English
Related papers

Related papers: Nonlinear static isogeometric analysis of arbitrar…

200 papers

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…

Analysis of PDEs · Mathematics 2026-02-24 Gui-Qiang G. Chen , Siran Li , Marshall Slemrod

The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…

Pattern Formation and Solitons · Physics 2017-10-11 C. Chong , Mason A. Porter , P. G. Kevrekidis , C. Daraio

A lattice dynamical formalism based on nonaffine response theory is derived for non-centrosymmetric crystals, accounting for long-range interatomic interactions using the Ewald method. The framework takes equilibrated static configurations…

Materials Science · Physics 2020-01-08 Bingyu Cui , Alessio Zaccone , David Rodney

Pressurized elastic shells are ubiquitous in nature and technology, from the outer walls of yeast and bacterial cells to artificial pressure vessels. Indentation measurements simultaneously probe the internal pressure and elastic properties…

Soft Condensed Matter · Physics 2021-08-11 Wenqian Sun , Jayson Paulose

In a recent feature article in this journal, co-authored by Gert van der Heijden, I described the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures, looking exclusively at integrable…

Pattern Formation and Solitons · Physics 2015-06-22 J. Michael T. Thompson

This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…

Numerical Analysis · Mathematics 2021-11-03 Sansit Patnaik , Sai Sidhardh , Fabio Semperlotti

We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the…

Analysis of PDEs · Mathematics 2020-09-16 Ionel-Dumitrel Ghiba , Mircea Bîrsan , Peter Lewintan , Patrizio Neff

Hysteretic damping is often modeled by means of linear viscoelastic approaches such as "nearly constant Attenuation (NCQ)" models. These models do not take into account nonlinear effects either on the stiffness or on the damping, which are…

Classical Physics · Physics 2010-07-28 Nicolas Delépine , Luca Lenti , Guy Bonnet , Jean-François Semblat

A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates,…

Numerical Analysis · Mathematics 2018-08-15 Qingyuan Hu , Franz Chouly , Ping Hu , Gengdong Cheng , Stéphane Pierre Alain Bordas

We study the static and dynamic structure of thermally fluctuating elastic thin sheets by investigating the overdamped dynamic F\"oppl-von K\'arm\'an equation, in which the F\"oppl-von K\'arm\'an equation from elasticity theory is driven by…

Soft Condensed Matter · Physics 2023-05-10 Chanania Steinbock , Eytan Katzav

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

It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…

Mathematical Physics · Physics 2015-10-09 Christian G. Boehmer , Nicola Tamanini

We examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and…

Soft Condensed Matter · Physics 2017-04-19 Bin Li , Marino Arroyo

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…

Materials Science · Physics 2021-09-01 M. I. Hussein , R. Khajehtourian , M. H. Abedinnasab

Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. In this paper, we determine and study the necessary and sufficient conditions for the…

General Relativity and Quantum Cosmology · Physics 2021-08-11 M. Manzano , M. Mars

Accurate finite element analysis of refined shell theories is crucial but often hindered by membrane and shear locking effects. While various element-based locking-free techniques exist, this work addresses the problem at the theoretical…

Numerical Analysis · Mathematics 2025-08-26 Khanh Chau Le , Hoang-Giang Bui

The paper is concerned with the geometrically non-linear theory of 6-parametric elastic shells with drilling degrees of freedom. This theory establishes a general model for shells, which is characterized by two independent kinematic fields:…

Analysis of PDEs · Mathematics 2013-03-11 Mircea Birsan , Patrizio Neff

We consider nonlinear elastic wave equations generalizing Gol'dberg's five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements…

Analysis of PDEs · Mathematics 2018-05-11 Maarten de Hoop , Gunther Uhlmann , Yiran Wang

A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three dimensional,…

Numerical Analysis · Mathematics 2024-12-20 Reza Ghaffari , Roger A. Sauer

In the framework of the geometrically nonlinear 6-parameter resultant shell theory we give a characterization of the shells without drilling rotations. These are shells for which the strain energy function $W$ is invariant under the…

Analysis of PDEs · Mathematics 2013-12-10 Mircea Birsan , Patrizio Neff