Elastoplastic analyses

Elastoplastic analyses of bimaterial comers have also been conducted, albeit more recently. A singularity analysis based on 72-deformation theory was devel-... 

Giannakopolous, A.E., Suresh, S., Finot, M., Olsson, M., (1995), Elastoplastic analysis of thermal cycling - layered materials with compositional gradients , Acta. Metall. Mater., 43, 1335-1354. 

As discussed in Chapter 4, a strain description based on displacement gradients becomes nonlinear, which may result in computational difficulties for elastoplastic analysis. Therefore, the deformation gradient and multiplicative decomposition technique are usually used ... 

Simo, J.C. and Ortiz, M. (1985) A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Computer Methods in Applied Mechanics and Engineering, 49, 221-245. 

W. Guo, C. H. Wang, and L. R. F. Rose Elastoplastic analysis of notch-tip fields in strain hardening materials. Technical Report AR-010-065, Aeronautical and Maritime Research Laboratory, Melbourne, 1998. 

Suresh, S., Giannakopoulos, A. E. and Olsson, M. (1994), Elastoplastic analysis of thermal cycling Layered materials with sharp interfaces, Journal of the Mechanics and Physics of Solids 42, 979-1018. 

Post-1930, the difference of the response spectrum to various structural periods was looked at, with the influence being that the lateral forces would be changed depending on the fundamental period of the building. Elastic analysis was, however, stiU undertaken, as opposed to elastoplastic analysis (ductile analysis). 

Shahrour I, Khoshnoudian F, Sadek M, Mroueh H (2010) Elastoplastic analysis of the seismic response of tunnels in soft soils. Tunn Undergr Space Technol 25 478-482... 

Progress in modelling and analysis of the crack problem in solids as well as contact problems for elastic and elastoplastic plates and shells gives rise to new attempts in using modern approaches to boundary value problems. The novel viewpoint of traditional treatment to many such problems, like the crack theory, enlarges the range of questions which can be clarified by mathematical tools. 

Synthesis of Siloxane-Polyimide Elastoplastics. In a typical polymerization, a 5-L, three-neck, round-bottom flask equipped with an overhead mechanical stirrer, a Dean-Stark trap with condenser and a nitrogen inlet, and a thermometer was charged with 484.00 g (0.2406 mol) of D2o-DiSiAn, 41.61 g (0.431 mol) of mPD, 19.52 g (3 wt %) of 2-hydroxypyridine, and 2 L of o-dichlorobenzene. The mixture was warmed to 100 °C for 1 h to dissolve the monomers and the catalyst. The polyamic acids precipitated and then redissolved when the mixture was warmed to 150 °C for 2 h. To the oligomer solution was added 99.13 g of BPADA dissolved in 200 mL of o-dichlorobenzene. The mixture was maintained at 150 °C for an additional 2-h period to ensure incorporation of the dianhydride and then warmed to reflux. After approximately 100 mL of a solvent-water mixture had been removed, the solution was maintained at 180 °C for 40 h. The mixture was cooled to room temperature and diluted with 1 L of methylene chloride. Polymer was isolated from the solution by a slow addition of the polymer solution to 4 L of methanol. The resulting slurry was filtered, and the polymer was redissolved in 4 L of methylene chloride, extracted three times with 2 N aqueous HCl to remove catalyst, washed with water, dried with magnesium sulfate, reprecipitated into methanol as before, filtered, and dried in vacuo at 100 °C to obtain 522 g (85%) of a rubbery material with an IV of 0.50 dL/g. IR, NMR, and Si NMR spectroscopic analysis indicated the absence of amic acid functionalities that could be present if imidization is incomplete. 

For the yield stress in compression, deviations from Tabor s relation giving values of 2Yc are found. This is presumably due to the elastic strain of the indented material. A detailed analysis of the H/Yc ratio on the basis of mechanical models of elastoplastic indentation reveals that H/Yc linearly increases with ln[(tan/3Ec)/Yc]. Compression-moulded (chain-folded) PE samples, which present the lowest crystallinity of all the samples investigated, also show the lowest H/Yc ratio as a consequence of the comparatively large elastic strains. 

Through disk-bend testing on a series of ZrOj/Ni composite specimens fabricated by powder processing, we have examined the fracture behavior of ceramic/metal composites under an equibiaxial plane-stress loading, and derived, by making a micromechanical analysis of elastoplastic stress states, a brittle phase-controlled fracture criterion of the form, ( )max const., in terms of the equivalent normal stress a. This criterion is conceptually simple and quite useful particularly for our micromechanics-based approach to the FGM architecture. 

Wang Y, Xu Z and Su B. 2000a. Complete coupled analysis of fluid flow and elastoplastic stress in complicated fractured rock masses. Chinese J. of Rock Mech. Engng, 19(2), pp. 177-181. 

Gens, A., Vaunat, J. Ledesma, A. 1995. Analysis of hydration of an engineered barrier in a radioactive waste repository scheme using an elastoplastic model. Proc. T Int. Conf. on Unsaturated Soils, Alonso Delage eds., Balkema, p. 1065-1073. 

The pioneering analytical solution by Eshelby [59], for an ellipsoidal inclusion embedded in an infinite elastic medium, has been extended to nonlinear cases in the literature. For example, the secant approach by Berveiller and Zaoui [63] and the self-consistent tangent method by HiU [64] and Hutchinson [65] are generalizations of this method for elastoplastic problems. The limitation of these analytical methods persists in their inability to simulate complex material stractures, which result in inelastic responses that are too stiff [62,66]. Also, accurate stress redistribution in an inelastic analysis cannot be captured by these models [67]. Several models have been developed to resolve these issues in the literature, such as the above-mentioned tangent [64,66,68,69], secant [63,70], and affine [67,71] methods. 

The elastoplastic multiscale analysis requires several computational modules, including (1) a microscale computation module, which consists of a set of numerical solutions for the local constitutive equation of each subphase, (2) a micromechanical computation module, which provides numerical tools to link the mechanical properties of each of the local subphases to the macroscopic responses, and (3) a macroscale computation module, in which the continuum mechanics governing equations are enforced to simulate the overall mechanical response of the material and to identify the local loading conditions over the R VE. Each of these computational modules is discussed in the following. A flowchart of the multiscale analysis is shown in Figure 5.24. 

A nonlinear dynamic analysis has been performed for the three monuments (Sect. 8.2.3), with the masses lumped at characteristic levels and applying a corresponding storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, with the load-bearing capacity of each of them limited to the bending and shear capacity, whichever is less. 

Dynamic analysis With the masses lumped at two characteristic levels, a nonlinear dynamic analysis has been performed with storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, whereas the load-bearing capacity of each of them has been limited to the lower value of bending and shear capacity (according to Sect. 8.3.3). To obtain the dynamic response, three different types of earthquake (Petrovac 1979, Ulcinj 1979 and El Centro 1940) with maximum input acceleration of 0.24g and return period of 1,000 years have been applied. Obtained as the results from the dynamic analysis are the storey displacements and ductility ratios required by the earthquake that have to comply with the design criteria defined in Sect. 8.3.4. 

Overburden of the tunnel 100.0 m The rock mass is considered as the idealized elastoplastic material with the Mohr-Coulomb yield criterion, and all the materials of support system are treated as elastic material. The initial stress field of analysis zone is calculated as self-weight... 

Au, S., Lam, H. Ng, C. 2007. Reliability analysis of single-degree-of-freedom elastoplastic systems. I Critical excitations./oMr <2/ of Engineering Mechanics 133(10), 1072-1080. 

Klaas, O., Kreienmeyer, M. Stein, E. 1994. Elastoplastic finite element analysis on a MIMD parallel-computer. Engineering Computations, 11 347—355. 

The stresses in an adhesive joint depend, once a constitutive model is chosen, on the geometry, boundary conditions, the assumed mechanical properties of the regions involved, and the type and distribution of loads acting on the joint. In practice, most adhesives exhibit, depending on the stress levels, nonlinear-viscoelastic behavior, and the adhetends exhibit elastoplastic behavior. Most theoretical studies conducted to date on the stress analysis of adhesively bonded joints have made simplifying assumptions of linear and elastic and/or viscoelastic behavior in the interest of tracking solutions. 

Schaffer and Adams< 2) carried out a nonlinear viscoelastic analysis of a unidirectional composite laminate using the finite-element method. The nonlinear viscoelastic constitutive law proposed by Schapery<26) was used in conjunction with elastoplastic constitutive relations to model the composite response beyond the elastic limit. 

Again restricting to SDOF-structures, using of Eq. (10), and applying the similarity analysis of Sec. 4, it is easily shown that the nonstationary random response of the elastoplastic structure is... 

It is known [5], that at elastoplastic behavior a system crack-local deformation zone deviates from thermodynamical equilibrium and for its analysis a principles, correct for close to equilibrium systems, for example, Griffith theory, are inapplicable. Besides, prefailure zone structure is differed from elastically deformed material structure (Fig. 5.3) that complicates additionally process analysis. As it was noted above, for polymers this effect is displayed as the formation of local deformation zones near crack tip, containing microvoids and oriented material (crazes) or oriented material only (ZD) [20]. Therefore, for fracture analysis in such cases fracture fractal theory is applied, using fractal analysis and general principles of synergetics [28]. 

At solid body deformation the heat flow is formed, which is due to deformation. The thermodynamics first law establishes that the internal eneigy change in sample dU is equal to the sum of woik dW, carried out on a sample, and the heat flow dQ into sample (see the Eq. (4.31)). This relation is valid for any deformation, reversible or irreversible. There are two thermo-d5mamically irreversible cases, for which dQ = -dW, uniaxial deformation of Newtonian liquid and ideal elastoplastic deformation. For solid-phase polymers deformation has an essentially different character the ratio QIW is not equal to one and varies within the limits of 0.35 0.75, depending on testing conditions [37]. In other words, for these materials thermodynamically ideal plasticity is not realized. The cause of such effect is thermodynamically nonequilibrium nature or fractality of solid-phase polymers structure. Within the frameworks of fractal analysis it has been shown that this results to polymers yielding process realization not in the entire sample volume, but in its part only. 

More specific values of the fracture toughness are obtained by the application of the experimental procedures derived from the fracture mechanics theories. In the case of no plastic deformation in front of the crack tip, the LEFM is employed, obtaining the values of the stress critical intensity factor (fQ) or critical stress energy release rate (G,.). On the other hand, when there is plasticity in front of the crack tip, we must use the principles of the elastoplastic fracture mechanics in this sense, two experimental procedures are widely employed the J-integral analysis and the EWF. 

Buildings and Bridges Equipped with Passive Dampers Under Seismic Actions Modeling and Analysis, Fig. 8 Idealized elastoplastic pushover curve used for linear analysis (Symans et al. 2008)... 

The 2003 NEHRP Recommended Provisions (BSSC 2004) specify procedures for ncmtinear static analysis and nonlinear dynamic (response-history) analysis. The nonlinear static analysis procedure is similar to the ELF procedure, in that the pushover capacity curve is used to define the nonlinear behavior of the structure. However, in the nonlinear static analysis procedure, the actual nonlinear force-displacement relation is used, rather than an idealized elastoplastic curve. In addition, since actual pushover strength is known from the nonlinear pushover analysis, the force reduction for design of the seismic-force-resisting system is based on overstrength alone with no additional reduction (Symans et al. 2008). 

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