Related papers: Asymptotically exact strain-gradient models for no…
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.…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…