike Materials with Different Response in Tension and Compression

2016 ◽  
Vol 44 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Qian Li ◽  
David A. Dillard ◽  
Romesh C. Batra
Keyword(s):  
Constitutive Relation ◽  
Large Deformations ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Strain Tensor ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Tension And Compression ◽  
Different Response ◽  
Rubberlike Materials

ABSTRACT Fiber-reinforced rubberlike materials commonly used in tires undergo large deformations and exhibit different responses in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function in terms of the five invariants of the right Cauchy-Green strain tensor and account for different response in tension and compression along the fiber direction. The constitutive relation accounts for both material and geometric nonlinearities and incorporates effects of the fifth strain invariant, I5. It has been shown by Merodio and Ogden that in shear dominated deformations, I5 makes a significant contribution to the stress-strain curve. We have implemented the proposed constitutive relation in the commercial software, LS-DYNA. The numerical solutions of a few boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which part of the solution is assumed and unknowns in the presumed solution are found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. When test data become available, one can modify the form of the strain energy density and replace the proposed constitutive relation by the new one in LS-DYNA.

scholarly journals Comparison of Mode Shapes of Carbon-Fiber-Reinforced Plastic Material Considering Carbon Fiber Direction

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 311
Author(s):  
Chan-Jung Kim
Keyword(s):  
Carbon Fiber ◽  
Modal Analysis ◽  
Dynamic Behavior ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Carbon Fiber Reinforced Plastic ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Fiber Reinforced Plastic ◽  
Reinforced Plastic

Previous studies have demonstrated the sensitivity of the dynamic behavior of carbon-fiber-reinforced plastic (CFRP) material over the carbon fiber direction by performing uniaxial excitation tests on a simple specimen. However, the variations in modal parameters (damping coefficient and resonance frequency) over the direction of carbon fiber have been partially explained in previous studies because all modal parameters have only been calculated using the representative summed frequency response function without modal analysis. In this study, the dynamic behavior of CFRP specimens was identified from experimental modal analysis and compared five CFRP specimens (carbon fiber direction: 0°, 30°, 45°, 60°, and 90°) and an isotropic SCS13A specimen using the modal assurance criterion. The first four modes were derived from the SCS13A specimen; they were used as reference modes after verifying with the analysis results from a finite element model. Most of the four mode shapes were found in all CFRP specimens, and the similarity increased when the carbon fiber direction was more than 45°. The anisotropic nature was dominant in three cases of carbon fiber, from 0° to 45°, and the most sensitive case was found in Specimen #3.

scholarly journals The Optimum Design of Stepped Shafts: A Study in Computational Optimization

1982 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Optimum Design ◽  
Critical Speed ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Minimum Principle ◽  
Problem Formulation ◽  
Rayleigh Quotient ◽  
Computational Optimization ◽  
Stepped Shaft ◽  
Determine Step

Optimum stepped shaft designs are obtained through an application of Pontryagin’s Minimum Principle. Optimum designs are obtained for a given critical speed of specified order. Indexes of Performance to be minimized include mass and rotating inertia. A general problem formulation illustrates how constraints on stress, deflections, and geometric design are taken in account. Numerical solutions are obtained to nonlinear multi-point-boundary-value-problems. A Newton-Raphson algorithm was developed to determine step locations precisely in order to facilitate the convergence of the shooting method used to solve the boundary value problem. Numerical solutions are determined with an assumed critical speed; a Rayleigh quotient calculation is used to verify that the optimum design possesses the assumed value.

Dynamic Behavior of Fiber Reinforced Composites Under Multiaxial Compression

1999 ◽  
Author(s):  
Kenji Oguni ◽  
G. Ravichandran
Keyword(s):  
Failure Mode ◽  
Kink Band ◽  
Fiber Reinforced Composites ◽  
Fiber Direction ◽  
Strain Rates ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Band Formation ◽  
Multiaxial Compression ◽  
Axial Splitting

Abstract Results from an experimental investigation on the mechanical behavior of a unidirectional reinforced polymer composite with 50% volume fraction E-glass/vinylester under uniaxial and proportional multiaxial compression are presented. Specimens are loaded in the fiber direction using a servo-hydraulic material testing system for low strain rates and a Kolsky (split Hopkinson) pressure bar for high strain rates, up to 3000 s−1. The results indicate that the compressive strength of the composite increases with increasing levels of confinement and increasing strain rates. Post-test optical and scanning electron microscopy is used to identify the failure modes. The failure mode that is observed in unconfined specimen is axial splitting followed by fiber kink band formation. At high levels of confinement, the failure mode transitions from axial splitting to kink band formation and fiber failure. Also, a new energy based analytic model for studying axial splitting phenomenon in unidirectional fiber-reinforced composites is presented.

Visco-elastoplastic Characterization of a Flax-fiber Reinforced Biocomposite

2021 ◽  
Vol 58 (1) ◽  
pp. 78-84
Author(s):  
Constantin Stochioiu ◽  
Horia-Miron Gheorghiu ◽  
Flavia-Petruta-georgiana Artimon
Keyword(s):  
Viscoelastic Behavior ◽  
Flax Fiber ◽  
Creep Recovery ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Glass Fiber Composites ◽  
Creep Stress ◽  
Static Mechanical ◽  
Long Term Behavior ◽  
Sample Damage

In the presented study, the load induced long-term behavior of a biocomposite material is analyzed. The studied material is a unidirectional flax fiber reinforced epoxy resin, material, whose quasi-static mechanical properties can compare with those of glass fiber composites. Samples with a fiber direction of 0� were subjected to two types of multi-level creep-recovery tests, one with a varying creep duration, and the other with a varying creep stress, with the purpose of discriminating the viscoplastic and viscoelastic behavior of the composite. Results show a significant viscous response in time, dependent on both creep duration and creep stress, up to 20% of the elastic one. Sample damage is absent, leading to the conclusion that the viscoplastic response is caused by the permanent reorganization of the fiber�s internal structure.

scholarly journals Applying ASTM Standards to Tensile Tests of Musculoskeletal Soft Tissue: Methods to Reduce Grip Failures and Promote Reproducibility

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Madison E. Wale ◽  
Derek Q. Nesbitt ◽  
Bradley S. Henderson ◽  
Clare K. Fitzpatrick ◽  
Jaremy J. Creechley ◽  
...  
Keyword(s):  
Tensile Testing ◽  
Soft Tissues ◽  
Tensile Tests ◽  
Standard Test ◽  
International Standards ◽  
Fiber Reinforced Composites ◽  
Fiber Direction ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Test Standards

Abstract Tensile testing is an essential experiment to assess the mechanical integrity of musculoskeletal soft tissues, yet standard test methods have not been developed to ensure the quality and reproducibility of these experiments. The ASTM International standards organization has created tensile test standards for common industry materials that specify geometric dimensions of test specimens (coupons) that promote valid failures within the gage section (midsubstance), away from the grips. This study examined whether ASTM test standards for plastics, elastomers, and fiber-reinforced composites are suitable for tensile testing of bovine meniscus along the circumferential fiber direction. We found that dumbbell (DB) shaped coupons based on ASTM standards for elastomers and plastics had an 80% and 60% rate of midsubstance failures, respectively. The rate of midsubstance failures dropped to 20% when using straight (ST) coupons based on ASTM standards for fiber-reinforced composites. The mechanical properties of dumbbell shaped coupons were also significantly greater than straight coupons. Finite element models of the test coupons revealed stress distributions that supported our experimental findings. In addition, we found that a commercial deli-slicer was able to slice meniscus to uniform layer thicknesses that were within ASTM dimensional tolerances. This study provides methods, recommendations, and insights that can advance the standardization of tensile testing in meniscus and other soft fibrous tissues.

Tension and compression moduli characterization of a bimodular ceramic-fiber reinforced SiO2 aerogel composite

2020 ◽  
Vol 62 (10) ◽  
pp. 1003-1009
Author(s):  
Yantao Sun ◽  
Jia Huang ◽  
Duoqi Shi ◽  
Shengliang Zhang ◽  
Zhizhong Fu ◽  
...  
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Image Correlation ◽  
Bending Test ◽  
Ceramic Fiber ◽  
Fiber Reinforced ◽  
Compression Tests ◽  
Tension Tests ◽  
Aerogel Composite ◽  
Tension And Compression

Abstract Comprehensive characterization mechanical properties of aerogels and their composites are important for engineering design. In particular, some aerogel composites were reported to have varied tension and compression moduli. But conducting tension tests is difficult for the reason that low strength and brittleness will lead to unexpected failure in the non-test area. A method is presented for measuring both the tension and compression moduli of a ceramic-fiber reinforced SiO2 aerogel composite by bending via digital image correlation. First, the relationship between bending behavior and the tension/compression moduli was introduced for bimodular materials. Then a bending test was conducted to predict tension and the compression moduli of the ceramicfiber- reinforced SiO2 aerogel composite via digital image correlation. In addition, uniaxial tension and compression tests of the aerogel composites were carried out, respectively for measuring tension and compression moduli. The tension and compression moduli measured were numerically similar to results obtained from uniaxial tests with a difference of less than 14 %.

On prismatic and bending bifurcations of fiber-reinforced elastic membranes under swelling with application to aortic aneurysms

2021 ◽  
pp. 108128652110587
Author(s):  
Murtadha J. Al-Chlaihawi ◽  
Heiko Topol ◽  
Hasan Demirkoparan ◽  
José Merodio
Keyword(s):  
Axial Loading ◽  
Material Constant ◽  
Exponential Model ◽  
Aortic Aneurysms ◽  
Orthotropic Materials ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
The Matrix ◽  
Elastic Membranes ◽  
Fiber Winding

The influence of swelling on prismatic and bending bifurcation modes of inflated thin-walled cylinders under axial loading is examined. The bifurcation criteria for a membrane cylinder subjected to combined axial loading, internal pressure, and swelling is provided. We consider orthotropic materials with two preferred directions which are mechanically equivalent and symmetrically disposed. The mechanical behavior of the matrix is described by a swellable isotropic model. The isotropic material is augmented with two functions that are equal, each one of them accounting for the existence of a unidirectional reinforcement. Two reinforcing models that depend only on the stretch in the fiber direction are considered: the so-called standard reinforcing model and an exponential one. The analysis of bifurcation modes for these models under the conditions at hand may establish the connection with modeling of the normal and diseased aorta in arterial wall tissue. The effects of the axial stretch, the strength of the fiber reinforcement and the fiber winding angle on the onset of prismatic and bending bifurcations are investigated. It is shown that for membranes without fibers, prismatic bifurcation is not feasible. On the other hand, bending bifurcation is more likely to occur for swollen cylinders. However, for a particular model of fiber-reinforced membranes, the standard model, there exists a domain of deformation values together with material constant values that may trigger prismatic bifurcation. The exponential model does not allow prismatic bifurcations. Both models allow bending bifurcation and may or may not trigger it depending on the deformation together with material parameters.

Numerical Solutions of Boundary Value Problems with So-Called Shooting Method

2021 ◽  
Author(s):  
Sujaul Chowdhury ◽  
Mubin Md. Al Furkan ◽  
Nazmus Sayadat Ifat
Keyword(s):  
Boundary Value Problems ◽  
Shooting Method ◽  
Numerical Solutions ◽  
Boundary Value
Sign in / Sign up

Export Citation Format

Share Document