The Viscoelastic Fiber Composite with Nonlinear Interface

2005 ◽  
Vol 73 (2) ◽  
pp. 268-280 ◽  
Author(s):  
Mayue Xie ◽  
Alan J. Levy
Keyword(s):  
Differential Equations ◽  
Fiber Composite ◽  
Elastic Fiber ◽  
Maxwell Model ◽  
Time Dependent ◽  
Shear Mode ◽  
Interface Failure ◽  
Shear Creep ◽  
The Matrix ◽  
Composite Cylinders

Effective viscoelastic response of a unidirectional fiber composite with interfaces that may separate or slip according to uniform Needleman-type cohesive zones is analyzed. Previous work on the solitary elastic composite cylinder problem leads to a formulation for the mean response consisting of a stress-strain relation depending on the interface separation∕slip discontinuity together with an algebraic equation governing its evolution. Results for the fiber composite follow from the composite cylinders representation of a representative volume element (RVE) together with variational bounding. Here, the theory is extended to account for viscoelastic matrix response. For a solitary elastic fiber embedded in a cylindrical matrix which is an nth-order generalized Maxwell model in shear relaxation, a pair of nonlinear nth-order differential equations is obtained which governs the relaxation response through the time dependent stress and interface separation∕slip magnitude. When the matrix is an nth-order generalized Kelvin model in shear creep, a pair of nonlinear nth-order differential equations is obtained governing the creep response through the time dependent strain and interface separation∕slip magnitude. We appeal to the uniqueness of the Laplace transform and its inverse to show that these equations also apply to an RVE with the composite cylinders microstructure. For a matrix, which is a standard linear solid (n=2), the governing equations are analyzed in detail paying particular attention to issues of bifurcation of response. Results are obtained for transverse bulk response and antiplane shear response, while axial tension with related lateral Poisson contraction and transverse shear are discussed briefly. The paper concludes with an application of the theory to the analysis of stress relaxation in the pure torsion of a circular cylinder containing unidirectional fibers aligned parallel to the cylinder axis. For this problem, the redistribution of shear stress and interface slip throughout the cross section, and the movement of singular surfaces, are investigated for an interface model that allows for interface failure in shear mode.

Dimensional changes during shear without normal tractions (the Poynting effect) in nonlinear viscoelastic fiber-reinforced solids

2019 ◽  
Vol 25 (3) ◽  
pp. 582-596
Author(s):  
Alan Wineman
Keyword(s):  
Constitutive Equation ◽  
Numerical Solutions ◽  
Elastic Fiber ◽  
Time Dependent ◽  
Nonlinear Material ◽  
Fiber Reinforced ◽  
Dimensional Changes ◽  
Fiber Reinforced Materials ◽  
The Matrix ◽  
Poynting Effect

When a rectangular block of a nonlinear material is subjected to a simple shearing deformation, specific normal tractions are required to ensure that the distances between the faces of the block, i.e. its dimensions, do not change. This work investigates the time-dependent dimensional changes during shear in the absence of these normal tractions (the Poynting effect) that occur in a block composed of an incompressible nonlinearly viscoelastic fiber-reinforced solid. The material is modeled using the Pipkin–Rogers nonlinear single integral constitutive equation for viscoelasticity. This constitutive equation is used because (1) it exhibits the essential features of nonlinear viscoelasticity; (2) it is straightforward to include the material symmetry restrictions due to the reinforcing fibers. A system of nonlinear Volterra integral equations is formulated for the dimensional changes in the block. Numerical solutions are presented for the case when the standard reinforcing model for nonlinearly elastic fiber-reinforced materials is incorporated in the Pipkin–Rogers constitutive framework. The results illustrate how the time-dependent dimensional changes depend on the fiber orientation and the viscoelastic properties of the fibers relative to those of the matrix.

The Fiber Composite With Nonlinear Interface—Part I: Axial Tension

2000 ◽  
Vol 67 (4) ◽  
pp. 727-732 ◽  
Author(s):  
A. J. Levy
Keyword(s):  
Fiber Composite ◽  
Total Potential ◽  
Tension Response ◽  
Axial Tension ◽  
The Matrix ◽  
Nonlinear Interface ◽  
Tension Loading ◽  
Related Paper ◽  
Composite Cylinders ◽  
Poisson Contraction

This paper treats the effective axial tension response of a composite consisting of fibers that debond from the matrix according to nonlinear Needleman-type cohesive zones. A second, related paper (Part II) treats effective antiplane shear response. The composite cylinders representation of a representative volume element (RVE) is employed throughout. For axial tension loading a simple rotationally symmetric boundary value problem for a single composite cylinder is solved. Bounds on the total potential energy and the total complementary energy are shown to coincide and an exact solution for axial extension and Poisson contraction of an RVE of the composite is obtained. Nonlinear interfacial debonding, however, is shown to have a negligible effect on extensional response and only a small, though potentially destabilizing, effect on Poisson contraction response. [S0021-8936(00)02004-3]

scholarly journals Expression of VEGF-A Signaling Pathway in Cartilage of ACLT-induced Osteoarthritis Mouse Model

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Jia-jia Qian ◽  
Qi Xu ◽  
Wei-min Xu ◽  
Ren Cai ◽  
Gui-cheng Huang
Keyword(s):  
Signaling Pathway ◽  
Cruciate Ligament ◽  
Time Dependent ◽  
Pathological Changes ◽  
The Matrix ◽  
Vegfr2 Signaling ◽  
Cox 2 ◽  
Anterior Cruciate ◽  
A Disintegrin And Metalloproteinase ◽  
Safranin O

Abstract Background Anterior cruciate ligament transection surgery (ACLT)-induced OA model was often used to investigate the molecular mechanism of knee osteoarthritis (KOA). Researches have shown that vascular endothelial growth factor (VEGF) played an important role in OA. The present study aimed to investigate the pathological changes after ACLT surgery and reveal the expression characteristics of the VEGF-A/VEGFR2 signaling pathway in this model. Methods Moderate KOA model was established by ACLT, and 1, 2, 4, 8, and 12 weeks after surgery, hematoxylin-eosin (HE) and Safranin-O(S-O) staining were used to detect the pathological changes in mouse knee cartilage, and the matrix biomarkers A Disintegrin and Metalloproteinase with Thrombospondin Motifs 5(ADAMTS5), Collagen II (COL-II) were detected using immunohistochemistry (IHC), CD31 was detected by immunofluorescence (IF) to show the vascular invasion in cartilage, and proteins expression of VEGF-A pathway were detected by Western blot (WB). Meanwhile, the inflammatory biomarkers cyclooxygenase-2 (COX-2) and inducible nitric oxide synthase (iNOS) in cartilage were detected by WB. Results ACLT surgery can lead to degeneration of cartilage in mice, and the characteristics of the lesion were time-dependent. The ADAMTS5-positive cells increased while COL-II decreased in OA cartilage with time, and new blood vessels labeled by CD31 can be seen from 1 week in OA cartilage, and increased in 8 and 12 weeks. The expression of VEGF-A, VEGFR2, COX-2, and iNOS were higher than control groups, which were basically consistent with the degree of osteoarthritis. Conclusions The degenerative degree of articular cartilage was time-dependent; angiogenesis and inflammation were important pathological changes of cartilage in KOA. The expression of the VEGF-A/VEGFR2 signaling pathway was basically correlated with the degree of KOA.

scholarly journals Time-Dependent Response of a Recycled C&D Material-Geotextile Interface under Direct Shear Mode

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3070
Author(s):  
Fernanda Bessa Ferreira ◽  
Paulo M. Pereira ◽  
Castorina Silva Vieira ◽  
Maria de Lurdes Lopes
Keyword(s):  
Shear Stress ◽  
Stress Relaxation ◽  
Shear Displacement ◽  
Time Dependent ◽  
Shear Behaviour ◽  
Displacement Rate ◽  
Shear Mode ◽  
Direct Shear ◽  
Constant Displacement ◽  
Shear Box

Geosynthetic-reinforced soil structures have been used extensively in recent decades due to their significant advantages over more conventional earth retaining structures, including the cost-effectiveness, reduced construction time, and possibility of using locally-available lower quality soils and/or waste materials, such as recycled construction and demolition (C&D) wastes. The time-dependent shear behaviour at the interfaces between the geosynthetic and the backfill is an important factor affecting the overall long-term performance of such structures, and thereby should be properly understood. In this study, an innovative multistage direct shear test procedure is introduced to characterise the time-dependent response of the interface between a high-strength geotextile and a recycled C&D material. After a prescribed shear displacement is reached, the shear box is kept stationary for a specific period of time, after which the test proceeds again, at a constant displacement rate, until the peak and large-displacement shear strengths are mobilised. The shear stress-shear displacement curves from the proposed multistage tests exhibited a progressive decrease in shear stress with time (stress relaxation) during the period in which the shear box was restrained from any movement, which was more pronounced under lower normal stress values. Regardless of the prior interface shear displacement and duration of the stress relaxation stage, the peak and residual shear strength parameters of the C&D material-geotextile interface remained similar to those obtained from the conventional (benchmark) tests carried out under constant displacement rate.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

Pressuremeter Testing of Normally Consolidated Clays—The Effects of Varying Test Technique

1986 ◽  
Vol 2 (1) ◽  
pp. 125-132
Author(s):  
W. F. Anderson ◽  
I. C. Pyrah ◽  
F. Haji-Ali
Keyword(s):  
Test Methods ◽  
Time Dependent ◽  
Clay Soils ◽  
Shear Creep ◽  
Test Technique ◽  
Pressuremeter Test ◽  
Numerical Predictions ◽  
Cylindrical Cavities ◽  
Undrained Conditions ◽  
Insight Into

AbstractAlthough BS 5930:1981 describes both Menard and self-boring pressuremeter tests, little guidance is given on test methods. A number of techniques, both stress controlled and strain controlled, have been used and it has been shown that for clays the test technique has a significant influence on the derived strength and modulus parameters.When a pressuremeter test is carried out in a clay, it is assumed that shearing occurs under undrained conditions. However, in addition to immediate shear strain, some creep and local consolidation will occur in the soil around the expanding borehole. These two phenomena are time-dependent and variations in test technique will affect the test data and hence the derived strength and modulus values.To obtain a better understanding of these effects, pressuremeter tests have been studied both experimentally and numerically. Experimentally, pressuremeter tests have been simulated by expanding cylindrical cavities in samples of three clays prepared with known stress history and the results compared with numerical predictions where the effects of immediate shear, creep and consolidation can be separated. The experimental results compare well with the numerical predictions.This has given a new insight into the behaviour of clay soils during pressuremeter tests. The results indicate that any simple standardization of pressuremeter test technique should be approached with caution.

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