Related papers: Linearization of finite elasticity with surface te…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This adhesion balance implies boundary conditions which depend on the characteristic surface deformation…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in…
We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in…
Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials:…
We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of…
The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four…
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
Three models with nonlinear realizations of conformal symmetry are discussed. The simplest model can only describe a universe expanding with a deceleration and does not include inflation. The other models are equivalent up to a variables…
In [Bonito et al., J. Comput. Phys. (2022)], a local discontinuous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this…
Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon…
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured…
Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact…
An elasto-plasticity model with coupled hardening variables of strain type is presented. In the theoretical framework of generalized associativity, the formulation of this model is based on the introduction of two hardening variables with a…
In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…
The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that…
We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $\lambda$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship…
We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic…
We study the effect of mergers in the force chain model describing the stress profile in static granular materials. Combining numerical and analytical calculations we show that granular materials do not generally behave in an elastic-like…