A finite deformation brick element with inhomogeneous mode enhancement

In this paper we describe a new enhanced assumed strain finite element for finite deformations. The element is based on the split of the deformation of an element into a homogeneous and inhomogeneous part. The enhancement is applied to the inhomogeneous part only. For the homogeneous part a compressible Neo-Hooke material is used, while for the inhomogeneous part linear elasticity is assumed. In several examples it is shown that the element is locking and hourglassing free as well as insensitive to initial element distortion. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  J. C. Rice,et al.  On numerically accurate finite element solutions in the fully plastic range , 1990 .

[2]  Francisco Armero,et al.  On the formulation of enhanced strain finite elements in finite deformations , 1997 .

[3]  Peter Wriggers,et al.  A FORMULATION OF THE QS6 ELEMENT FOR LARGE ELASTIC DEFORMATIONS , 1996 .

[4]  B. Wohlmuth,et al.  Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D , 2007 .

[5]  Francisco Armero,et al.  Assumed strain finite element methods for conserving temporal integrations in non‐linear solid dynamics , 2008 .

[6]  Peter Wriggers,et al.  Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing , 2005 .

[7]  E. Wilkes ON THE STABILITY OF A CIRCULAR TUBE UNDER END THRUST , 1955 .

[8]  L. P. Bindeman,et al.  Assumed strain stabilization of the eight node hexahedral element , 1993 .

[9]  Stefanie Reese,et al.  A new stabilization technique for finite elements in non-linear elasticity , 1999 .

[10]  N. S. Ottosen,et al.  Accurate eight‐node hexahedral element , 2007 .

[11]  Peter Wriggers,et al.  On enhanced strain methods for small and finite deformations of solids , 1996 .

[12]  S. Reese On a physically stabilized one point finite element formulation for three-dimensional finite elasto-plasticity , 2005 .

[13]  Peter Wriggers,et al.  Consistent gradient formulation for a stable enhanced strain method for large deformations , 1996 .

[14]  Ekkehard Ramm,et al.  EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements , 1993 .

[15]  K. Bathe,et al.  A finite element formulation for nonlinear incompressible elastic and inelastic analysis , 1987 .

[16]  S. Reese,et al.  A new locking-free brick element technique for large deformation problems in elasticity ☆ , 2000 .

[17]  J. M. Kennedy,et al.  Hourglass control in linear and nonlinear problems , 1983 .

[18]  Peter Wriggers,et al.  A new finite element based on the theory of a Cosserat point—extension to initially distorted elements for 2D plane strain , 2007 .

[19]  M. Rubin Numerical solution of axisymmetric nonlinear elastic problems including shells using the theory of a Cosserat point , 2005 .

[20]  T. Belytschko,et al.  Efficient implementation of quadrilaterals with high coarse-mesh accuracy , 1986 .

[21]  M. Rubin,et al.  A new 3-D finite element for nonlinear elasticity using the theory of a Cosserat point , 2003 .

[22]  J. C. Simo,et al.  Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes , 1992 .

[23]  J. C. Simo,et al.  Variational and projection methods for the volume constraint in finite deformation elasto-plasticity , 1985 .

[24]  Yavuz Başar,et al.  Finite-rotation shell elements for the analysis of finite-rotation shell problems , 1992 .

[25]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[26]  Eric P. Kasper,et al.  A mixed-enhanced strain method , 2000 .

[27]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[28]  Edward L. Wilson,et al.  Incompatible Displacement Models , 1973 .

[29]  Robert L. Taylor,et al.  A mixed-enhanced strain method: Part II: Geometrically nonlinear problems , 2000 .

[30]  Robert L. Taylor,et al.  Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems☆ , 1993 .