scholarly journals Use of a bounding surface model in predicting element tests and capacity in boundary value problems

2020 ◽  
Author(s):  
Anamitra Roy ◽  
Shiao Huey Chow ◽  
Conleth D O'Loughlin ◽  
Mark F. Randolph ◽  
Scott Whyte
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
System Level ◽  
Triaxial Tests ◽  
Parameter Determination ◽  
Surface Model ◽  
Model Parameters ◽  
Plasticity Model ◽  
Surface Plasticity ◽  
Simple Boundary

The paper examines the merit of a two surface plasticity model through an optimised calibration procedure and assesses the model performance in capturing the response at both element and system level. The governing equations are based essentially on the parent two surface plasticity model developed by Dafalias and Manzari (2004) with some simple yet practical changes to enable realistic predictions for monotonic loading along different load paths. This is achieved by scaling the influence of state parameter based on a normalised measure of anisotropy, thus leading to suitable change in dilatancy and plastic modulus for different loading directions. The paper presents a simple optimisation technique for calibrating the model parameters, providing an objective approach to reduce the uncertainties in parameter determination that leads to good agreement with responses measured in drained and undrained triaxial tests. The model has also been implemented for the boundary value problem of a buried circular plate anchor and a surface circular footing. Comparisons of the simulated responses with those measured in centrifuge tests demonstrate the potential of the model, whilst also pointing to the challenges in capturing the global response at all strain levels, even for rather simple boundary value problems.

A Two Surface Plasticity Model With Bounding Surface Softening

1996 ◽  
Vol 118 (1) ◽  
pp. 37-42 ◽  
Author(s):  
C. S. White
Keyword(s):  
Yield Surface ◽  
Cyclic Plasticity ◽  
Surface Model ◽  
Plasticity Model ◽  
Bounding Surface ◽  
Phase Cycling ◽  
Surface Plasticity ◽  
Cycling Behavior ◽  
Natural Way

Two surface plasticity models have been used increasingly in recent years to model not only uniaxial, cyclic plasticity but also multiaxial and nonproportional histories. A two surface model is presented here which predicts the increased hardening due to out-of-phase cycling in a natural way. It includes a mechanism by which the bounding surface contracts when the yield surface is not in contact. This provides a mechanism that is useful for modeling cycling behavior. Predictions of the model with experiments at moderate strain are presented.

Some boundary-value problems for uniform isotropic incompressible materials

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Boundary Value Problems ◽  
Explicit Solution ◽  
Spherical Symmetry ◽  
Boundary Value ◽  
Plane Shear ◽  
Simple Boundary ◽  
Incompressible Materials ◽  
Azimuthal Shear

This chapter outlines the formulation and explicit solution of a number of simple boundary-value problems. Analysis is facilitated by the constraint of incompressibility. Examples include expansionand contraction of cylinders, torsion, azimuthal shear, and cavitation under conditions of spherical symmetry Further examples involving anti-plane shear are discussed in the Problems.

On the Boundary Value Problems of Bending of Thin Elastic Plates With Surface Effects

2020 ◽  
Vol 88 (2) ◽  
Author(s):  
Alireza Gharahi ◽  
Peter Schiavone
Keyword(s):  
Boundary Value Problems ◽  
Plate Theory ◽  
Boundary Value ◽  
Integral Equation Method ◽  
Surface Effects ◽  
Boundary Integral ◽  
Thin Plates ◽  
Surface Model ◽  
Elastic Plates ◽  
Uniqueness Results

Abstract We modify classical thin plate theory by incorporating surface effects via the Gurtin–Murdoch surface model to accommodate the mechanical behavior of thin plates at the nanoscale. We formulate the corresponding Dirichlet and Neumann boundary value problems and establish uniqueness results in the appropriate function spaces. In addition, we obtain the fundamental solution of the governing system of equations, which is central to further studies concerning well-posedness analysis of the model by the boundary integral equation method. Finally, we validate our model by comparison with results in the existing literature.

XXI—The Whittaker-Hill Equation and the Wave Equation in Paraboloidal Co-ordinates

1967 ◽  
Vol 67 (4) ◽  
pp. 265-276 ◽  
Author(s):  
F. M. Arscott
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Formal Solution ◽  
Boundary Value ◽  
Hill Equation ◽  
Hill’S Equation ◽  
Simple Boundary ◽  
Hill's Equation ◽  
Helmholz Equation

SynopsisThe problem considered is that of obtaining solutions of the Helmholz equation ∇2V + k2V = 0, suitable for use in connection with paraboloidal co-ordinates. In these co-ordinates the Helmholz equation is separable, and each of the separated equations is reducible to Hill's equation with three terms (the Whittaker-Hill equation). The properties of solutions of this equation are developed sufficiently to make possible the formal solution of simple boundary-value problems for paraboloidal surfaces, principally for the case k2 < 0.

Existence of solution in the bending of thin plates with Gurtin–Murdoch surface elasticity

2021 ◽  
pp. 108128652110134
Author(s):  
Alireza Gharahi ◽  
Peter Schiavone
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Surface Elasticity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Thin Plates ◽  
Surface Model ◽  
Existence Of A Solution ◽  
Classical Boundary ◽  
Robin Boundary

We consider the well-posedness of classical boundary value problems in a theory of bending of thin plates which incorporates the effects of surface elasticity via the Gurtin–Murdoch surface model. We employ the fundamental solution of the governing system of equations to develop integral-type solutions of the corresponding Dirichlet, Neumann, and Robin boundary value problems. Using the boundary integral equation method, we subsequently establish results for the existence of a solution in the appropriate function spaces.

scholarly journals The basic elliptic equations in an equilateral triangle

2005 ◽  
Vol 461 (2061) ◽  
pp. 2721-2748 ◽  
Author(s):  
G Dassios ◽  
A.S Fokas
Keyword(s):  
Boundary Value Problems ◽  
Infinite Series ◽  
Equilateral Triangle ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Heat Diffusion ◽  
Global Relation ◽  
Neumann Problems ◽  
Change Of Variables ◽  
Simple Boundary

In his deep and prolific investigations of heat diffusion, Lamé was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular, he derived explicit results for the Dirichlet and Neumann cases using an ingenious change of variables. The relevant eigenfunctions are a complicated infinite series in terms of his variables. Here we first show that boundary-value problems with simple boundary conditions, such as the Dirichlet and the Neumann problems, can be solved in an elementary manner. In particular, the unknown Neumann and Dirichlet boundary values can be expressed in terms of a Fourier series for the Dirichlet and the Neumann problems, respectively. Our analysis is based on the so-called global relation, which is an algebraic equation coupling the Dirichlet and the Neumann spectral values on the perimeter of the triangle. As Lamé correctly pointed out, infinite series are inadequate for expressing the solution of more complicated problems such as mixed boundary-value problems. In this paper we show, further utilizing the global relation, that such problems can be solved in terms of generalized Fourier integrals .

scholarly journals ASSESSMENT OF A NEW ISOTROPIC HYPERELASTIC CONSTITUTIVE MODEL FOR A RANGE OF RUBBERLIKE MATERIALS AND DEFORMATIONS

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Cornelius O. Horgan ◽  
Giuseppe Saccomandi
Keyword(s):  
Boundary Value Problems ◽  
Linear Function ◽  
Mechanical Response ◽  
Boundary Value ◽  
Structural Basis ◽  
Model Parameters ◽  
Parameter Values ◽  
Deformation Modes ◽  
Single Set ◽  
Rubberlike Materials

ABSTRACT The choice of an appropriate strain energy function W is key to accurate modeling and computational finite element analysis of the mechanical behavior of unfilled non-crystalizing rubberlike materials. Despite the existing variety of models, finding a suitable model that can capture many deformation modes of a rubber specimen with a single set of parameter values and satisfy the a priori mathematical and structural requirements remains a formidable task. Previous work proposed a new generalized neo-Hookean W (I1) function, showing a promising fitting capability and enjoying a structural basis. We now use two extended forms of that model that include an I1 term adjunct, W (I1, I2), for application to various boundary value problems commonly encountered in rubber mechanics applications. Specifically, two functional forms of the I2 invariant are considered: a linear function and a logarithmic function. The boundary value problems of interest include the in-plane uniaxial, equi-biaxial, and pure shear deformations and simple shear, inflation, and nonhomogeneous deformations such as torsion. By simultaneous fitting of each model to various deformation modes of rubber specimens, it is demonstrated that a single set of model parameter values favorably captures the mechanical response for all the considered deformations of each specimen. It is further shown that the model with a logarithmic I2 function provides better fits than the linear function. Given the functional simplicity of the considered W (I1, I2) models, the low number of model parameters (three in total), the structurally motivated bases of the models, and their capability to capture the mechanical response for various deformations of rubber specimens, the considered models are recommended as a powerful tool for practical applications and analysis of rubber elasticity.

scholarly journals Application of advanced bounding surface plasticity model in static and seismic analyses of Zipingpu Dam

2016 ◽  
Vol 53 (3) ◽  
pp. 455-471 ◽  
Author(s):  
Mojtaba E. Kan ◽  
Hossein A. Taiebat
Keyword(s):  
Dynamic Behaviour ◽  
Constitutive Models ◽  
Numerical Procedure ◽  
In Situ Monitoring ◽  
Triaxial Tests ◽  
Plasticity Model ◽  
Bounding Surface ◽  
Bounding Surface Plasticity ◽  
Surface Plasticity ◽  
Simplified Procedures

The strong ground motion of the Wenchuan earthquake that hit the Zipingpu Dam in China in 2008 has provided an excellent benchmark to study the behaviour of large modern rockfill dams subjected to seismic loading. The performance of the dam during construction and prior to and after the earthquake loading has been recorded with good accuracy, and provides a reliable database to examine the reliability of available constitutive models and numerical methods in predicting the static and dynamic behaviour of embankment dams. In this paper, an advanced bounding surface plasticity model has been used in a series of numerical analyses to study the static and dynamic behaviour of Zipingpu Dam. The model can take into account particle breakage that may occur in monotonic and cyclic loading of rockfill materials. The material parameters required for the model are calibrated based on the results of available monotonic and cyclic triaxial tests. In the numerical procedure, the staged construction of the dam and the subsequent impounding of the reservoir are simulated, followed by dynamic loading. At each stage, the results of the numerical analysis are compared with in situ monitoring records of the dam. The results of the numerical simulation and the displacements measured after the earthquake are also compared with those estimated by two simplified engineering procedures that are routinely used in practice. The effectiveness and applicability of the simplified procedures to such a large dam subjected to an earthquake with a long duration is also discussed.

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