TY - JOUR
T1 - Reduced quadrature for Finite Element and Isogeometric methods in nonlinear solids
AU - Li, Weican
AU - Moutsanidis, Georgios
AU - Behzadinasab, Masoud
AU - Hillman, Michael
AU - Bazilevs, Yuri
N1 - Funding Information:
W. Li, M. Behzadinasab, and Y. Bazilevs were supported through the ONR, USA Grant No. N00014- 21-1-2670 . Some of the computations presented in the article were carried by implementing the proposed methods in PetIGA, which is a software framework that implements NURBS-based IGA [62] .
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - We extend the recently proposed framework using reduced quadrature in the Finite Element and Isogeometric methods for solid mechanics to the nonlinear realm. The proposed approach makes use of the governing equations in the updated Lagrangian formulation in combination with the rate form of the constitutive laws. The key ingredient in the framework is the careful development and use of the Taylor series expansion in the integrands of the internal work terms. The resulting formulation relies on the evaluation of stress gradients, for which the evolution equations and update algorithms are developed. The versatility of the proposed approach is demonstrated on an extensive set of numerical examples employing a variety of constitutive models. The resulting formulations are especially effective in alleviating volumetric locking for the cases of nearly-incompressible and plastic deformations.
AB - We extend the recently proposed framework using reduced quadrature in the Finite Element and Isogeometric methods for solid mechanics to the nonlinear realm. The proposed approach makes use of the governing equations in the updated Lagrangian formulation in combination with the rate form of the constitutive laws. The key ingredient in the framework is the careful development and use of the Taylor series expansion in the integrands of the internal work terms. The resulting formulation relies on the evaluation of stress gradients, for which the evolution equations and update algorithms are developed. The versatility of the proposed approach is demonstrated on an extensive set of numerical examples employing a variety of constitutive models. The resulting formulations are especially effective in alleviating volumetric locking for the cases of nearly-incompressible and plastic deformations.
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U2 - 10.1016/j.cma.2022.115389
DO - 10.1016/j.cma.2022.115389
M3 - Article
AN - SCOPUS:85134882780
SN - 0045-7825
VL - 399
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 115389
ER -