Transient multi-scale analysis with micro-inertia effects using Direct $$\hbox {FE}^{2}$$ method

Autor:	Vincent B. C. Tan, Jie Zhi, Tong Earn Tay, Karthikayen Raju
Rok vydání:	2021
Předmět:	Physics Applied Mathematics Mechanical Engineering media_common.quotation_subject Mathematical analysis Computational Mechanics Metamaterial Ocean Engineering 02 engineering and technology Inertia 01 natural sciences Finite element method 010101 applied mathematics Computational Mathematics 020303 mechanical engineering & transports 0203 mechanical engineering Computational Theory and Mathematics Dynamic problem Fictitious force Scale analysis (mathematics) Boundary value problem 0101 mathematics Energy (signal processing) media_common
Zdroj:	Computational Mechanics. 67:1645-1660
ISSN:	1432-0924 0178-7675
DOI:	10.1007/s00466-021-02012-6
Popis:	This paper presents an extension of Direct $$\hbox {FE}^{2}$$ method for the study of dynamic problems in heterogeneous materials. The proposed method can be formulated based on either the Hill–Mandel principle or the extended Hill–Mandel principle, the latter of which enforces the energy contributed by the internal force and the inertial force consistent at two scales. Unlike the traditional $$\hbox {FE}^{2}$$ method, it is not necessary to conduct two levels of finite element simulations linked by extensive information interchange. Instead, we reformulate the macroscopic variational statement with the microscopic contributions, leading to only a single coupled boundary value problem. The classical microscopic boundary condition used in the traditional $$\hbox {FE}^{2}$$ method can be employed but it is implemented through kinematical constraints between the macro nodes and the micro nodes in the Direct $$\hbox {FE}^{2}$$ method. The proposed method is illustrated by two numerical examples including a fiber-reinforced composite and an acoustic metamaterial. The results are verified by direct numerical simulations and it is shown that micro-inertia effects are not important in modeling low-velocity impact behavior of the composite but they are essential in capturing wave attenuation performance of locally resonant acoustic metamaterials.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::edc17630b754890cb3bae62eab5be27c https://doi.org/10.1007/s00466-021-02012-6 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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