Elastic and Plastic Response of Perforated Metal Sheets With Different Porosity Architectures

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Hamed Khatam ◽  
Linfeng Chen ◽  
Marek-Jerzy Pindera
Keyword(s):  
Elastic Moduli ◽  
Volume Fraction ◽  
Stress Transfer ◽  
Local Stress ◽  
Shear Loading ◽  
Homogenization Theory ◽  
Plastic Response ◽  
Elastic Plastic ◽  
Aluminum Sheets ◽  
Metal Sheets

The effects of porosity architecture and volume fraction on the homogenized elastic moduli and elastic-plastic response of perforated thin metal sheets are investigated under three fundamental loading modes using an efficient homogenization theory. Steel and aluminum sheets weakened by circular, hexagonal, square, and slotted holes arranged in square and hexagonal arrays subjected to inplane normal and shear loading are considered with porosity volume fractions in the range 0.1–0.6. Substantial variations are observed in the homogenized elastic moduli with porosity shape and array type. The differences are rooted in the stress transfer mechanism around traction-free porosities whose shape and distribution play major roles in altering the local stress fields and thus the homogenized response in the elastic-plastic domain. This response is characterized by four parameters that define different stages of micro- and macrolevel yielding. The variations in these parameters due to porosity architecture and loading direction provide useful data for design purposes under monotonic and cyclic loading.

Locally Exact Homogenization of Unidirectional Composites With Cylindrically Orthotropic Fibers

2016 ◽  
Vol 83 (7) ◽  
Author(s):  
Guannan Wang ◽  
Marek-Jerzy Pindera
Keyword(s):  
Volume Fraction ◽  
Local Stress ◽  
Transversely Isotropic ◽  
Local Fields ◽  
Homogenization Theory ◽  
Classical Solutions ◽  
Equilibrium Equations ◽  
Fiber Volume ◽  
Unidirectional Composites ◽  
Cylindrically Orthotropic

The elasticity-based, locally exact homogenization theory for unidirectional composites with hexagonal and tetragonal symmetries and transversely isotropic phases is further extended to accommodate cylindrically orthotropic reinforcement. The theory employs Fourier series representations of the fiber and matrix displacement fields in cylindrical coordinate system that satisfy exactly equilibrium equations and continuity conditions in the interior of the unit cell. Satisfaction of periodicity conditions for the inseparable exterior problem is efficiently accomplished using previously introduced balanced variational principle which ensures rapid displacement solution convergence with relatively few harmonic terms. As demonstrated in this contribution, this also applies to cylindrically orthotropic reinforcement for which the eigenvalues depend on both the orthotropic elastic moduli and harmonic number. The solution's demonstrated stability facilitates rapid identification of cylindrical orthotropy's impact on homogenized moduli and local fields in wide ranges of fiber volume fraction and orthotropy ratios. The developed theory provides a unified approach that accounts for cylindrical orthotropy explicitly in both the homogenization process and local stress field calculations previously treated separately through a fiber replacement scheme. Comparison of the locally exact solution with classical solutions based on an idealized microstructural representation and fiber moduli replacement with equivalent transversely isotropic properties delineates their applicability and limitations.

scholarly journals Fractal Pattern Formation at Elastic-Plastic Transition in Heterogeneous Materials

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
J. Li ◽  
M. Ostoja-Starzewski
Keyword(s):  
Fractal Dimension ◽  
Elastic Moduli ◽  
Heterogeneous Materials ◽  
Shear Loading ◽  
Flow Rule ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Fractal Patterns ◽  
Random Fluctuations

Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random fluctuations in elastic moduli and/or yield limits and (2) a polycrystal made of randomly oriented anisotropic grains. In each case, the spatial assignment of material randomness is a nonfractal strict-white-noise field on a 256×256 square lattice of homogeneous square-shaped grains; the flow rule in each grain follows associated plasticity. These lattices are subjected to simple shear loading increasing through either one of three macroscopically uniform boundary conditions (kinematic, mixed-orthogonal, or static) admitted by the Hill–Mandel condition. Upon following the evolution of a set of grains that become plastic, we find that it has a fractal dimension increasing from 0 toward 2 as the material transitions from elastic to perfectly plastic. While the grains possess sharp elastic-plastic stress-strain curves, the overall stress-strain responses are smooth and asymptote toward perfectly plastic flows; these responses and the fractal dimension-strain curves are almost identical for three different loadings. The randomness in elastic moduli in the model with isotropic grains alone is sufficient to generate fractal patterns at the transition but has a weaker effect than the randomness in yield limits. As the random fluctuations vanish (i.e., the composite becomes a homogeneous body), a sharp elastic-plastic transition is recovered.

Plasticity Analysis of Fibrous Composites

1982 ◽  
Vol 49 (2) ◽  
pp. 327-335 ◽  
Author(s):  
G. J. Dvorak ◽  
Y. A. Bahei-El-Din
Keyword(s):  
Volume Fraction ◽  
Mechanical Load ◽  
Kinematic Hardening ◽  
Small Diameter ◽  
Local Stress ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Elastic Filaments ◽  
Stress Concentration Factors ◽  
Hardening Rules

The elastic-plastic behavior of composites consisting of aligned, continuous elastic filaments and an elastic-plastic matrix is described in terms of constituent properties, their volume fractions, and mutual constraints between the phases indicated by the geometry of the microstructure. The composite is modeled as a continuum reinforced by cylindrical fibers of vanishingly small diameter which occupy a finite volume fraction of the aggregate. In this way, the essential axial constraint of the phases is retained. Furthermore, the local stress and strain fields are uniform. Elastic moduli, yield conditions, hardening rules, and overall instantaneous compliances, as well as instantaneous stress concentration factors are derived. Specific results are obtained for the case of a Mises-type matrix which obeys the Prager-Ziegler kinematic hardening rule. Any multiaxial mechanical load may be applied. Comparisons are made between the present results and certain other theories.

scholarly journals An effective thermal conductivity and thermomechanical homogenization scheme for a multiscale Nb3Sn filaments

2021 ◽  
Vol 10 (1) ◽  
pp. 187-200
Author(s):  
Xiaoyu Zhao ◽  
Guannan Wang ◽  
Qiang Chen ◽  
Libin Duan ◽  
Wenqiong Tu
Keyword(s):  
Volume Fraction ◽  
Material Design ◽  
Axial Direction ◽  
High Heat ◽  
Thermomechanical Properties ◽  
Homogenization Theory ◽  
High Heat Flux ◽  
Element Analysis ◽  
Hierarchical Microstructure ◽  
Thermal Conductivities

Abstract A comprehensive study of the multiscale homogenized thermal conductivities and thermomechanical properties is conducted towards the filament groups of European Advanced Superconductors (EAS) strand via the recently proposed Multiphysics Locally Exact Homogenization Theory (LEHT). The filament groups have a distinctive two-level hierarchical microstructure with a repeating pattern perpendicular to the axial direction of Nb3Sn filament. The Nb3Sn filaments are processed in a very high temperature between 600 and 700°C, while its operation temperature is extremely low, −269°C. Meanwhile, Nb3Sn may experience high heat flux due to low resistivity of Nb3Sn in the normal state. The intrinsic hierarchical microstructure of Nb3Sn filament groups and Multiphysics loading conditions make LEHT an ideal candidate to conduct the homogenized thermal conductivities and thermomechanical analysis. First, a comparison with a finite element analysis is conducted to validate effectiveness of Multiphysics LEHT and good agreement is obtained for the homogenized thermal conductivities and mechanical and thermal expansion properties. Then, the Multiphysics LEHT is applied to systematically investigate the effects of volume fraction and temperature on homogenized thermal conductivities and thermomechanical properties of Nb3Sn filaments at the microscale and mesoscale. Those homogenized properties provide a full picture for researchers or engineers to understand the Nb3Sn homogenized properties and will further facilitate the material design and application.

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multi-trace Bayesian AVO petrophysics inversion in multi-porosity reservoirs

Geophysics ◽  
2021 ◽  
pp. 1-101
Author(s):  
Kun Li ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Dario Grana
Keyword(s):  
Bulk Modulus ◽  
Pore Volume ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
Volume Fraction ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Pore Volume Fraction ◽  
Pp Wave ◽  
Matrix Shear

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmann’s poro-elasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 2 - Case Studies

2021 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Lower Bound ◽  
Case Studies ◽  
Power Law ◽  
Elastic Moduli ◽  
New Method ◽  
Stress Distributions ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Thick Cylinder ◽  
Better Than

Abstract An accompanying paper provides the theoretical underpinnings of a new method to determine statically admissible stress distributions in a structure, called Bounded elastic moduli multiplier technique (BEMMT). It has been shown that, for textbook cases such as thick cylinder, beam, etc., the proposed method offers statically admissible stress distributions better than the power law and closer to elastic-plastic solutions. This paper offers several examples to demonstrate the robustness of this method. Upper and lower bound limit loads are calculated using iterative elastic analyses using both power law and BEMMT. These results are compared with the ones obtained from elastic-plastic FEA. Consistently BEMMT has outperformed power law when it comes to estimating lower bound limit loads.

Studies of Elastic-Plastic Instabilities

1999 ◽  
Vol 66 (1) ◽  
pp. 3-9 ◽  
Author(s):  
V. Tvergaard
Keyword(s):  
Shear Band ◽  
Plastic Flow ◽  
Continuum Mechanics ◽  
Shear Band Formation ◽  
Band Formation ◽  
Elastic Plastic ◽  
Localized Necking ◽  
Focus On Results ◽  
Metal Sheets ◽  
Bifurcation Behavior

Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formation in solids, localized necking in biaxially stretched metal sheets, and the analogous phenomenon of buckling localization in structures. Also some recent results for cavitation instabilities in elastic-plastic solids are reviewed.

scholarly journals Stress Transfer from Axially Loaded Fiber to Matrix in a Microcomposite

1994 ◽  
Vol 365 ◽  
Author(s):  
Chun-Hway Hsueh
Keyword(s):  
Analytical Solutions ◽  
Volume Fraction ◽  
Axial Stress ◽  
Stress Transfer ◽  
Radial Dependence ◽  
Shear Lag ◽  
Shear Lag Model ◽  
The Matrix ◽  
Lag Model ◽  
Loaded Fiber

ABSTRACTThe shear lag model has been used extensively to analyze the stress transfer in a singe fiberreinforced composite (i.e., a microcomposite). To achieve analytical solutions, various simplifications have been adopted in the stress analysis. Questions regarding the adequacy of those simplifications are discussed in the present study for the following two cases: bonded interfaces and frictional interfaces. Specifically, simplifications regarding (1) Poisson's effect, and (2) the radial dependences of axial stresses in the fiber and the matrix are addressed. For bonded interfaces, the former can be ignored, and the latter can generally be ignored. However, when the volume fraction of the fiber is high, the radial dependence of the axial stress in the fiber should be considered. For frictional interfaces, the latter can be ignored, but the former should be considered; however, it can be considered in an average sense to simplify the analysis. Comparisons among results obtained from analyses with various simplifications are made.

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