An assumed strain formulation of geometrically nonlinear nine-node solid shell elements with improved performance

Thin structures are commonly designed and employed in engineering industries to save material, reduce weight and improve the overall performance of products. The finite element (FE) simulation of such thin structural components has become a powerful and useful tool in this field. For the last few decades, much attention and effort have been paid to establish accurate and efficient FE. In this regard, the solid–shell concept proved to be very attractive due to its multiple advantages. Several treatments are additionally applied to the formulation of solid–shell elements to avoid all locking phenomena and to guarantee the accuracy and efficiency during the simulation of thin structures. The current contribution presents a family of prismatic and hexahedral assumed-strain based solid–shell elements, in which an arbitrary number of integration points are distributed along the thickness direction. Both linear and quadratic formulations of the solid–shell family elements are implemented into ABAQUS static/implicit and dynamic/explicit software to model thin 3D problems with only a single layer through the thickness. Two popular benchmark tests are first conducted, in both static and dynamic analyses, for validation purposes. Then, attention is focused on a complex sheet metal forming process involving large strain, plasticity and contact.

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Stability analysis using a geometrically nonlinear assumed strain solid shell element model

Finite Elements in Analysis and Design ◽

10.1016/s0168-874x(98)00021-3 ◽

1998 ◽

Vol 29 (2) ◽

pp. 121-135 ◽

Cited By ~ 30

Author(s):

Chahngmin Cho ◽

Hoon C. Park ◽

Sung W. Lee

Keyword(s):

Stability Analysis ◽

Shell Element ◽

Element Model ◽

Geometrically Nonlinear ◽

Solid Shell ◽

Assumed Strain

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On the assumed strain formulation for geometrically nonlinear analysis

Finite Elements in Analysis and Design ◽

10.1016/0168-874x(95)00045-u ◽

1996 ◽

Vol 24 (1) ◽

pp. 31-47 ◽

Cited By ~ 15

Author(s):

Chahngmin Cho ◽

Sung W. Lee

Keyword(s):

Nonlinear Analysis ◽

Geometrically Nonlinear ◽

Geometrically Nonlinear Analysis ◽

Assumed Strain ◽

Strain Formulation

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Modeling of thin sheet forming processes by combining solid-shell finite element with isotropic elastoviscoplastic model. Application to magnetic pulse forming processes

10.25518/esaform21.2475 ◽

2021 ◽

Author(s):

Mohamed Mahmoud ◽

François Bay ◽

Daniel Pino Mũnoz

Keyword(s):

Sheet Metal ◽

Thin Sheet ◽

Magnetic Pulse ◽

Solid Shell ◽

Forming Process ◽

Thin Structures ◽

Shell Elements ◽

Tetrahedral Element ◽

Magnetic Pulse Forming ◽

Assumed Strain

Sheet metal alloys are used in many industries to save material, reduce weight and improve the overall performance of products. For the last decades, many types of elements have been developed to resolve the locking problems encountered in the simulation of thin structures. Among these approaches, a family of assumed-strain solid-shell elements has proved to be very efficient and attractive in simulating thin 3D structures with various constitutive models. Furthermore, these elements are able to account for anisotropic behavior of thin structures since isotropic yield functions cannot capture the real physics of some forming processes. In this work, von Mises isotropic yield criterion with Johnson-cook hardening model are combined with a linear prismatic solid-shell element to simulate sheet metal forming processes. A new element assembly technique has been developed to permit the assembly of prismatic elements in a tetrahedral element-based software. This technique splits the prism into multiple tetrahedral elements in such a way that all the cross-terms are accounted for. Furthermore, a tetrahedral based partitioning code has been modified to account for the new prismatic element shape without changing the core structure of the code. More accurate results were obtained using low number of solid-shell elements compared to its counterpart tetrahedral element (MINI element). This reduction in the number of elements accelerated the simulation, especially in the coupled magnetic-structure simulation used for magnetic pulse forming process. The proposed element and criteria are implemented into FORGE (in-house code developed at CEMEF) for simulating magnetic pulse forming process.

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Further Studies of General Shells by Hybrid Strain Based Triangular Elements

Volume 6: 16th Computers in Engineering Conference ◽

10.1115/96-detc/cie-1620 ◽

1996 ◽

Author(s):

Meilan L. Liu ◽

Cho W. S. To

Keyword(s):

Lower Order ◽

Element Formulation ◽

Hybrid Strain ◽

Linear Distribution ◽

Shell Elements ◽

Mesh Topology ◽

Assumed Strain ◽

Strain Formulation ◽

Membrane Bending ◽

Deep Shell

Abstract This paper presents a further study of various lower-order flat triangular shell elements that were based on the Hellinger-Reissner hybrid strain formulation and were developed previously by the authors. The present investigation is to examine the effects of including membrane-bending coupling feature in the shell element formulation on the performance of the lower-order shell elements. Several features are considered. These are, for example, the membrane-bending coupling, tue linear distribution of the assumed strain field of the membrane strain, and the hybrid strain formulation with linear assumed membrane strains and membrane-bending coupling. A study on mesh topology is also included. This relatively detailed study leads one to the conclusion that the hybrid strain based flat triangular shell elements previously developed by the authors are attractive and promising for economical analysis of general shells. It is also found that the inclusion of features such as membrane-bending coupling is unnecessary. Numerical results presented here seem to strongly substantiate the theoretical developments that flat triangular shell elements do converge to the correct solution of deep shell theory. Finally it is observed that for deep shell problems appropriate mesh topology becomes the key to an accurate finite element solution.

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