A Micromechanical Description of Granular Material Behavior

1981 ◽  
Vol 48 (2) ◽  
pp. 339-344 ◽  
Author(s):  
J. Christoffersen ◽  
M. M. Mehrabadi ◽  
S. Nemat-Nasser
Keyword(s):  
Granular Material ◽  
Virtual Work ◽  
Contact Forces ◽  
Material Behavior ◽  
Principle Of Virtual Work ◽  
General Representation ◽  
Volume Average ◽  
Macroscopic Deformation ◽  
The Individual ◽  
Tensorial Product

Considered is a sample of cohesionless granular material, in which the individual granules are regarded rigid, and which is subjected to overall macroscopic average stresses. On the basis of the principle of virtual work, and by an examination of the manner by which adjacent granules transmit forces through their contacts, a general representation is established for the macroscopic stresses in terms of the volume average of the (tensorial) product of the contact forces and the vectors which connect the centroids of adjacent contacting granules. Then the corresponding kinematics is examined and the overall macroscopic deformation rate and spin tensors are developed in terms of the volume average of relevant microscopic kinematical variables. As an illustration of the application of the general expressions developed, two explicit macroscopic results are deduced: (1) a dilatancy equation which both qualitatively and quantitatively seems to be in accord with experimental observation, and (2) a noncoaxiality equation which seems to support the vertex plasticity model. Since the development is based on a microstructural consideration, all material coefficients entering the results have well-defined physical interpretations.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

scholarly journals Discrete element model for general polyhedra

2021 ◽  
Author(s):  
Alfredo Gay Neto ◽  
Peter Wriggers
Keyword(s):  
Frictional Contact ◽  
Virtual Work ◽  
Particle Surface ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Principle Of Virtual Work ◽  
Dynamics Model ◽  
Railway Ballast ◽  
Multibody Dynamics Model

AbstractWe present a version of the Discrete Element Method considering the particles as rigid polyhedra. The Principle of Virtual Work is employed as basis for a multibody dynamics model. Each particle surface is split into sub-regions, which are tracked for contact with other sub-regions of neighboring particles. Contact interactions are modeled pointwise, considering vertex-face, edge-edge, vertex-edge and vertex-vertex interactions. General polyhedra with triangular faces are considered as particles, permitting multiple pointwise interactions which are automatically detected along the model evolution. We propose a combined interface law composed of a penalty and a barrier approach, to fulfill the contact constraints. Numerical examples demonstrate that the model can handle normal and frictional contact effects in a robust manner. These include simulations of convex and non-convex particles, showing the potential of applicability to materials with complex shaped particles such as sand and railway ballast.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

Static analysis of spatial parallel manipulators by means of the principle of virtual work

2012 ◽  
Vol 28 (3) ◽  
pp. 385-401 ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
José M. Rico-Martínez ◽  
Salvador Pacheco-Gutiérrez ◽  
Gustavo Cerda-Villafaña
Keyword(s):  
Static Analysis ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Principle Of Virtual Work

Optimal Design of Bi- and Multi-Stable Compliant Cellular Structures

2018 ◽  
Author(s):  
Quantian Luo ◽  
Liyong Tong
Keyword(s):  
Optimal Design ◽  
Virtual Work ◽  
Reaction Force ◽  
Nonlinear Finite Element ◽  
Cellular Structures ◽  
Stress And Strain ◽  
Principle Of Virtual Work ◽  
Stable States ◽  
Threshold Method ◽  
Element Analysis

This paper presents optimal design for nonlinear compliant cellular structures with bi- and multi-stable states via topology optimization. Based on the principle of virtual work, formulations for displacements and forces are derived and expressed in terms of stress and strain in all load steps in nonlinear finite element analysis. Optimization for compliant structures with bi-stable states is then formulated as: 1) to maximize the displacement under specified force larger than its critical one; and 2) to minimize the reaction force for the prescribed displacement larger than its critical one. Algorithms are developed using the present formulations and the moving iso-surface threshold method. Optimal design for a unit cell with bi-stable states is studied first, and then designs of multi-stable compliant cellular structures are discussed.

Affine Versus Non-Affine Fibril Kinematics in Collagen Networks: Theoretical Studies of Network Behavior

2005 ◽  
Vol 128 (2) ◽  
pp. 259-270 ◽  
Author(s):  
Preethi L. Chandran ◽  
Victor H. Barocas
Keyword(s):  
Network Model ◽  
Constitutive Modeling ◽  
Load Transfer ◽  
Critical Role ◽  
Affine Model ◽  
Tissue Equivalents ◽  
Scale Models ◽  
Macroscopic Deformation ◽  
The Individual ◽  
Open Question

The microstructure of tissues and tissue equivalents (TEs) plays a critical role in determining the mechanical properties thereof. One of the key challenges in constitutive modeling of TEs is incorporating the kinematics at both the macroscopic and the microscopic scale. Models of fibrous microstructure commonly assume fibrils to move homogeneously, that is affine with the macroscopic deformation. While intuitive for situations of fibril-matrix load transfer, the relevance of the affine assumption is less clear when primary load transfer is from fibril to fibril. The microstructure of TEs is a hydrated network of collagen fibrils, making its microstructural kinematics an open question. Numerical simulation of uniaxial extensile behavior in planar TE networks was performed with fibril kinematics dictated by the network model and by the affine model. The average fibril orientation evolved similarly with strain for both models. The individual fibril kinematics, however, were markedly different. There was no correlation between fibril strain and orientation in the network model, and fibril strains were contained by extensive reorientation. As a result, the macroscopic stress given by the network model was roughly threefold lower than the affine model. Also, the network model showed a toe region, where fibril reorientation precluded the development of significant fibril strain. We conclude that network fibril kinematics are not governed by affine principles, an important consideration in the understanding of tissue and TE mechanics, especially when load bearing is primarily by an interconnected fibril network.

On the Sufficiency of the Principle of Virtual Work for Mechanical Equilibrium: A Critical Reexamination

1989 ◽  
Vol 56 (3) ◽  
pp. 704-707 ◽  
Author(s):  
John G. Papastavridis
Keyword(s):  
Virtual Work ◽  
Mechanical Equilibrium ◽  
Principle Of Virtual Work ◽  
Holonomic Constraints ◽  
Kinetic Principle ◽  
Sufficiency Conditions

Starting from the general kinetic principle of d’Alembert/Lagrange, an energetic proof of the sufficiency conditions for equilibrium (known as Principle of Virtual Work) is presented. It is clearly demonstrated why to maintain equilibrium requires that, in addition to the familiar vanishing of the virtual work of the impressed forces on the originally motionless system, its geometrical (holonomic) constraints be explicitly time independent (stationary) and its nonintegrable kinematical (nonholonomic) ones be linear and homogeneous in the generalized velocities (catastatic).

Dynamic Analysis of Flexible Manipulator Arms With Distributed Viscoelastic Damping

1997 ◽  
Vol 119 (4) ◽  
pp. 831-833 ◽  
Author(s):  
Fan Zijie ◽  
Lu Bingheng ◽  
C. H. Ku
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Dynamic Analysis ◽  
Virtual Work ◽  
Robot Manipulators ◽  
Flexible Manipulator ◽  
Viscoelastic Damping ◽  
Principle Of Virtual Work ◽  
Flexible Robot ◽  
Damping Treatments

The main objective of this work is to predict the effect of distributed viscoelastic damping on the dynamic response of multilink flexible robot manipulators. A general approach, based on the principle of virtual work, is presented for the modeling of flexible robot arms with distributed viscoelastic damping. The finite element equations are developed, and a recurrence formulation for numerical integration of these equations is obtained. It is demonstrated, by a numerical example, that the viscoelastic damping treatments have a significant effect on the dynamic response of flexible robot manipulators.

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