Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: II—Effect of Variable Strain Rates

2000 ◽  
Vol 123 (2) ◽  
pp. 198-200 ◽  
Author(s):  
Mark R. DiSilvestro, ◽  
Qiliang Zhu, ◽  
Jun-Kyo Francis Suh
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Strain Rate ◽  
Viscoelastic Behavior ◽  
Viscoelastic Response ◽  
Strain Rates ◽  
Unconfined Compression ◽  
Rate Dependent ◽  
Linear Viscoelastic

This study investigated the abilities of the linear biphasic poroviscoelastic (BPVE) model and the linear biphasic poroelastic (BPE) model to simulate the effect of variable ramp strain rates on the unconfined compression stress relaxation response of articular cartilage. Curve fitting of experimental data showed that the BPVE model was able to successfully account for the ramp strain rate-dependent viscoelastic behavior of articular cartilage under unconfined compression, while the BPE model was able to account for the complete viscoelastic response at a slow strain rate, but only the long-term viscoelastic response at faster strain rates. We concluded that the short-term viscoelastic behavior of articular cartilage, when subjected to a fast ramp strain rate, is primarily governed by a fluid flow-independent (intrinsic) viscoelastic mechanism, whereas the long-term viscoelastic behavior is governed by a fluid flow-dependent (biphasic) viscoelastic mechanism. Furthermore, a linear viscoelastic representation of the solid stress was found to be a valid model assumption for the simulation of ramp strain rate-dependent relaxation behaviors of articular cartilage within the range of ramp strain rates investigated.

Strain-rate Dependent Stiffness of Articular Cartilage in Unconfined Compression

2003 ◽  
Vol 125 (2) ◽  
pp. 161-168 ◽  
Author(s):  
L. P. Li ◽  
M. D. Buschmann ◽  
A. Shirazi-Adl
Keyword(s):  
Articular Cartilage ◽  
Strain Rate ◽  
Compressive Strain ◽  
Fluid Pressure ◽  
Nonlinear Function ◽  
Protective Mechanism ◽  
Unconfined Compression ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Elastic Loading

The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinforced poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.

scholarly journals Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

2020 ◽  
Author(s):  
Chuang Liu ◽  
Dongzhi Sun ◽  
Xianfeng Zhang ◽  
Florence Andrieux ◽  
Tobias Gerster
Keyword(s):  
Cast Iron ◽  
Constitutive Model ◽  
Strain Rate ◽  
Mechanical Behavior ◽  
Damage Model ◽  
Iron Alloys ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Damage Models ◽  
Rate Dependent

Abstract Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry. To study the mechanical behavior of a typical ductile cast iron (GJS-450) with nodular graphite, uni-axial quasi-static and dynamic tensile tests at strain rates of 10− 4, 1, 10, 100, and 250 s− 1 were carried out. In order to investigate the effects of stress state, specimens with various geometries were used in the experiments. Stress–strain curves and fracture strains of the GJS-450 alloy in the strain-rate range of 10− 4 to 250 s− 1 were obtained. A strain rate-dependent plastic flow law based on the Voce model is proposed to describe the mechanical behavior in the corresponding strain-rate range. The deformation behavior at various strain rates is observed and analyzed through simulations with the proposed strain rate-dependent constitutive model. The available damage model from Bai and Wierzbicki is extended to take the strain rate into account and calibrated based on the analysis of local fracture strains. The validity of the proposed constitutive model including the damage model was verified by the corresponding experimental results. The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys. The predictions with the proposed constitutive model and damage models at various strain rates agree well with the experimental results, which illustrates that the rate-dependent flow rule and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.

scholarly journals Strain-Rate-Dependent Deformation Behavior and Mechanical Properties of a Multi-Phase Medium-Manganese Steel

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 344 ◽  
Author(s):  
Simon Sevsek ◽  
Christian Haase ◽  
Wolfgang Bleck
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Deformation Behavior ◽  
Rate Sensitivity ◽  
Manganese Steel ◽  
Strain Rates ◽  
Rate Dependent ◽  
Medium Manganese Steel ◽  
Multi Phase

The strain-rate-dependent deformation behavior of an intercritically annealed X6MnAl12-3 medium-manganese steel was analyzed with respect to the mechanical properties, activation of deformation-induced martensitic phase transformation, and strain localization behavior. Intercritical annealing at 675 °C for 2 h led to an ultrafine-grained multi-phase microstructure with 45% of mostly equiaxed, recrystallized austenite and 55% ferrite or recovered, lamellar martensite. In-situ digital image correlation methods during tensile tests revealed strain localization behavior during the discontinuous elastic-plastic transition, which was due to the localization of strain in the softer austenite in the early stages of plastic deformation. The dependence of the macroscopic mechanical properties on the strain rate is due to the strain-rate sensitivity of the microscopic deformation behavior. On the one hand, the deformation-induced phase transformation of austenite to martensite showed a clear strain-rate dependency and was partially suppressed at very low and very high strain rates. On the other hand, the strain-rate-dependent relative strength of ferrite and martensite compared to austenite influenced the strain partitioning during plastic deformation, and subsequently, the work-hardening rate. As a result, the tested X6MnAl12-3 medium-manganese steel showed a negative strain-rate sensitivity at very low to medium strain rates and a positive strain-rate sensitivity at medium to high strain rates.

Investigation of the axial compressive behavior of Kevlar fibers using the dynamic loop test

2019 ◽  
Vol 89 (18) ◽  
pp. 3825-3838
Author(s):  
Ahmad Abuobaid ◽  
Raja Ganesh ◽  
John W Gillespie
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Failure Strain ◽  
Kink Band ◽  
Test Method ◽  
Strain Rates ◽  
Compressive Failure ◽  
Band Formation ◽  
Rate Dependent ◽  
Strain And Strain Rate

A dynamic loop test method for measuring strain rate-dependent fiber properties was developed. During dynamic loop testing, the fiber ends are accelerated at constant levels of 20.8, 50 and 343 m/s2. The test method is used to study Kevlar® KM2-600, which fails in axial compression due to kink band formation. The compressive failure strain and strain rate at the onset of kink band formation is calculated from the critical loop diameter ( D C), which is monitored throughout the test using a high-speed camera. The results showed that compressive failure strain increases with strain rates from quasi-static to a maximum strain rate of 116 s−1 by a factor of ∼3. Kink angles (φ) and kink band spacing ( D S) were 60 ° ± 2 ° and 16 ± 3 μm, respectively, over the strain rates tested. Rate-dependent mechanisms of compressive failure by kink band formation were discussed.

scholarly journals Deformation behaviour and strength of frozen sand

1980 ◽  
Vol 17 (1) ◽  
pp. 74-88 ◽  
Author(s):  
V. R. Parameswaran
Keyword(s):  
Compressive Strength ◽  
Strain Rate ◽  
Deformation Behaviour ◽  
Unfrozen Water ◽  
Strain Rates ◽  
Linear Extrapolation ◽  
Compression Tests ◽  
Unconfined Compression ◽  
Ottawa Sand ◽  
Frozen Sand

Uniaxial unconfined compression tests were carried out on frozen saturated Ottawa sand containing about 20% by weight of water, at temperatures between −2 and − 15°C, and at strain rates varying between 10−7 and 10−2 s−1. The compressive strength and the initial tangent modulus increased with increasing strain rate and with decreasing temperature. At −2°C, values of strength and modulus were considerably lower than those predicted by linear extrapolation of the values observed at lower temperatures, on a log–log scale. This could be due to the presence of unfrozen water in the samples at −2°C.

Three-Parameter Viscoelasticity Models for Ballistic Fabrics

2008 ◽  
Author(s):  
N. V. David ◽  
X.-L. Gao ◽  
J. Q. Zheng ◽  
K. Masters
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Constitutive Relations ◽  
Viscoelastic Behavior ◽  
Strain Rates ◽  
Rheological Models ◽  
Maxwell Element ◽  
In Series ◽  
Low Strain Rate

Ballistic fabrics are made from high performance polymeric fibers such as Kevlar®, Twaron® and Spectra®. These fibers often behave viscoelastically in high strain rate deformations. The Kelvin-Voigt and Maxwell rheological models have been used to characterize such viscoelastic responses at different strain rates. However, these two-parameter models have been found to be inadequate and inaccurate in some applications. As a result, three-parameter rheological models have been utilized to develop constitutive relations for viscoelastic polymeric fabrics. In this study, a generalized Maxwell (GM) model and a generalized Kelvin-Voigt (GKV) model are proposed to describe the viscoelastic behavior of a ballistic fabric, Twaron® CT716, at the strain rates of 1 s−1 and 495 s−1. The GM model consists of a Maxwell element (including a viscous dashpot and a spring in series) and a second spring in parallel to the Maxwell element, while the GKV model is an assembly of a Kelvin-Voigt (KV) element (containing a viscous dashpot and a spring in parallel) and a second spring in series with the KV element. The predictions by the GM and GKV models are compared with existing experimental data, which shows that the two sets of results are in fairly good agreement. In particular, the comparison reveals that the GKV model gives more accurate results at the low strain rate, whereas the GM model performs better at the high strain rate while still providing accurate predictions for the low strain rate responses.

Constitutive Modeling of a Thermoplastic Olefin Over a Broad Range of Strain Rates

2006 ◽  
Vol 128 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Yan Wang ◽  
Ellen M. Arruda
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Elastic Response ◽  
Strain Rates ◽  
Strain Behavior ◽  
Rate Dependent ◽  
State Dependent ◽  
Deformation State ◽  
Ann Arbor

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

scholarly journals Inelastic Behavior in Repeated Shearing of Bovine White Matter

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Taylor S. Cohen ◽  
Andrew W. Smith ◽  
Panagiotis G. Massouros ◽  
Philip V. Bayly ◽  
Amy Q. Shen ◽  
...  
Keyword(s):  
White Matter ◽  
Strain Rate ◽  
Critical Strain ◽  
Mechanical Response ◽  
Tissue Mechanics ◽  
Strain Rates ◽  
Inelastic Behavior ◽  
Fiber Breakage ◽  
Rate Dependent ◽  
Strain Threshold

Understanding the brain’s response to multiple loadings requires knowledge of how straining changes the mechanical response of brain tissue. We studied the inelastic behavior of bovine white matter and found that when this tissue is stretched beyond a critical strain threshold, its reloading stiffness drops. An upper bound for this strain threshold was characterized, and was found to be strain rate dependent at low strain rates and strain rate independent at higher strain rates. Results suggest that permanent changes to tissue mechanics can occur at strains below those believed to cause physiological disruption or rupture of axons. Such behavior is characteristic of disentanglement in fibrous-networked solids, in which strain-induced mechanical changes may result from fiber realignment rather than fiber breakage.

Strain Rate Effects and Rate-Dependent Constitutive Models of Lead-Based and Lead-Free Solders

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Fei Qin ◽  
Tong An ◽  
Na Chen
Keyword(s):  
Strain Rate ◽  
Impact Analysis ◽  
Solder Joints ◽  
High Strain ◽  
Drop Impact ◽  
Lead Free ◽  
Strain Rates ◽  
High Strain Rates ◽  
Rate Dependent ◽  
Lead Free Solders

As traditional lead-based solders are banned and replaced by lead-free solders, the drop impact reliability is becoming increasingly crucial because there is little understanding of mechanical behaviors of these lead-free solders at high strain rates. In this paper, mechanical properties of one lead-based solder, Sn37Pb, and two lead-free solders, Sn3.5Ag and Sn3.0Ag0.5Cu, were investigated at strain rates that ranged from 600 s−1 to 2200 s−1 by the split Hopkinson pressure and tensile bar technique. At high strain rates, tensile strengths of lead-free solders are about 1.5 times greater than that of the Sn37Pb solder, and also their ductility are significantly greater than that of the Sn37Pb. Based on the experimental data, strain rate dependent Johnson–Cook models for the three solders were derived and employed to predict behaviors of solder joints in a board level electronic package subjected to standard drop impact load. Results indicate that for the drop impact analysis of lead-free solder joints, the strain rate effect must be considered and rate-dependent material models of lead-free solders are indispensable.

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