English
Related papers

Related papers: A homogenization bending shell theory for multisca…

200 papers

We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A…

Mathematical Physics · Physics 2015-06-26 Ayan Roychowdhury , Anurag Gupta

Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…

Applied Physics · Physics 2020-11-10 Steven Psaltis , Robert Timms , Colin Please , S. Jonathan Chapman

In this paper we derive, by means of $\Gamma$-convergence, the shallow shell models starting from non linear three dimensional elasticity. We use the approach analogous to the one for shells and plates. We start from the minimization…

Analysis of PDEs · Mathematics 2011-02-15 Igor Velčić

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of…

Classical Physics · Physics 2014-07-09 D. J. Colquitt , R. V. Craster , M. Makwana

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…

Mathematical Physics · Physics 2015-12-31 A. Bacigalupo , L. Morini , A. Piccolroaz

Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour…

Classical Physics · Physics 2024-07-09 Abhishek Ghosh , Andrew McBride , Zhaowei Liu , Luca Heltai , Paul Steinmann , Prashant Saxena

We consider a family of linear viscoelastic shells with thickness $2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of their lateral face, all having the same middle surface $S$. We formulate the three-dimensional…

Analysis of PDEs · Mathematics 2017-02-16 G. Castiñeira , Á. Rodríguez-Arós

We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new…

Applied Physics · Physics 2019-10-01 Patrizio Neff , Bernhard Eidel , Marco Valerio d'Agostino , Angela Madeo

We study the periodic buckling patterns that emerge when elastic shells are subjected to geometric confinement. Residual swelling provides access to range of shapes (saddles, rolled sheets, cylinders, and spherical sections) which vary in…

Soft Condensed Matter · Physics 2018-10-12 Lucia Stein-Montalvo , Paul Costa , Matteo Pezzulla , Douglas P. Holmes

In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong…

Analysis of PDEs · Mathematics 2020-12-22 M. T. Cao-Rial , G. Castiñeira , Á. Rodríguez-Arós , S. Roscani

We show how bilateral, linear, elastic foundations (i.e. Winkler foundations) often regarded as heuristic, phenomenological models, emerge asymptotically from standard, linear, three-dimensional elasticity. We study the parametric…

Mathematical Physics · Physics 2014-10-03 Andrés A León Baldelli , Blaise Bourdin

The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and {\delta}_h,…

Analysis of PDEs · Mathematics 2011-07-01 Elisa Davoli

The new linear theory of elastic shells is presented in this paper. This theory is free from various logical imperfections, that may be found in the approaches of earlier researchers. On the base of this theory the equations of shells of…

Mathematical Physics · Physics 2007-05-23 Vladimir V. Eliseev , Alexey S. Skoblikov

We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotical method. Biological materials may exhibit remarkable compressibility when under…

Soft Condensed Matter · Physics 2024-07-23 Xiang Yu , Xiaoyi Chen

In this paper, we propose a multi-layered hyperelastic plate theory of growth within the framework of nonlinear elasticity. First, the 3D governing system for a general multi-layered hyperelastic plate is established, which incorporates the…

Materials Science · Physics 2022-07-05 Ping Du , Zhanfeng Li , Xiaoyi Chen , Jiong Wang

Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out…

Computational Engineering, Finance, and Science · Computer Science 2020-12-16 Xiang Yu , Yibin Fu , Hui-Hui Dai

In this paper, the starting point of our analysis is a coupled system of linear elasticity and Stokes equation. We consider two small parameters: the thickness $h$ of the thin plate and the pore scale $\varepsilon(h)$ which depends on $h$.…

Analysis of PDEs · Mathematics 2025-01-16 Marin Bužančić , Pedro Hernandez-Llanos , Igor Velčić , Josip Žubrinić

Using a geometrically motivated 8-parameter ansatz through the thickness, we reduce a three-dimensional shell-like geometrically nonlinear Cosserat material to a fully two-dimensional shell model. Curvature effects are fully taken into…

Analysis of PDEs · Mathematics 2019-09-30 Mircea Birsan , Ionel-Dumitrel Ghiba , Robert J. Martin , Patrizio Neff

We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the…

Soft Condensed Matter · Physics 2015-06-22 L. M. Pismen

The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…

Analysis of PDEs · Mathematics 2014-01-09 Marta Lewicka , L. Mahadevan , Mohammad Reza Pakzad