Elasto-plastic analysis

Sandorf, 1980 Whitney, 1985 Whitney and Browning, 1985). According to the classical beam theory, the shear stress distribution along the thickness of the specimen is a parabolic function that is symmetrical about the neutral axis where it is at its maximum and decreases toward zero at the compressive and tensile faces. In reality, however, the stress field is dominated by the stress concentration near the loading nose, which completely destroys the parabolic shear distribution used to calculate the apparent ILSS, as illustrated in Fig 3.18. The stress concentration is even more pronounced with a smaller radius of the loading nose (Cui and Wisnom, 1992) and for non-linear materials displaying substantial plastic deformation, such as Kevlar fiber-epoxy matrix composites (Davidovitz et al., 1984 Fisher et al., 1986), which require an elasto-plastic analysis (Fisher and Marom, 1984) to interpret the experimental results properly. 

We used an elasto-plastic analysis for WC/Co and visco-elasto-plastic analysis for Cu/Ni samples. Then, the physical and mechanical properties as function of the temperature and composition were compiled from the literature or determined by mechanical tests. 

In 1871, French mathematician and engineer Barre de Saint-Venant (1797-1886) wrote a paper on elasto-plastic analysis of partly plastic problems, such as the twisting of rods, bending of rectangular beams and pressurizing of hollow cylinders. Sain-Venant considered the following assumptions ... 

Elasto-plastic analysis on seismic response of PC continuous box-girder bridge with corrugated steel webs based on section fiber model... 

However, the T)-value is often fixed to be a constant in the existing analysis for the underground engineering projects in the HB rock mass (Chen Tonon 2011, Fraldi Guarracino 2010, Li et al. 2009, Park Kim 2006, Shen et al. 2010, Zhong et al. 2009, Zhou Li 2011). In this study D is treated as a variable. To formulate the elasto-plastic analysis solution for an axisymmetrical cavern, a linear function is chosen to quantitatively describe D. Compared with the elastic perfectly-plastic and elastic-brittle-plastic results, the present analysis can objectively reflect the excavation disturbance of the surrounding rocks. 

In practice of rock engineering projects, the generalized HB criterion is suited to a homogeneous, isotropic and massive rock with few discontinuities or to a heavily jointed rock mass. When a cavern or cavern group is constructed in the heavily jointed rock mass, it has been observed that the surrounding rock failure depends on mutual separation and slip of discontinuities. For this case in the elasto-plastic analysis, it can be accepted that the three parameters of cr, m- and GSI m the generalized HB criterion are fixed to be constants, but D is treated as a variable related to the confining pressure... 

Khuri AI, Cornell JA (1996) Response surfaces designs and analyses. Marcel Dekker, New York Kondoh K, Atluri SN (1987) Large-deformation, elasto-plastic analysis of fi ames under nonconservative... 

Lee J, Kim H (2007) Elasto-plastic analysis of adhesively bonded symmetric single lap joints under in-plane tension and edge moments. J Adhes 83(9) 837-870 Liljedahl CDM, Crocombe AD, hab I4A, Ashcroft lA (2006) Damage modelling of adhesively bonded joints. Int J Fract 141(1—2) 147—161 Luo Q, Tong L (2002) Exact static solutions to piezoelectric smart beams including peel stresses-1 theoretical formulation. Int J Solids Struct 39( 18) 4677-4695... 

The theoretical predictions should therefore be backed up by experimental evidence. This is especially important in the case of brittle materials, for which cracking mechanisms in tensile zones are accompanied by plastic deformation in zones under compressive stresses, with different rates of softening in these zones. The rigid-plastic analysis provides only a much simplified insight into failure mechanism. The sequence of progressive failure could be traced by an elasto-plastic analysis with account for crack gro th and development of plastic flow. 

In figure 11, the residual stress distribution in the "NCN part obtained from the analysis is plotted against the experimental results from the electrochemical thinning method. The agreement between the results is highly satisfactory and validates the visco-elasto-plastic approach taken in the FE-analysis as well as the values of the input data. 

The theory of elasto-plastic time history analysis based on section fiber model has been rapid developed in recent years, especially in seismic technology developed country such as American and Japan (D Ambrisi Filippou 1999, Spacone et al. 1999). In this paper, Shenzhen Nanshan Bridge is taken as the engineering background. Time history method based on section fiber model is used to analyze the nonlinear seismic responses of the bridge under rare earthquake. 

Lubarda, V.A. (1991) Constitutive analysis of large elasto-plastic deformation based on the multiplicative decomposition of deformation gradient. International Journal of Solids and Structures, 27, 885-895. 

Zhang Zhang (2010), referring to the modified criterion, conducted a three-dimensional elasto-plastic finite element analysis in order to propose an empirical expression of cohesion (c) and friction angle (( )) for layered rocks, which are transversely isotropic. 

Zhou T Q, Li Z X and Jia J B (2001), Elasto-plastic interface stress analysis of FRP retrofitted beam , in Teng J G (ed.) Proceedings of the International Conference on FRP Composites in Civil Engineeering, Hong Kong Elsevier, 527-536. 

A. T. Liu, Linear Elastic and Elasto-Plastic Stress Analysis for Adhesive Lap Joints, T.A.M. Report No. 410, University of Illinois at Urbana-Champaign (July 1976). 

Ahmad has idealised the same vessel, as shown in Fig. 5.30. He has used the vessel bonded and unbonded and produced deformations (Figs. 5.30, 5.31, 5.32 and 5.33) for normal operation and for 40 years of creep. He has also produced a graph (Fig. 5.34) showing deformation for this vessel at various pressures. He has included creep in his analysis. This vessel has also been considered for elasto-plastic and cracking effects by Bangash. The deformation of the vessel at the cracking stage under the influence of creep and with the steel liner anchored to concrete is shown in Fig. 5.35. 

On the analysis side both elastic and plastic methods are allowed. In case of plastic global analysis either rigid plastic or elasto-plastic methods are used in EC-3. 

Field and Swain have studied elasto-plastic response on a number of brittle materials, including silicate glass, silicon single crystal and single crystalline sapphire, by the indentation with small micron sized spherical tipped indenters. The analysis of indentation stress-strain curve was performed from the indentation on... 

GroBmayer, R. Stochastic Analysis of Elasto-Plastic Systems. Proc. ASCE, Journal of the Engineering Mechanics Division 107,... 

Haidar A, Nee KM (1989) Elasto-plastic large deformation analysis of PR steel frames for LRFD. Comput Struct 31(5) 811-823... 

Shi G, Atluri SN (1988) Elasto-plastic large deformation analysis of space frames. Int J Numer Methods Eng 26 589-615... 

In this analysis (Yang et al. 2004), the material nonlinear FEA was conducted for numerical comparison and cohesive failure was studied. Lee and Kim (2007) presented a closed-form analytical model for material nonlinear analysis of symmetric SLJs, in which the elasto-plastic perfect material property for adhesive was considered. The analysis was conducted for independent shear and peel stresses in the adhesive. 

An element will have hoth geometric and material properties. Spatially, an element is defined by its nodes however, additional geometric input is usually required for line and surface elements. For structural analysis the minimum material property is the modulus of elasticity. In most cases, Poisson s ratio or shear modulus must also be specified. If an orthotropic material is used then the orientation of the material must be specified as well as the elastic constants relative to each principal axis. If post-yield behavior is to be modelled then an elasto-plastic material model must be applied and the yield and hardening behavior defined. Constitutive adhesive and sealant models are discussed in more detail in O Chap. 23. Additional material properties will also be required for dynamic or thermal analysis. 

Bulk tensile testing has shown that adhesives generally exhibit plasticity and, hence, nonlinear material properties are required to model their behavior over the fiill load range. Nonlinear properties may also be required for adherends. Thus, a combination of elasto-plastic material models may be used to predict the behavior of adhesive joints under load. The definition of the yield surface is important when using elasto-plastic material models. Von Mises yield surface is commonly used for the analysis of metals, which assumes that the yield behavior is independent of hydrostatic stress. As a result, the yield surface is identical in tension and compression. However, the yield behavior of polymers has been shown to exhibit hydrostatic stress dependence (Ward and Sweeney 2004) as the yielding starts earlier in tension than in compression. Thus, a yield criterion which includes hydrostatic stress effects should be used to determine the yield surface. Various yield criteria with hydrostatic stress dependence such as Drucker-Prager, Mohr-Columb, and modified Drucker-Prager/cap plasticity model have been implemented in commercially available finite element software. 

Maximum-stress-and-strain-based failure criteria were used by Harris and Adams (1984) to predict the failure of single lap joints. A nonlinear finite element analysis with an elasto-plastic material model for the adhesive and adherends was carried out. The selection of stressor strain-based failure criterion was based on the results of uniaxial tensile test results. For an un-toughened adhesive, a brittle failure was observed and a maximum stress criterion was used, while for a toughened adhesive, failure was ductile and a maximum-strain-based criteria was used. However, these criteria are difficult to implement when highly localized stress concentrations or stress singularities exist in an adhesive joint. 

Crocombe AD, Bigwood DA (1992) Development of a full elasto-plastic adhesive joint design analysis. J Strain Anal Eng 27(4) 211-218... 

Marzi S, Hesebeck O et al (2009c) A rate-dependent, elasto-plastic cohesive zone mixed-mode model for crash analysis of adhesively bonded joints. Procedings of the 7th European LS-DYNA conference. Salzburg, Austria... 

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