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The strain incompatibility equations are discussed for nonlinear Kirchhoff-Love shells with sources of inhomogeneity arising due to a distribution of topological defects, such as dislocations and disclinations, and metric anomalies, such as…

Soft Condensed Matter · Physics 2017-06-13 Ayan Roychowdhury , Anurag Gupta

We formulate a model describing the evolution of thickness in a shallow ice sheet lying over a lithosphere. The model is thus governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the…

Analysis of PDEs · Mathematics 2024-07-09 Paolo Piersanti , Roger Temam

An isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialised to infinitesimal deformations and follow the Kirchhoff-Love hypothesis. Both the geometry and…

Numerical Analysis · Mathematics 2021-05-20 Zhaowei Liu , Andrew McBride , Prashant Saxena , Luca Heltai , Yilin Qu , Paul Steinmann

Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of…

Soft Condensed Matter · Physics 2018-06-05 Salem Al Mosleh , Ajay Gopinathan , Christian Santangelo

This work focuses on the development of a posteriori error estimates for fourth-order, elliptic, partial differential equations. In particular, we propose a novel algorithm to steer an adaptive simulation in the context of Kirchhoff plates…

Numerical Analysis · Mathematics 2020-04-22 Pablo Antolin , Annalisa Buffa , Luca Coradello

The wide adoption of thermoplastic composites to reduce weight in structural parts requires reliable numerical methods to account for debonding between overmolded parts. Although cohesive elements are effective for debonding, the need for…

Computational Engineering, Finance, and Science · Computer Science 2026-03-31 Sérgio G. F. Cordeiro , Boyang Chen , Frans P. van der Meer

The Kirchhoff-Love shell theory is recasted in the frame of the tangential differential calculus (TDC) where differential operators on surfaces are formulated based on global, three-dimensional coordinates. As a consequence, there is no…

Computational Engineering, Finance, and Science · Computer Science 2018-10-11 D. Schöllhammer , T. P. Fries

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the…

Mathematical Physics · Physics 2017-06-16 Giulio G. Giusteri , Luca Lussardi , Eliot Fried

In this paper we present a generalization of a simple solid-on-solid epitaxial model of thin films growth, when surface morphology anisotropy is provoked by anisotropy in model control parameters: binding energy and/or diffusion barrier.…

Condensed Matter · Physics 2007-05-23 K. Malarz , A. Z. Maksymowicz

The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…

Fluid Dynamics · Physics 2021-01-19 Qing Zhang , Amin Amooie , Martin Z. Bazant , Irmgard Bischofberger

In the late 1950's, Eshelby's linear solutions for the deformation field inside an ellipsoidal inclusion and, subsequently, the infinite matrix in which it is embedded were published. The solutions' ability to capture the behavior of an…

Soft Condensed Matter · Physics 2024-11-08 J. E. Bonavia , S. Chockalingam , T. Cohen

We study the asymptotic behavior of thin heterogeneous elastoplastic plates in the framework of linearized elastoplasticity, focusing on the regime where the plate thickness vanishes much faster than the characteristic scale of the…

Analysis of PDEs · Mathematics 2026-05-14 Marin Bužančić , Igor Velčić , Josip Žubrinić

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…

Computational Engineering, Finance, and Science · Computer Science 2022-01-21 Bartosz Borzeszkowski , Izabela Lubowiecka , Roger A. Sauer

A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…

Numerical Analysis · Mathematics 2018-10-23 Javier Videla , Sundararajan Natarajan , Stephane PA Bordas

Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…

Soft Condensed Matter · Physics 2020-12-30 Virginia von Streng , Rami Abi-Akl , Bianca Giovanardi , Tal Cohen

Shell analysis is a well-established field, but achieving optimal higher-order convergence rates for such simulations is a difficult challenge. We present an isogeometric Kirchhoff-Love shell framework that treats every numerical aspect in…

Computational Engineering, Finance, and Science · Computer Science 2020-12-23 Daniel Schöllhammer , Benjamin Marussig , Thomas-Peter Fries

We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the…

Numerical Analysis · Mathematics 2023-06-23 Norbert Heuer , Torsten Linß

This work considers simultaneous homogenization dimension reduction of a poroelastic model for thin fiber-reinforced hydrogels. The analysed medium is defined as a two-component system consisting of a continuous fiber framework with…

Analysis of PDEs · Mathematics 2026-02-03 Amartya Chakrabortty , Haradhan Dutta , Hari Shankar Mahato

Nitsche's method is a well-established approach for weak enforcement of boundary conditions for partial differential equations (PDEs). It has many desirable properties, including the preservation of variational consistency and the fact that…

Numerical Analysis · Mathematics 2022-03-08 Joseph Benzaken , John A. Evans , Rasmus Tamstorf

The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…

Numerical Analysis · Mathematics 2020-10-20 Lukasz Kaczmarczyk , Hoang Nguyen , Zahur Ullah , Mebratu Wakeni , Chris Pearce