Micromechanics as a Basis of Stochastic Finite Elements and Differences: An Overview

1993 ◽  
Vol 46 (11S) ◽  
pp. S136-S147 ◽  
Author(s):  
M. Ostoja-Starzewski
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Classical Method ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Solution Methods ◽  
Stochastic Solution ◽  
Stochastic Finite Elements

A generalization of conventional deterministic finite element and difference methods to deal with spatial material fluctuations hinges on the problem of determination of stochastic constitutive laws. This problem is analyzed here through a paradigm of micromechanics of elastic polycrystals and matrix-inclusion composites. Passage to a sought-for random meso-continuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that the microstructure cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields may be introduced to bound the material response from above and from below. Since the RVE corresponds to a single finite element, or finite difference cell, not infinitely larger than the crystal size, these two random fields are to be used to bound the solution of a given boundary value problem at a given scale of resolution. The window-based random continuum formulation is also employed in analysis of rigid perfectly-plastic materials, whereby the classical method of slip-lines is generalized to a stochastic finite difference scheme. The present paper is complemented by a comparison of this methodology to other existing stochastic solution methods.

Identification Scheme to Assess the Role of Interfacial Damage in a Hemp-Starch Biocomposite

2014 ◽  
Vol 875-877 ◽  
pp. 524-528
Author(s):  
Sofiane Guessasma ◽  
Mohameden Hbib ◽  
David Bassir
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Precise Determination ◽  
Mechanical Parameters ◽  
Interfacial Damage ◽  
Failure Properties ◽  
Experimental Response

This paper aims at studying the effect of interfacial damage on the mechanical behavior of starch - hemp composite. The procedure encompasses an experimental investigation towards the determination of microstructural features and mechanical testing of the material. A finite element model is developed to account for a particular damage kinetics that triggers failure properties. Our results show that the experimental evidence of interfacial damage driven failure is achieved. Finite element model is able to capture this feature using an abrupt damage criterion. But in order to identify the observed behavior, the experimental response is matched with the numerical one. This process tunes the mechanical parameters to fit the experimental response. The optimization process conducted in this way leads to a precise determination of the mechanical parameters that quantifies the observed ultimate properties.

Computational mechanical property determination of viscoelastic/plastic materials from nanoindentation creep test data

2009 ◽  
Vol 24 (3) ◽  
pp. 1245-1257 ◽  
Author(s):  
Jianjun Wang ◽  
Timothy C. Ovaert
Keyword(s):  
Mechanical Properties ◽  
Mechanical Property ◽  
Finite Element ◽  
Test Data ◽  
Plastic Material ◽  
Test Method ◽  
Element Formulation ◽  
Unknown Parameters ◽  
Plastic Materials

Nanoindentation is a widely accepted test method for materials characterization. On account of the complexity of contact deformation behavior, design of parametric constitutive models and determination of the unknown parameters is challenging. To address the need for identification of mechanical properties of viscoelastic/plastic materials from nanoindentation data, a combined numerical finite element/optimization-based indentation modeling tool was developed, fully self-contained, and capable of running on a PC as a stand-alone executable program. The approach uses inverse engineering and formulates the material characterization task as an optimization problem. The model development consists of finite element formulation, viscoelastic/plastic material models, heuristic estimation to obtain initial solution boundaries, and a gradient-based optimization algorithm for fast convergence to extract mechanical properties from the test data. A four-parameter viscoelastic/plastic model is presented, then a simplified three-parameter model with more rapid convergence. The end result is a versatile tool for indentation simulation and mechanical property analysis.

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

Plastic Flow of Random Media: Micromechanics, Markov Property and Slip-Lines

1992 ◽  
Vol 45 (3S) ◽  
pp. S75-S81 ◽  
Author(s):  
Martin Ostoja-Starzewski
Keyword(s):  
Random Media ◽  
Classical Method ◽  
Mean Field ◽  
Markov Property ◽  
Continuum Approximation ◽  
Field Equations ◽  
Slip Lines ◽  
Perfectly Plastic ◽  
Stochastic Solution ◽  
Difference Form

The classical method of slip-lines (characteristics) of planar flow of perfectly-plastic media is generalized to a stochastic setting. The media are charaterized by space-homogeneous statistics of the yield limit k, whose derivation is outlined on the basis of micromechanics. The field equations of the random continuum approximation lead to a stochastic hyperbolic system. This system, when stated in a finite difference form, displays a Markov property for the forward evolution. On that basis, two methods of solution of boundary value problems - an exact one and a mean-field one - are outlined through an example of a Cauchy problem. The principal observation is that even for a weak material randomness the stochastic solution may differ qualitatively from that of a homogeneous deterministic medium and have a strong scatter.

Finite Element Based Plastic Loads for Elbows With Local Wall Thinning

2007 ◽  
Author(s):  
Jong-Hyun Kim ◽  
Chang-Sik Oh ◽  
Joon-Hyuk Ahn ◽  
Yun-Jae Kim ◽  
Chi-Yong Park ◽  
...  
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Three Dimensional ◽  
Geometry Effect ◽  
Perfectly Plastic ◽  
Wall Thinning ◽  
Plastic Materials ◽  
Wide Range ◽  
Elastic Perfectly Plastic ◽  
Local Wall Thinning

Based on systematic three-dimensional (3-D), large strain FE limit analyses using elastic-perfectly plastic materials, this paper quantifies the effect of local wall thinning on plastic behaviors and TES (twice-elastic-slope) plastic loads for 90° elbows under in-plane bending. The thinning geometry is assumed to be rectangular rather than circular, but the nonlinear geometry effect is fully considered. Results from systematic analyses lead to simple approximations for TES plastic loads, covering a wide range of elbow and thinning geometries.

Incorporating topography into 2D resistivity modeling using finite-element and finite-difference approaches

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. F135-F142 ◽  
Author(s):  
Erhan Erdoğan ◽  
Ismail Demirci ◽  
Mehmet Emin Candansayar
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
High Resistivity ◽  
Topographic Effects ◽  
Surface Geometry ◽  
Forward Solution ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
2D Resistivity ◽  
Resistivity Modeling

We incorporate topography into the 2D resistivity forward solution by using the finite-difference (FD) and finite-element (FE) numerical-solution methods. To achieve this, we develop a new algorithm that solves Poisson’s equation using the FE and FD approaches. We simulate topographic effects in the modeling algorithm using three FE approaches and two alternative FD approaches in which the air portion of the mesh is represented by very resistive cells. In both methods, we use rectangular and triangular discretization. Furthermore, we account for topographic effects by distorting the FE mesh with respect to the topography. We compare all methods for accuracy and calculation time on models with varying surface geometry and resistivity distributions. Comparisons show that model responses are similar when high-resistivity values are assigned to the top half of the rectangular cells at the air/earth boundary with the FE and FD methods and when the FE mesh is distorted. This result supports the idea that topographic effects can be incorporated into the forward solution by using the FD method; in some cases, this method also shortens calculation times. Additionally, this study shows that an FD solution with triangular discretization can be used successfully to calculate 2D DC-resistivity forward solutions.

Determination of Young's modulus by spherical indentation

1997 ◽  
Vol 12 (9) ◽  
pp. 2459-2469 ◽  
Author(s):  
N. Huber ◽  
D. Munz ◽  
Ch. Tsakmakis
Keyword(s):  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Indentation Test ◽  
Spherical Indentation ◽  
Plastic Materials ◽  
Finite Element Calculations ◽  
Loading And Unloading ◽  
Elastic Plastic Materials

In this paper we consider elastic plastic materials that are tested by spherical indentation. Finite element calculations, which take into account nonlinear geometry properties, are carried out in order to determine the influence of the plastic history on the unloading response of the material. Two different iterative methods are proposed for determining Young's modulus under the assumption of a bilinear plasticity law. The first method deals with loading and unloading parts of the indentation test, whereas the second one deals only with unloading parts of the indentation test.

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