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Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems. (English) Zbl 0742.73019
Summary: Stabilization methods which are based on material and geometric parameters are developed via the Simo-Hughes assumed strain method. The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking are eliminated by projection. The stabilization forces are then independent of the bulk modulus making them ideal for nonlinear incompressible problems such as plasticity in metals. Convergence studies are made for several test problems.

74S05 Finite element methods applied to problems in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
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