Elastic foundation model

Compliance versus crack length for wood-wood TDCB specimen (Fig. 8). Exp., experi- FEA, finite element analysis TBEF, tapered beam on elastic foundation model. 

Elastic-foundation models have been used to analyze the effects of both the compliance [23,55] and the plastic deformation of an adhesive layer [55]. Cohesive-zone models in which the adhesive layer is replaced by cohesive-zone elements provide powerful techniques to analyze the phenomena and to couple them to the fracture process. Using the trapezoidal traction-separation law shown in Fig. 4, normalized load-displacement curves for a DCB specimen are shown in Fig. 12 [4]. The maximum loads supported by the DCB joints are of the form [29]... 

Williams, G.J., Fracture in adhesive Joints — the beam on elastic foundation model. In Proceedings of ASME International Mechanical Congress and Expositions, 1995, pp. 1112-1117. 

If the adhesive energy dissipation is very local then o arises mostly from the elastic deformation of the adhered part of the strip as shown in Fig. 8. The deformation, v, may be deduced from a beam on an elastic foundation model in which the stiffness arises from the half height of the beam, i.e. ... 

The data reduction for the tapered ENF (TENF) specimen can take the form of an experimental compliance or a simple beam theory approach, as reported by Edde and Verrenman (1995) or a corrected beam theory approach following the work of Qiao et al. (2003), using a beam on an elastic foundation model. These authors showed that substrates with a linear taper gave an almost linear relationship between compliance and crack length, within a certain range of crack lengths. 

Qiao P, Wang J et al (2003b) Tapered beam on elastic foundation model for compliance rate of change of TDCB specimen. Eng Fract Mech 70 339-353 Reeder JR (1993) A bilinear failure criterion for mixedmode delamination. In Camponeschi ET (ed) Composite materials testing and design, vol 11. ASTM STP, Philadelphia, pp 303-322... 

The effect of excavating manifests itself as two aspects. Firstly it results in the unbalance of the soil pressure between the retainin< wall s interior and exterior,and it can be considered as load acting oi retaining wall secondly,it causes part of the retaining wall to miss th< elastic support, in the saturated clay, the interactive problem betweei structure and soil is considered as Winkler s elastic foundation model so that it can be considered as the model change in the finite elemen analysis. For above ground structure, there is no excavating problem. 

The first milestone in modeling the process is credited to Pearson and Petrie (42—44). who laid the mathematical foundation of the thin-film, steady-state, isothermal Newtonian analysis presented below. Petrie (45) simulated the process using either a Newtonian fluid model or an elastic solid model in the Newtonian case, he inserted the temperature profile obtained experimentally by Ast (46), who was the first to deal with nonisothermal effects and solve the energy equation to account for the temperature-dependent viscosity. Petrie (47) and Pearson (48) provide reviews of these early stages of mathematical foundation for the analysis of film blowing. 

A study of numerical modeling of rutting in flexible pavement foundations under cyclic loading was reported by Huang Yu et al., 2001. On the basis of a coupled dynamic soil-pore water system theory a visco-elastic dynamic model has been developed to predict the non-linear response of pavement structure. 

Abstract Accidents of some arch dams show that dam failures are mainly caused by crack or failure of their foundation rocks, which are directly related to water seepage in the rock. This kind of fluid-rock interaction has an important influence on deformation and stress characters of the dam-rock system. In this paper, the stress and flow fields of dams and their foundation rocks are studied as a coupled system, using visco-elastic constitutive models and finite element solution method. The developed models and FEM technique were applied for analysing the continuous displacement of the 13 dam section of the Longyangxia Dam, and the calculated results agree well with the measured ones. 

Recognizing the importance of the coupled hydro-mechanical effects on the performance of civil engineering structures involving fractured rocks, the stress-flow coupling mechanism of the dam-foundation system at Longyangxia site was simulated using a three-dimensional Finite Element code, supported by two visco-elastic constitutive models to represent the time-dependent material behaviour of the dam concrete and the foundation rock. The calculated results were concord with the measured ones and helped to interpret the causes of this continuous displacement at the 13" dam section of the Longyangxia hydropower project, towards the left bank. 

For studying the viscous deformation caused by the creep of dam and its base rock under time-dependent loading, different visco-elastic constitutive models are developed to identify the most suitable models and parameters for more accurate simulation of the time-dependent deformation of the dam-foundation system. 

The visco-elastic constitutive model of the foundation rock... 

Figure 12 Modeling of TDCB specimen on an elastic foundation (after Ref. 13). 

The compression of the first layer of liquid crystal molecules was analyzed using the solid foundation model [22]. It models the first layer just as a thin elastic layer with an elastic modulus K on top of an incompressible surface. Force and indentation are related by F =, where 5 is the depth of indentation, R the... 

Another fundamental mechanics solution that has many applications in bonded joints is that of a beam on an elastic foundation. Emil Winkler first reported this analysis in 1867 [49]. The method has been widely applied to a variety of problems, perhaps most obviously that of trains passing over rails supported by the earth, and has been included in most texts on advanced mechanics of materials [16]. Since many bonded Joints have beam-like adherends supported by a more flexible adhesive layer, this model of a beam on an elastic foundation is also of great importance for a variety of joints ranging from the lap shear specimen to fracture specimens, from peel specimens to the loop tack test. 

Andrianopoulos et al. (2006), Lopez-Caballero and Modaressi Farahmand-Razavi (2008), Andrianopoulos et al. (2010), Shahir and Pak (2010), Dashti and Bray (2013), Lopez-Caballero and Modaressi Farahmand-Razavi (2013), and Karamitros et al. (2013) conducted 2-D (plane strain) and 3-D, fully coupled, nonlinear, finite element and finite difference analyses to study the dynamic interaction between homogeneous and layered liquefiable sand and a structure. In these analyses, the stmcture was simulated either as a surface load, rigid stmcture, or an elastic SDOF model. The foundation was mostly... 

Katz and Li [61,62] modelled the flexural behaviour by simulating the fibre partially as a beam resting on an elastic foundation and partially as a cantilever... 

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