scholarly journals Stabilized Mixed Finite Elements With Embedded Strong Discontinuities for Shear Band Modeling

2006 ◽  
Vol 73 (6) ◽  
pp. 995-1004 ◽  
Author(s):  
P. J. Sánchez ◽  
V. Sonzogni ◽  
A. E. Huespe ◽  
J. Oliver
Keyword(s):  
Shear Band ◽  
Mixed Finite Element ◽  
Mixed Finite Elements ◽  
Material Model ◽  
Strong Discontinuity ◽  
Strong Discontinuities ◽  
Alternative Procedures ◽  
Solution Accuracy ◽  
Stabilized Mixed Finite Element ◽  
Continuum Strong Discontinuity Approach

A stabilized mixed finite element with elemental embedded strong discontinuities for shear band modeling is presented. The discrete constitutive model, representing the cohesive forces acting across the shear band, is derived from a rate-independent J2 plastic continuum material model with strain softening, by using a projection-type procedure determined by the Continuum-Strong Discontinuity Approach. The numerical examples emphasize the increase of the numerical solution accuracy obtained with the present strategy as compared with alternative procedures using linear triangles.

scholarly journals Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra

2019 ◽  
Vol 29 (06) ◽  
pp. 1037-1077 ◽  
Author(s):  
Ilona Ambartsumyan ◽  
Eldar Khattatov ◽  
Jeonghun J. Lee ◽  
Ivan Yotov
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Mixed Finite Element ◽  
Mixed Finite Elements ◽  
Higher Order ◽  
Local Velocity ◽  
New Family ◽  
Gauss Points ◽  
Theoretical Results ◽  
Optimal Formula

We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure systems. The methods are based on a new family of mixed finite elements, which are enhanced Raviart–Thomas spaces with bubbles that are curls of specially chosen polynomials. The velocity degrees of freedom of the new spaces can be associated with the points of tensor-product Gauss–Lobatto quadrature rules, which allows for local velocity elimination and leads to a symmetric and positive definite cell-based system for the pressures. We prove optimal [Formula: see text]th order convergence for the velocity and pressure in their natural norms, as well as [Formula: see text]st order superconvergence for the pressure at the Gauss points. Moreover, local postprocessing gives a pressure that is superconvergent of order [Formula: see text] in the full [Formula: see text]-norm. Numerical results illustrating the validity of our theoretical results are included.

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