Numerical treatment of generalized plasticity with anisotropic elastic range in the case of plane stress

2000 ◽  
Vol 25 (5) ◽  
pp. 448-455
Author(s):  
C. Huettel ◽  
A. Matzenmiller
Keyword(s):  
Plane Stress ◽  
Numerical Treatment ◽  
Elastic Range ◽  
Generalized Plasticity ◽  
Anisotropic Elastic

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

Antiplane Deformations

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Antiplane Deformation ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Rectangular Coordinate System ◽  
Elastic Bodies ◽  
Basic Solutions ◽  
Anisotropic Elastic ◽  
Anisotropic Elastic Material

As a starter for anisotropic elastostatics we study special two-dimensional deformations of anisotropic elastic bodies, namely, antiplane deformations. Not all anisotropic elastic materials are capable of an antiplane deformation. When they are, the inplane displacement and the antiplane displacement are uncoupled. The deformations due to inplane displacement are plane strain deformations. Associated with plane strain deformations are plane stress deformations. After defining these special deformations in Sections 3.1 and 3.2 we present some basic solutions of antiplane deformations. They provide useful references for more general deformations we will study in Chapters 8, 10, and 11. The derivation and motivation in solving more general deformations in those chapters become more transparent if the reader reads this chapter first. The solutions obtained in those chapters reduce to the solutions presented here when the materials are restricted to special materials and the deformations are limited to antiplane deformations. In a fixed rectangular coordinate system xi (i=1, 2, 3), let ui, σij, and εij be the displacement, stress, and strain, respectively. The strain-displacement relations and the equations of equilibrium are . . .εij = 1/2 (ui,j + uj,i),. . . . . . (3.1 -1) . . . . . .σij,j =0,. . . . . . (3.1 - 2). . . in which repeated indices imply summation and a comma stands for differentiation. The stress-strain laws for an anisotropic elastic material can be written as σij = Cijks εks or εij = Sijksσks, . . .(3.1 - 3). . . where Cijks and Sijks are, respectively, the elastic stiffnesses and compliances.

Reexamination of Jumps Across Quasi-Statically Propagating Surfaces Under Generalized Plane Stress in Anisotropically Hardening Elastic-Plastic Solids

1987 ◽  
Vol 54 (3) ◽  
pp. 519-524 ◽  
Author(s):  
R. Narasimhan ◽  
A. J. Rosakis
Keyword(s):  
Plane Stress ◽  
Velocity Vector ◽  
Sliding Velocity ◽  
Previous Approach ◽  
Elastic Plastic ◽  
Strong Discontinuities ◽  
Perfectly Plastic ◽  
Constitutive Response ◽  
Anisotropic Elastic ◽  
Elastic Perfectly Plastic

Strong discontinuities across quasi-statically propagating surfaces in anisotropic elastic-plastic solids under generalized plane stress are reexamined allowing for some generality in constitutive response and taking into account the phenomenon of necking. Jumps in stresses are ruled out on the basis of material stability postulates and a previous approach (by Pan, 1982) is discussed. It is noted that for elastic-perfectly plastic solids, sliding velocity discontinuities occur under restrictive and exceptional conditions (when both the surface and its normal are stress characteristics) for generalized plane stress as compared to plane strain. Necks may form along (stress) characteristic directions with the relative velocity vector orthogonal to the other family of characteristics.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

Sign in / Sign up

Export Citation Format

Share Document