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Material plasticity to track the elastic anisotropy at finite strains
Author(s) -
Weber Martin,
Glüge Rainer,
Bertram Albrecht
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710210
Subject(s) - plasticity , anisotropy , stiffness , microscale chemistry , tensor (intrinsic definition) , cauchy stress tensor , materials science , representative elementary volume , finite element method , stress (linguistics) , structural engineering , microstructure , mechanics , mathematical analysis , mathematics , geometry , physics , composite material , engineering , linguistics , mathematics education , philosophy , quantum mechanics
We present a phenomenological finite elasto‐plasticity theory that includes the evolution of the elastic anisotropy. The theory is called Material Plasticity after [1] and [2], assuming that the axes of anisotropy deform as material line elements. It is applicable to fiber‐reinforced materials. The main feature is the different evolutions of the stiffness tetrad and of the stress‐free placement. For this purpose we extend the well known isomorphy concept (see [3]). To identify and compare the stiffness tetrads before and after large plastic deformations a representative volume element (RVE) [4] with a fiberous microstructure is used. Uni‐, bi‐ and and tridirectionally reinforced samples are considered. On the microscale a standard elastic‐plastic material model is used. After calculating the effective stiffnesses of the different material samples we investigate their evolution during different deformations. It turns out that it is possible to denote the change of the stiffness with sufficient accuracy using one additional second order tensor. After investigating the change in the stiffness tetrads we finally propose an analytical evolution equation for this tensor. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)