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A compatible mixed finite element method for large deformation analysis of two-dimensional compressible solids in spatial configuration

Jahanshahi, M ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1002/nme.6978
  3. Publisher: John Wiley and Sons Ltd , 2022
  4. Abstract:
  5. In this article, a new mixed finite element formulation is presented for the analysis of two-dimensional compressible solids in finite strain regime. A three-field Hu–Washizu functional, with displacement, displacement gradient and stress tensor considered as independent fields, is utilized to develop the formulation in spatial configuration. Certain constraints are imposed on displacement gradient and stress tensor so that they satisfy the required continuity conditions across the boundary of elements. From theoretical standpoint, simplex elements are best suited for the application of continuity constraints. The techniques that are proposed to implement the constraints facilitate their automatic imposition and, hence, they can be regarded as an important feature of the work. Since the exterior calculus provides the basis for the developments presented herein, the relevant topics are discussed within the context of the work. Various technical aspects of the formulation are described in detail. These aspects help to illuminate the mathematical formulation that might seem vague in the first place and, more importantly, they help to provide an efficient implementation for ensuing developments. The performance of the mixed finite element method is studied through benchmark numerical examples and it is compared with other similar elements. It is shown that the element has excellent convergence properties and it is numerically stable, especially for problems where classical first order elements demonstrate stiff or unstable behavior. © 2022 John Wiley & Sons Ltd
  6. Keywords:
  7. Mixed finite element method ; Benchmarking ; Calculations ; Finite element method ; Nonlinear analysis ; Numerical methods ; Assumed strain methods ; Displacement gradients ; Enhanced assumed strain ; Enhanced assumed strain method ; Finite element exterior calculus ; Finite strain ; Gradient tensors ; Mixed finite element methods ; Spatial configuration ; Two-dimensional ; Stress tensor
  8. Source: International Journal for Numerical Methods in Engineering ; Volume 123, Issue 15 , 2022 , Pages 3530-3566 ; 00295981 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6978