A Solid-Shell Element with Enhanced Assumed Strains for Higher Order Shear Deformations in Laminates

Based on previous research, our approach aims towards the analysis of laminated structures with solid-shell elements, combined with the higher order shear deformation theory to improve the transverse shear behaviour, necessary for stress based failure criteria in the analysis of inter-laminar fracture in multi-layer shells. As a side effect shear-locking is alleviated by incorporating the higher order transverse shear interpolation instead of using assumed natural strain formulations. The solid-shell element is used for the analysis of delamination in layered composite shells, where the onset of fracture in mode II and III critically depends on the transverse shear stress distribution in the cross section of the shell.

[1]  J. M. A. César de Sá,et al.  Enhanced transverse shear strain shell formulation applied to large elasto‐plastic deformation problems , 2005 .

[2]  P. Camanho,et al.  Decohesion Elements using Two and Three-Parameter Mixed-Mode Criteria , 2001 .

[3]  M. A. Crisfield,et al.  Progressive Delamination Using Interface Elements , 1998 .

[4]  Sven Klinkel,et al.  A geometrical non‐linear brick element based on the EAS‐method , 1997 .

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

[6]  Sven Klinkel,et al.  A robust non-linear solid shell element based on a mixed variational formulation , 2006 .

[7]  R. R. James,et al.  Refinements to the Mixed-Mode Bending Test for Delamination Toughness , 2000 .

[8]  R. Hauptmann,et al.  `Solid-shell' elements with linear and quadratic shape functions at large deformations with nearly incompressible materials , 2001 .

[9]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[10]  Sven Klinkel,et al.  A continuum based 3d-shell element for laminated structures , 1999 .

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

[12]  A. Matzenmiller,et al.  On the resolution of transverse stresses in solid-shells with a multi-layer formulation , 2006 .

[13]  Anton Matzenmiller,et al.  Consistent discretization of thickness strains in thin shells including 3D‐material models , 1999 .

[14]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[15]  F. D. Sciarra.  Relations between enhanced strain methods and the HR method , 2002 .

[16]  G. N. Jazar,et al.  Linear static analysis and finite element modeling for laminated composite plates using third order shear deformation theory , 2003 .

[17]  John C. Brewer,et al.  Quadratic Stress Criterion for Initiation of Delamination , 1988 .

[18]  E. Wilson,et al.  A non-conforming element for stress analysis , 1976 .

[19]  Ekkehard Ramm,et al.  An assessment of assumed strain methods in finite rotation shell analysis , 1989 .

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

[21]  Jeong Whan Yoon,et al.  A new approach to reduce membrane and transverse shear locking for one‐point quadrature shell elements: linear formulation , 2006 .

[22]  Renato Natal Jorge,et al.  Development of shear locking‐free shell elements using an enhanced assumed strain formulation , 2002 .

[23]  X. G. Tan,et al.  Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics , 2003 .

[24]  Wilfried B. Krätzig,et al.  Multi-layer multi-director concepts for D-adaptivity in shell theory , 2002 .

[25]  Mark Fiolka.  Theorie und Numerik volumetrischer Schalenelemente zur Delaminationsanalyse von Faserverbundlaminaten , 2008 .

[26]  J. N. Reddy,et al.  Vibration suppression of laminated shell structures investigated using higher order shear deformation theory , 2004 .

[27]  Lorenzo Iannucci,et al.  Dynamic delamination modelling using interface elements , 2006 .

[28]  J. N. Reddy,et al.  A higher-order shear deformation theory of laminated elastic shells , 1985 .

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

[30]  A. Morais,et al.  Application of the effective crack method to mode I and mode II interlaminar fracture of carbon/epoxy unidirectional laminates , 2007 .