The patch test—a condition for assessing FEM convergence

Numerical simulations of localized deformation in solids should capture the structural phenomenon of localization and associated loss of material body strength in a manner independent of spatial discretization. Many regularization techniques have been proposed to address the ill posedness associated with rate-independent softening plasticity that leads to mesh-dependent numerical simulations. One approach to alleviating mesh dependence is the strong discontinuity approach, which represents localized deformation as a slip surface within a plasticity model; a strong discontinuity is a discontinuous displacement ®eld. This approach is used in this paper to formulate a plane strain, pressure sensitive, nonassociative plasticity model with strong discontinuity and to implement the model, along with an enhanced bilinear quadrilateral element, via an assumed enhanced strain method. Numerical examples demonstrate mesh independence of the method for pressure sensitive materials. Ó

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“…(45b) is satis®ed for piecewise constant stress ®elds (i.e., the patch test is passed, Taylor et al, 1986) such that …”

Section: Petrov±galerkin Formmentioning

confidence: 99%

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Regueiro

Borja

2001

International Journal of Solids and Structures

117

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“…In contrast. this patch test is not passed with standard eight-node quadrilateral elements because all elements are not parallelograms [9]. This is noteworthy.…”

Section: Second-order Patch Testsmentioning

confidence: 98%

Polynomial approximation of shape function gradients from element geometries

Dohrmann

Rashid

2001

Numerical Meth Engineering

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Abstract..A method is presented for the polynomial appro.ximat ion of shape function gradients based solely on the geometry of finite element boundaries. The method is founded on a least squares approach which leads to an intebg+ation scheme satisfying a necessary condition for convergence. In its simplest form the method reduces to the w-ell-lmown uniform strain approach for finite elements. The method is applicable to a broad class of problems such as connecting dissimilar meshes. mesh adaptivity and transitioning. and the construction of finite elements with variable topologies. Finite elements based on the polynomizd approximate ions are shown to pass patch tests of I-arious orders. 111contrast to standard elements. higher-order pat ch tests are passed wit bout the need for nodes internal to the element boundaries.Less sensitivity to Yolumet ric locking under plane strain conditions is demonstrated through comparisons with a standard element formulation.

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“…The concept is so important that it can be easily found in many textbooks in finite elements, either classical (Hughes, 1987;Cook et al, 2002;Bathe, 1995) or more recent (Belytschko et al, 2000;Zienkiewicz and Taylor, 2000) ones, and it is needed to ensure reliability of the finite element method (FEM) (Babuška and Strouboulis, 2001). The original patch test provided a necessary consistency condition and thus turned out to be very useful for assessing convergence of finite elements analysis, including nonconforming elements Taylor et al, 1976;Taylor et al, 1986). An early mathematical treatment was given by Strang (1972), and Strang and Fix (1973).…”

Section: Introductionmentioning

confidence: 99%

“…An early mathematical treatment was given by Strang (1972), and Strang and Fix (1973). For an element which appears to be convergent but fails the Iron's patch test, the weak patch test is an alternative test, as suggested by Taylor et al (1986). In addition, Belytschko and Lasry (1988) have studied the behavior of a distorted element with a fractal patch test, which is also valid in the weak patch test sense.…”

Section: Introductionmentioning

confidence: 99%