Related papers: On morphoelastic rods
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
Mechanical densification of granular bodies is a process in which a loose material becomes increasingly cohesive as the applied pressure increases. A constitutive description of this process faces the formidable problem that granular and…
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Understanding the origins of such rheologic behaviors is crucial to find proper technological applications. Using an elastic…
We derive the Eshelby stress tensor, the angular momentum tensor and the dilatational vector flux for micromorphic elasticity. We give the corresponding balance laws and the J, L, and M integrals. Also we discuss when the balance laws…
We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and…
Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…
Evolution and development operate at different timescales; generations for the one, a lifetime for the other. These two processes, the basis of much of life on earth, interact in many non-trivial ways, but their temporal hierarchy --…
Motivated by an application involving additively manufactured bioresorbable polymer scaffolds supporting bone tissue regeneration, we investigate the impact of uncertain geometry perturbations on the effective mechanical properties of…
We suggest a new focus for turbulence studies -- multi-mode correlations -- which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such…
Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient $F$ into an elastic part $F_e$ and a…
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…
Brownian motion and viscoelasticity of semiflexible polymers is a subject that has been studied for many years. Still, rigorous analysis has been hindered due to the difficulty in handling the constraint that polymer chains cannot be…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
We present a variational principle governing the quasistatic evolution of a linearized elastoplastic material. In case of linear hardening, the novel characterization allows to recover and partly extend some known results and proves itself…
The simulation of growth processes within soft biological tissues is of utmost importance for many applications in the medical sector. Within this contribution we propose a new macroscopic approach fro modelling stress-driven volumetric…
Laplacian growth is the study of interfaces that move in proportion to harmonic measure. Physically, it arises in fluid flow and electrical problems involving a moving boundary. We survey progress over the last decade on discrete models of…