# A path-dependent necking instability analysis of the thin substrate composite plates considering nonlinear reinforced layer effects

A path-dependent necking instability analysis of the thin substrate composite plates considering... In this paper, an analytical path-dependent instability model is proposed for the thin substrate composite plates, considering the nonlinear reinforced layer effects. The model is introduced by extending a modified maximum force criterion (MMFC) and the vertex criteria to predict diffuse and localized necking, respectively, for the thin substrate-supported plates. The MMFC considers the strain hardening on the diffuse necking as well as the loading conditions. The vertex criteria presented by St o ¨ re $$\ddot{\mathrm{o}}\mathrm{re}$$ n and Rice are usually based on the J 2 deformation theory of classical plasticity, which explores the localized necking through the rate discontinuity assumption at the necking band. Both models will be combined with the strain path effect through a linear adoption of an equivalent strain. It will be investigated by applying a pre-strain in the major and minor directions. Moreover, a dependent to yield criterion (DYC) angle is used for prediction of the necking band angle in the vertex theory. Also, a nonlinear neo-Hookean reinforced layer is considered to make a sensible delay at plastic deformation. Since the reinforcing layers are the materials with high stretchability, the effects of material properties and thickness values will be studied for supporting metal layers. Also, it is assumed that the incompressibility condition remains for corresponded elastomer and metal layer strains. Finally, the quadratic Hill criterion is used to investigate the anisotropy effect. The model is verified by experimental and other theoretical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The International Journal of Advanced Manufacturing Technology Springer Journals

# A path-dependent necking instability analysis of the thin substrate composite plates considering nonlinear reinforced layer effects

, Volume 95 (4) – Nov 3, 2017
16 pages

/lp/springer_journal/a-path-dependent-necking-instability-analysis-of-the-thin-substrate-IvtxGx4x48
Publisher
Springer London
Subject
Engineering; Industrial and Production Engineering; Media Management; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design
ISSN
0268-3768
eISSN
1433-3015
D.O.I.
10.1007/s00170-017-1230-0
Publisher site
See Article on Publisher Site

### Abstract

In this paper, an analytical path-dependent instability model is proposed for the thin substrate composite plates, considering the nonlinear reinforced layer effects. The model is introduced by extending a modified maximum force criterion (MMFC) and the vertex criteria to predict diffuse and localized necking, respectively, for the thin substrate-supported plates. The MMFC considers the strain hardening on the diffuse necking as well as the loading conditions. The vertex criteria presented by St o ¨ re $$\ddot{\mathrm{o}}\mathrm{re}$$ n and Rice are usually based on the J 2 deformation theory of classical plasticity, which explores the localized necking through the rate discontinuity assumption at the necking band. Both models will be combined with the strain path effect through a linear adoption of an equivalent strain. It will be investigated by applying a pre-strain in the major and minor directions. Moreover, a dependent to yield criterion (DYC) angle is used for prediction of the necking band angle in the vertex theory. Also, a nonlinear neo-Hookean reinforced layer is considered to make a sensible delay at plastic deformation. Since the reinforcing layers are the materials with high stretchability, the effects of material properties and thickness values will be studied for supporting metal layers. Also, it is assumed that the incompressibility condition remains for corresponded elastomer and metal layer strains. Finally, the quadratic Hill criterion is used to investigate the anisotropy effect. The model is verified by experimental and other theoretical results.

### Journal

The International Journal of Advanced Manufacturing TechnologySpringer Journals

Published: Nov 3, 2017

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