A stabilized mixed three-field formulation for stress accurate analysis including the incompressible limit in finite strain solid dynamics

被引:7
|
作者
Castanar, Inocencio [1 ]
Codina, Ramon [1 ,2 ]
Baiges, Joan [1 ,2 ,3 ]
机构
[1] Univ Politecn Cataluna, Barcelona Tech, Barcelona, Spain
[2] Ctr Int Metodes Numer Engn CIMNE, Barcelona, Spain
[3] Univ Politecn Cataluna, Barcelona Tech, Jordi Girona1-3,Edif C1, Barcelona 08034, Spain
关键词
incompressible hyperelasticity; mixed interpolations; orthogonal subgrid scales; solid dynamics; stabilization methods; 1ST-ORDER HYPERBOLIC FRAMEWORK; MOMENTUM CONSERVING ALGORITHMS; PETROV-GALERKIN FORMULATION; ELEMENT APPROXIMATION; PROJECTION METHODS; EXACT ENERGY; SIMULATIONS; ELASTICITY; STOKES;
D O I
10.1002/nme.7213
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this work a new methodology for finite strain solid dynamics problems for stress accurate analysis including the incompressible limit is presented. In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint in finite strain solid dynamics. To this end, the momentum equation is complemented with a constitutive law for the pressure which emerges from the deviatoric/volumetric decomposition of the strain energy function for any hyperelastic material model. The incompressible limit is attained automatically depending on the material bulk modulus. This work exploits the concept of mixed methods to formulate stable displacement/pressure/deviatoric stress finite elements. The final goal is to design a finite element technology able to tackle simultaneously problems which may involve incompressible behavior together with a high degree of accuracy of the stress field. The variational multi-scale stabilization technique and, in particular, the orthogonal subgrid scale method allows the use of equal-order interpolations. These stabilization procedures lead to discrete problems which are fully stable, free of volumetric locking, stress oscillations and pressure fluctuations. Numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding stabilized mixed displacement/pressure formulation.
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页码:2341 / 2366
页数:26
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