A finite-strain solid–shell using local Löwdin frames and least-squares strains

Areias, P.; Soares, Carlos A. Mota; Rabczuk, Timon; Garção, J.

doi:10.1016/j.cma.2016.07.044

Cited by 11 publications

(2 citation statements)

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“…The use of relative strain measures is convenient for general finite element applications (see, e.g., Reference 41). We consider three configurations: configuration

Ω_{0}

is undeformed,

Ω_{b}

is the reference configuration, and

Ω_{a}

is the equilibrium configuration.…”

Section: Finite‐element Implementationmentioning

confidence: 99%

See 1 more Smart Citation

Extrapolation and Ce‐based implicit integration of anisotropic constitutive behavior

Areias

Rabczuk

Ambrósio

2021

Numerical Meth Engineering

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For finite strain plasticity with both anisotropic yield functions and anisotropic hyperelasticity, we use the Kröner‐Lee decomposition of the deformation gradient to obtain a differential‐algebraic system (DAE) in the semi‐implicit form and solve it by an implicit Richardson‐extrapolated method based on intermediate substeps. The source is here the right Cauchy‐Green tensor and the consistent Jacobian of the second Piola‐Kirchhoff stress is determined with respect to this source. The system is composed by a smooth nonlinear first‐order differential equation and a non‐smooth algebraic equation. The development of a Richardson‐extrapolated implicit integrator for any hyperelastic case and any yield function is the goal of this work. The integration makes use of a backward‐Euler method for the flow law complemented by the solution of a yield constraint. The resulting system is solved by the Newton‐Raphson method to obtain the plastic multiplier and the elastic right Cauchy‐Green tensor Ce. To ensure power consistency, we make use of the elastic Mandel stress construction. Iso‐error maps for three yield functions and three numerical examples are presented.

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“…The use of relative strain measures is convenient for general finite element applications (see, e.g., Reference 41). We consider three configurations: configuration

Ω_{0}

is undeformed,

Ω_{b}

is the reference configuration, and

Ω_{a}

is the equilibrium configuration.…”

Section: Finite‐element Implementationmentioning

confidence: 99%

“…We test the Hill yield function and the Barlat and Yoon Yld2004‐18p yield function 24,47 . Contrary to known references, 48 we use solid‐shell technology 41 . In addition, constitutive properties are slightly different.…”

Section: Cup Drawing Problemmentioning

confidence: 99%