Geometrically nonlinear crystal plasticity implemented into a discontinuous Galerkin element formulation

ABSTRACTIn the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

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Mixed Finite Element of Geometrically Nonlinear Shallow Shells of Revolution

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.501-504.514 ◽

2014 ◽

Vol 501-504 ◽

pp. 514-517 ◽

Cited By ~ 9

Author(s):

Leonid U. Stupishin ◽

Konstantin E. Nikitin

Keyword(s):

Finite Element ◽

Shallow Shell ◽

Mixed Finite Element ◽

Computation Method ◽

Element Formulation ◽

Geometrically Nonlinear ◽

Shells Of Revolution ◽

Test Task ◽

Shallow Shells ◽

The Galerkin Method

The computation method for shallow shell of revolution in mixed finite-element formulation is developed. Final equations are constructed by the Galerkin method. Results of solution of test task are represented. Precision and convergence of results is analyzed.

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Element-Independent Pure Deformational and Co-Rotational Methods for Triangular Shell Elements in Geometrically Nonlinear Analysis

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418500657 ◽

2018 ◽

Vol 18 (05) ◽

pp. 1850065 ◽

Cited By ~ 1

Author(s):

Y. Q. Tang ◽

Y. P. Liu ◽

S. L. Chan

Keyword(s):

Nonlinear Analysis ◽

Nonlinear Problems ◽

Shell Element ◽

Benchmark Problems ◽

Element Formulation ◽

Geometrically Nonlinear ◽

Plate Element ◽

Membrane Element ◽

Geometrically Nonlinear Analysis ◽

Shell Elements

Proposed herein is a novel pure deformational method for triangular shell elements that can decrease the element quantities and simplify the element formulation. This approach has computational advantages over the conventional finite element method for linear and nonlinear problems. In the element level, this method saves time for computing stresses, internal forces and stiffness matrices. A flat shell element is formed by a membrane element and a plate element, so that the pure deformational membrane and plate elements are derived and discussed separately in this paper. Also, it is very convenient to incorporate the proposed pure deformational method into the element-independent co-rotational (EICR) framework for geometrically nonlinear analysis. Thus, on the basis of the pure deformational method, a novel EICR formulation is proposed which is simpler and has more clear physical characteristics than the traditional formulation. In addition, a triangular membrane element with drilling rotations and the discrete Kirchhoff triangular plate element are used to verify the proposed pure deformational method, although several benchmark problems are employed to verify the robustness and accuracy of the proposed EICR formulations.

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