Micropolar hyperelasticity: constitutive model, consistent linearization and simulation of 3D scale effects

被引：12

作者：

Bauer, S. ^{[1
]}

Dettmer, W. G. ^{[2
]}

Peric, D. ^{[2
]}

Schaefer, M. ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Chair Numer Methods Mech Engn, D-64293 Darmstadt, Germany

[2] Swansea Univ, Civil & Computat Engn Res Ctr, Coll Engn, Swansea SA2 8PP, W Glam, Wales

来源：

COMPUTATIONAL MECHANICS | 2012年 / 50卷 / 04期

关键词：

Cosserat; Micropolar; Neo-Hooke hyperelasticity; Consistent linearization; Size effect; FINITE-ELEMENT IMPLEMENTATION; STRESS-CONCENTRATION; PLASTICITY; DEFORMATION; LOCALIZATION; MECHANICS; SOLIDS;

D O I：

10.1007/s00466-012-0679-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This study describes a computational framework for three-dimensional finite strain and finite curvature micropolar hyperelasticity. The model is based on the non-linear kinematic setting and features an appropriate hyperelastic material law which is derived within the thermodynamically consistent framework. The material tangent operator is obtained by consistent linearization. An implicit finite element method with a Newton-Raphson procedure is employed for the computation of the nodal displacements and rotations. A number of numerical examples is presented. The results demonstrate (i) that the methodology is capable of capturing 3D length scale effects in finite deformation, (ii) that it is robust and computationally efficient and (iii) that the proposed micropolar element tangent renders asymptotically quadratic convergence of the Newton-Raphson procedure. It is shown that the classical Neo-Hooke type material behaviour is recovered as a special case within the proposed micropolar setting.

引用

页码：383 / 396

页数：14