On a tensor cross product based formulation of large strain solid mechanics

被引:60
作者
Bonet, Javier [1 ]
Gil, Antonio J. [2 ]
Ortigosa, Rogelio [2 ]
机构
[1] Univ Greenwich, London SE10 9LS, England
[2] Swansea Univ, Coll Engn, Zienkiewicz Ctr Computat Engn, Bay Campus, Swansea SA1 8EN, W Glam, Wales
关键词
Large strain elasticity; Polyconvex elasticity; Complementary energy; Incompressible elasticity; Tensor cross product; Generalised Gibbs energy function; FINITE-ELEMENT-ANALYSIS; FRAMEWORK;
D O I
10.1016/j.ijsolstr.2015.12.030
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
This paper describes in detail the formulation of large strain solid mechanics based on the tensor cross product, originally presented by R. de Boer (1982) and recently re-introduced by Bonet et al. (2015a) and Bonet et al. (2015b). The paper shows how the tensor cross product facilitates the algebra associated with the area and volume maps between reference and final configurations. These maps, together with the fibre map, make up the fundamental kinematic variables in polyconvex elasticity. The algebra proposed leads to novel expressions for the tangent elastic operator which neatly separates material from geometrical dependencies. The paper derives new formulas for the spatial and material stress and their corresponding elasticity tensors. These are applied to the simple case of a Mooney-Rivlin material model. The extension to transversely isotropic material models is also considered. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码:49 / 63
页数:15
相关论文
共 44 条
  • [1] [Anonymous], 1992, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)
  • [2] [Anonymous], 1982, VektorUnd Tensorrechnung Fur Ingenieure
  • [3] Ball J.M., 1983, P INT C MATH WARS
  • [4] Some open problems in elasticity
    Ball, JM
    [J]. GEOMETRY, MECHANICS AND DYNAMICS: VOLUME IN HONOR OF THE 60TH BIRTHDAY OF J. E. MARSDEN, 2002, : 3 - 59
  • [5] BALL JM, 1984, J FUNCT ANAL, V58, P225, DOI 10.1016/0022-1236(84)90041-7
  • [6] BALL JM, 1977, ARCH RATION MECH AN, V63, P337, DOI 10.1007/BF00279992
  • [7] A polyconvex framework for soft biological tissues.: Adjustment to experimental data
    Balzani, D.
    Neff, P.
    Schroeder, J.
    Holzapfel, G. A.
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2006, 43 (20) : 6052 - 6070
  • [8] Belytschko T., 2013, Nonlinear Finite Elements For Continua and Structures
  • [9] Bonet J, 2008, NONLINEAR CONTINUUM MECHANICS FOR FINITE ELEMENT ANALYSIS, 2ND EDITION, P1, DOI 10.1017/CBO9780511755446
  • [10] Large strain viscoelastic constitutive models
    Bonet, J
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2001, 38 (17) : 2953 - 2968