Stabilized tetrahedral elements for crystal plasticity finite element analysis overcoming volumetric locking
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Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element.
KeywordsTetrahedral elements Locking-free stabilization Crystal plasticity FEM Finite deformation
This work has been supported by the National Science Foundation, Mechanics and Structure of Materials Program through grant No. CMMI-1100818 (Program Manager: Dr. T. Siegmund), by the Army Research Office through grant No. W911NF-12-1-0376 (Program Manager: Dr. A. Rubinstein) and by the Air Force Office of Scientific through a grant FA9550-13-1-0062, (Program Manager: Dr. David Stargel). Computing support by the Homewood High Performance Compute Cluster (HHPC) is gratefully acknowledged.
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