Energy-momentum time integration of gradient-based models for fiber-bending stiffness in anisotropic thermo-mechanical continua

Dietzsch, Julian; Groß, Michael; Kalaimani, Iniyan

doi:10.23967/coupled.2021.024

Cited by 1 publication

(1 citation statement)

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“…We introduce the independent fields C for the right Cauchy-Green tensor, J for the Jacobian determinant to prevent volumetric locking, CA for the anisotropic deformation tensor to prevent fiber locking [2], F for the deformation gradient, Γ for the gradient of F and the referential representation as independent field Λ to have an objective quantity for the energy-momentum scheme. The necessary superimposed fields ( S,p, SA ) to achieve energy-consistency are shown in [4] and the new field H regarding to the fiber bending stiffess is given by…”

Section: Introductionmentioning

confidence: 99%

A mixed finite element formulation for energy‐momentum time integrations of composites with fiber bending stiffness

Dietzsch

Groß

Kalaimani

2021

Proc Appl Math & Mech

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We aim at dynamic simulations of 3D‐fiber‐reinforced materials in light‐weight structures, which are reinforced by fiber rovings comprised of thousands of filaments. Each roving possesses a separate bending stiffness, which has a large influence on the material behaviour on the macro scale. For the description of this material behavior, we extend a hyperelastic anisotropic Cauchy continuum formulation, which models only the macro‐scopic behaviour of a reinforcement by filaments, by a higher‐order gradient of the deformation mapping as an independent field. The new mixed finite element formulation is based on well‐known mixed finite elements for anisotropic polyconvex material formulations, but include new additional mixed fields concernd with the fiber bending stiffness. As we aim at dynamic long‐term simulations, we apply higher‐order accurate time integrators. Here, we include the new mixed finite element formulation in a variational‐based time finite element method. As numerical examples serve a simple cantilever beam. Here, we first analyze the influence of the fiber bending stiffness.

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Section: Introductionmentioning

confidence: 99%