TY - JOUR

T1 - Micro–macro constitutive modeling and finite element analytical-based formulations for fibrous materials

T2 - A multiscale structural approach for crimped fibers

AU - Marino, Michele

AU - Wriggers, Peter

N1 - Funding Information: This work has been carried out within the framework of the SMART BIOTECS alliance between the Technical University of Braunschweig and the Leibniz University of Hannover. This initiative is financially supported by the Ministry of Science and Culture (MWK) of Lower Saxony, Germany. This work has been carried out within the framework of the SMART BIOTECS alliance between the Technical University of Braunschweig and the Leibniz University of Hannover. This initiative is financially supported by the Ministry of Science and Culture (MWK) of Lower Saxony, Germany.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - Materials with crimped fibers have special properties that can be effectively explored only when using a micro–macro perspective. In this framework, a novel constitutive model based on a multiscale structural rationale is introduced. Material micromechanics, depending on fiber straightening mechanisms, is described introducing a beam model which drives material model response. This rationale leads to a quasi-analytical formulation, coupling the advantages of purely-analytical and computational approaches. The proposed model is also proven to be polyconvex. Furthermore, a finite-element formulation is developed, enriched by a quasi-analytical core associated with the multiscale constitutive formulation. Different solution strategies are tested in order to optimize the numerical performances in terms of accuracy, robustness and cost. Moreover, a mixed finite element formulation based on a simplified-kinematics-for-anisotropy (SKA) is introduced. For the tested boundary value problems, the SKA-element is an optimal choice in terms of displacement and fiber stress convergence behavior, especially for coarse meshes.

AB - Materials with crimped fibers have special properties that can be effectively explored only when using a micro–macro perspective. In this framework, a novel constitutive model based on a multiscale structural rationale is introduced. Material micromechanics, depending on fiber straightening mechanisms, is described introducing a beam model which drives material model response. This rationale leads to a quasi-analytical formulation, coupling the advantages of purely-analytical and computational approaches. The proposed model is also proven to be polyconvex. Furthermore, a finite-element formulation is developed, enriched by a quasi-analytical core associated with the multiscale constitutive formulation. Different solution strategies are tested in order to optimize the numerical performances in terms of accuracy, robustness and cost. Moreover, a mixed finite element formulation based on a simplified-kinematics-for-anisotropy (SKA) is introduced. For the tested boundary value problems, the SKA-element is an optimal choice in terms of displacement and fiber stress convergence behavior, especially for coarse meshes.

KW - Crimped fibers

KW - Fibrous materials

KW - Micro–macro constitutive modeling

KW - Mixed FEM for anisotropy

KW - Multiscale structural approach

UR - http://www.scopus.com/inward/record.url?scp=85056875798&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2018.10.016

DO - 10.1016/j.cma.2018.10.016

M3 - Article

AN - SCOPUS:85056875798

VL - 344

SP - 938

EP - 969

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -