相关论文: Energies for elastic plates and shells from quadra…
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…
This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…
Large deformations play a central role in the shape transformations of slender active and biological structures. A classical example is the eversion of the Volvox embryo, which demonstrates the need for shell theories that can describe…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
We developed a physics-based analytical model to describe the nonlinear mechanical response of aspirated elastic shells. By representing the elastic energy through a stretching modulus, $K$, and a dimensionless ratio, $\delta$, capturing…
The second invariant of the left Cauchy-Green deformation tensor $\mathbf{B}$ (or right $\mathbf{C}$) has been argued to play a fundamental role in nonlinear elasticity. Generalized neo-Hookean materials, which depend only on the first…
We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…
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…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…
We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…
We show that nonlinearly elastic plates of thickness $h\to 0$ with an $\varepsilon$-periodic structure such that $\varepsilon^{-2}h\to 0$ exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
The purpose of this work is to develop a model for a rectangular plate made of an orthotropic material. If compared with the classical model of the isotropic plate, the relaxed condition of orthotropy increases the degrees of freedom as a…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
We prove a relation between the scaling $h^\beta$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates…
The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total…
In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat…
Shapes and energies of icosahedral fullerenes are studied on an atomically detailed level. The numerical results based on the effective binary carbon-carbon potential are related to the theory of elasticity of crystalline membranes with…