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Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…

Numerical Analysis · Mathematics 2017-11-13 Nora Lüthen , Martin Rumpf , Sascha Tölkes , Orestis Vantzos

These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving…

Analysis of PDEs · Mathematics 2026-04-16 Athanasios E. Tzavaras

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…

Applied Physics · Physics 2024-07-31 Samuel P. Wallen , Michael R. Haberman , Washington DeLima

We investigate numerically the yielding transition of a two dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, that we derive from the full (tensorial) description of…

Statistical Mechanics · Physics 2018-07-18 I. Fernández Aguirre , E. A. Jagla

We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral…

Numerical Analysis · Mathematics 2024-09-23 Daobo Zhang , Josef Kiendl

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these…

Pattern Formation and Solitons · Physics 2020-03-17 F. E. Garbuzov , K. R. Khusnutdinova , I. V. Semenova

This paper establishes a universal framework for the nonlocal modeling of anisotropic damage at finite strains. By the combination of two recent works, the new framework allows for the flexible incorporation of different established…

Computational Engineering, Finance, and Science · Computer Science 2025-05-16 Tim van der Velden , Stefanie Reese , Hagen Holthusen , Tim Brepols

Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…

Soft Condensed Matter · Physics 2016-04-12 Jingchen Feng , Herbert Levine , Xiaoming Mao , Leonard M. Sander

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…

Numerical Analysis · Mathematics 2025-03-20 H. M. Verhelst , M. Möller , J. H. Den Besten

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

Numerical Analysis · Mathematics 2021-09-22 Alessandra Vizzaccaro , Andrea Opreni , Loïc Salles , Attilio Frangi , Cyril Touzé

To facilitate the understanding of the mechanisms underlying the electric breakdown of dielectric elastomers, we derive a one-dimensional (1d) model for axisymmetric necking in a dielectric membrane subjected to equibiaxial stretching and…

Soft Condensed Matter · Physics 2025-02-19 Xiang Yu , Yibin Fu

We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end…

Soft Condensed Matter · Physics 2016-07-06 Jan Plagge , Andreas Fischer , Claus Heussinger

We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…

Analysis of PDEs · Mathematics 2023-11-30 Manuel Friedrich , Leonard Kreutz , Konstantinos Zemas

We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…

Fluid Dynamics · Physics 2011-05-03 Adam C. Perkins , Roman O. Grigoriev , Michael F. Schatz

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Numerical Analysis · Mathematics 2017-12-04 Anindya Bhaduri , Lori Graham-Brady

Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of…

Classical Physics · Physics 2022-11-30 Giovanni Corsi , Antonino Favata , Stefano Vidoli

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…

Statistics Theory · Mathematics 2016-01-25 Ben Sherwood , Lan Wang

Implant placement under soft tissues operation is described. In this operation tissues can reach such deformations that nonlinear properties are appeared. A mass-spring model modification for modeling nonlinear tissue operation is…

Numerical Analysis · Computer Science 2014-03-11 Sergei Nikolaev

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli using a coarse-graining procedure. We study this process for a simple…

Soft Condensed Matter · Physics 2015-05-14 K. Franzrahe , P. Nielaba , S. Sengupta

The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the full shell metric and examination of its influence on the…

Numerical Analysis · Mathematics 2023-07-19 G. Radenković , A. Borković , B. Marussig