A. Pagani

B. Wu

E. Carrera

W. Q. Chen

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALELarge-deformation analysis of isotropic elastomeric structures by Carrera Unified Formulation / Wu, B.; Pagani, A.; Chen,W. Q.; Carrera, E.. - STAMPA. - (2019). ((Intervento presentato al convegno Second International Conference onMechanics of Advanced Materials and Structures - ICMAMS 2019 tenutosi a Nanjing, China nel 19-22 October 2019.OriginalLarge-deformation analysis of isotropic elastomeric structures by Carrera Unified FormulationPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2764087 since: 2019-10-29T11:57:06ZInternational Conference of Mechanics of Advanced Materials and StructuresICMAMS 2019 Second International Conference on Mechanics of Advanced Materials and Structures Nanjing, 19-22 October 2019 www.icmams.com  Large-deformation analysis of isotropic elastomeric structures by Carrera Unified Formulation B. Wu1, A. Pagani1, W. Q. Chen2, and E. Carrera1,* 1 Mul2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino 10129, Italy. 2 Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province and Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P.R. China. * Corresponding author: erasmo.carrera@polito.it Keywords: elastomeric structures, Carrera unified formulation, large-deformation Owing to their specific mechanical and physical properties, elastomeric structures made of soft materials are constantly employed in various applications, such as in civil and aerospace engineering, seismology, oil prospecting, automotive industry, signal processing, phononic crystals and metamaterials, as well as biomechanics and biomedical devices. Soft materials are usually susceptible to undergoing large deformations under external stimuli such as mechanical loadings. Therefore, accurate predictions of their large-deformation response accounting for both geometrical and physical nonlinearities are of paramount importance for their design and failure evaluation. Based on the well-known nonlinear hyperelasticity theory and by using the Carrera Unified Formulation (CUF) as well as a total Lagrangian approach, the unified theory of slightly compressible elastomeric structures including geometrical and physical nonlinearities is developed in this work. By exploiting CUF, the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to the slightly compressible elastomeric structures are straightforwardly formulated in terms of the fundamental nuclei, which are independent of the theory approximation order. Accordingly, the internal nodal force vector and the tangent stiffness matrix of the unified 1D beam and 2D plate elements are derived by using the 3D Cauchy-Green deformation tensor and the nonlinear constitutive equation for slightly compressible isotropic hyperelastic materials. A class of nonlinear constitutive equations is implemented where the isochoric strain energy functions are based on the first invariant of the right Cauchy-Green deformation tensor. The Newton-Raphson linearization scheme along with a path-following method based on the arc-length constraint is employed to solve the geometrically and physically nonlinear problem. Several numerical assessments are conducted, including uniaxial tension nonlinear response of rectangular elastomeric beams as well as uniaxial and equiaxial tension response of elastomeric plates. Numerical findings confirm the capabilities of the CUF model to predict the large-deformation equilibrium curves and the stress distributions with high accuracy.  References [1] A. Pagani and E. Carrera. Unified formulation of geometrically nonlinear refined beam theories. Mech. Adv. Mater. Struct., 25(1):15-31, 2018. [2] B. Wu, A. Pagani, M. Filippi, W.Q. Chen, and E. Carrera. Accurate stress fields of post-buckled laminated composite beams accounting for various kinematics. Int. J. Non-Lin. Mech., 111: 60-71, 2019. [3] B. Wu, A. Pagani, M. Filippi, W.Q. Chen, and E. Carrera. Large-deflection and post-buckling analyses of isotropic rectangular plates by Carrera Unified Formulation. Int. J. Non-Lin. Mech., 116: 18-31, 2019. 

Large-deformation analysis of isotropic elastomeric structures by Carrera Unified Formulation

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Large-deformation analysis of isotropic elastomeric structures by Carrera Unified Formulation

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