Interaction and Microfracturing Pattern for Successive Origination (Introduction) of Pores in Elastic Bodies: Finite Deformation

1998 ◽  
Vol 65 (2) ◽  
pp. 431-435 ◽  
Author(s):  
V. A. Levin ◽  
K. M. Zingerman
Keyword(s):  
Finite Deformation ◽  
Elastic Interaction ◽  
Finite Deformations ◽  
Qualitative And Quantitative ◽  
Elastic Bodies

The elastic interaction of holes, micropores, and narrow slots (cracks), introduced (originated) successively or simultaneously in previously loaded bodies, is analyzed under finite deformations. Their origination raises an additional finite deformations superimposed on the finite initial ones. The influence of mutual positions of holes, distances between them, their eccentricities and sizes on interaction is investigated. Qualitative and quantitative effects concerned with the finiteness of strains are considered.

Tensorial Deformation Measures for Flexible Joints

2010 ◽  
Vol 6 (3) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Leihong Li ◽  
Pierangelo Masarati ◽  
Marco Morandini
Keyword(s):  
Finite Deformation ◽  
Nonlinear Behavior ◽  
Critical Issue ◽  
Finite Deformations ◽  
Flexible Joints ◽  
Elastic Bodies ◽  
Infinitesimal Deformations ◽  
Stiffness Characteristics ◽  
Definition Of

Flexible joints, sometimes called bushing elements or force elements, are found in all multibody dynamics codes. In their simplest form, flexible joints simply consist of sets of three linear and three torsional springs placed between two nodes of a multibody system. For infinitesimal deformations, the selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements. If the joint undergoes finite deformations, the identification of its stiffness characteristics is not so simple, especially if the joint itself is a complex system. When finite deformations occur, the definition of deformation measures becomes a critical issue. Indeed, for finite deformation, the observed nonlinear behavior of materials is partly due to material characteristics and partly due to kinematics. This paper focuses on the determination of the proper finite deformation measures for elastic bodies of finite dimension. In contrast, classical strain measures, such as the Green–Lagrange or Almansi strains, among many others, characterize finite deformations of infinitesimal elements of a body. It is argued that proper finite deformation measures must be of a tensorial nature, i.e., must present specific invariance characteristics. This requirement is satisfied if and only if the deformation measures are parallel to the eigenvector of the motion tensor.

Finite Deformations of a Rigid Perfectly Plastic Arch

1962 ◽  
Vol 29 (3) ◽  
pp. 549-553 ◽  
Author(s):  
E. T. Onat ◽  
L. S. Shu
Keyword(s):  
Closed Form ◽  
Yield Point ◽  
Finite Deformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Deformations ◽  
Deformation History ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
History Of

The quasi-static postyield deformation of a rigid-plastic arch in the presence of geometry changes is considered. The problem is formulated in terms of a series of boundary-value problems concerned with rates of stress and velocities. In the present simple case, the consideration of the rate problem associated with the yield-point state of the structure enables one to construct a closed-form solution which describes the entire deformation history of the arch. However, the principal aim of the present study is to stress the central role played by the rate problem in the investigation of the finite deformation of structures.

The Singularity Strength at the Apex of a Wedge Undergoing Finite Deformations

1990 ◽  
Vol 57 (3) ◽  
pp. 577-580 ◽  
Author(s):  
J. M. Duva
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Finite Deformation ◽  
Finite Deformations ◽  
The Other ◽  
Nonlinear Material ◽  
Singular Behavior ◽  
Arbitrary Size

Herein we establish general formulae for characterizing the singular behavior at the apex of a wedge of nonlinear material of arbitrary size undergoing plane-strain finite deformation. Two sets of boundary conditions are considered: (a) both wedge flanks are clamped, and (b) one flank is clamped and the other free. The mode of deformation is obtained in one simple case for illustration.

Generalized FVDAM Theory for Periodic Materials Undergoing Finite Deformations—Part I: Framework

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Marek-Jerzy Pindera
Keyword(s):  
Finite Volume ◽  
Finite Deformation ◽  
Large Deformations ◽  
Finite Deformations ◽  
Stress Concentrations ◽  
Field Representation ◽  
Deformation Features ◽  
Elasticity Problems ◽  
Periodic Materials ◽  
Artificial Stress

The recently constructed generalized finite-volume theory for two-dimensional linear elasticity problems on rectangular domains is further extended to make possible simulation of periodic materials with complex microstructures undergoing finite deformations. This is accomplished by embedding the generalized finite-volume theory with newly incorporated finite-deformation features into the 0th order homogenization framework, and introducing parametric mapping to enable efficient mimicking of complex microstructural details without artificial stress concentrations by stepwise approximation of curved surfaces separating adjacent phases. The higher-order displacement field representation within subvolumes of the discretized unit cell microstructure, expressed in terms of elasticity-based surface-averaged kinematic variables, substantially improves interfacial conformability and pointwise traction and nontraction stress continuity between adjacent subvolumes. These features enable application of much larger deformations in comparison with the standard finite-volume direct averaging micromechanics (FVDAM) theory developed for finite-deformation applications by minimizing interfacial interpenetrations through additional kinematic constraints. The theory is constructed in a manner which facilitates systematic specialization through reductions to lower-order versions with the 0th order corresponding to the standard FVDAM theory. Part I presents the theoretical framework. Comparison of predictions by the generalized FVDAM theory with its predecessor, analytical and finite-element results in Part II illustrates the proposed theory's superiority in applications involving very large deformations.

Velocity field and strain-rates in plastic deformation

1967 ◽  
Vol 2 (3) ◽  
pp. 196-206 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Velocity Field ◽  
Finite Deformation ◽  
Finite Deformations ◽  
The Other ◽  
Strain Rates ◽  
Steady State Flow ◽  
Quantitative Results ◽  
The One

Grid lines have often been scribed, printed or photographed on metal surfaces for studying plastic deformation. Hitherto, most of them have been used only for qualitative results. It has been shown in a previous paper (2)∗ how quantitative results on finite deformations can be derived from a deformed grid. As a sequel to that paper, a method is presented here for deriving the rates of deformation from deformed grids. The relation between the velocity field on the one hand and the strain-rates and rotations on the other is first discussed. The theory thus developed is then applied to the cases of steady-state and non-steady-state flow, with practical example for the former. The connection between finite deformation and rate of deformation is also explained.

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