Random Fiber Networks and Special Elastic Orthotropy of Paper |
| |
Authors: | M Ostoja-Starzewski DC Stahl |
| |
Institution: | (1) Institute of Paper Science and Technology, Atlanta, GA, 30318-5794, U.S.A.;(2) Architectural Engineering and Building Construction, Milwaukee School of Engineering, Milwaukee, WI, 53202-3109, U.S.A. |
| |
Abstract: | We consider a particular in-plane elastic orthotropy observed experimentally for various types of paper, namely: S
1111+S
2222−2S
1122=S
1212, where S
ijkm
are components of the in-plane compliance tensor. This is a statement of the invariance of in-plane shear compliance S
1212, which has been observed in some studies but questioned in others. We present a possible explanation of this “special orthotropy”
of paper, using an analysis in which paper is modeled as a quasi-planar random microstructure of interacting fiber-beams –
a model especially well suited for low basis weight papers. First, it is shown analytically that without disorder a periodic
fiber network fails the special orthotropy. Next, using a computational mechanics model, we demonstrate that two-scale geometric
disorder in a fiber network is necessary to explain this orthotropy. Indeed, disordered networks with weak flocculation best
satisfy this relationship. It is shown that no special angular distribution function of fibers is required, and that the uniform
strain assumption should not be used. Finally, it follows from an analogy to the thermal conductivity problem that the kinematic
boundary conditions, rather than the traction ones, lead quite rapidly to relatively scale-independent effective constitutive
responses.
This revised version was published online in July 2006 with corrections to the Cover Date. |
| |
Keywords: | random media special orthotropy fiber networks micromechanics scale effects |
本文献已被 SpringerLink 等数据库收录! |
|