Related papers: Growth of Form in Thin Elastic Structures
This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
Experiments on quasistatic crack propagation in gelatin hydrogels reveal a new branching instability triggered by wetting the tip opening with a drop of aqueous solvent less viscous than the bulk one. We show that the emergence of unstable…
Glass-forming liquids grow dramatically sluggish upon cooling. This slowdown has long been thought to be accompanied by a growing correlation length. Characteristic dynamical and static length scales, however, have been observed to grow at…
Confined thin structures are ubiquitous in nature. Spatial and length constraints have led to a number of novel packing strategies at both the micro-scale, as when DNA packages inside a capsid, and the macro-scale, seen in plant root…
We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
We use numerical simulations to study the dynamics of dense assemblies of self-propelled particles in the limit of extremely large, but finite, persistence times. In this limit, the system evolves intermittently between mechanical…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
We examine the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a flexible structure. This brief but violent event appears to be a regularized finite-time singularity, with…
We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system…
An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…
The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…
We present a non-linear stability analysis of quasi-static slip in a spring-block model. The sliding interface is governed by rate- and state-dependent friction, with an intermediate state evolution law that spans between aging and slip…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
Differentiating structural evolution from structural development or formation opens many avenues of research. The study particularly advances the chemical and physical sciences, material science, energy science, and chemical engineering. By…
Stall cells are spanwise-periodic flow structures that spontaneously form on airfoils operating near stall, fundamentally altering the aerodynamic loading distribution. Despite decades of experimental observations, a complete theoretical…
By means of sophisticated Monte Carlo methods, we investigate the conformational phase diagram of a simple model for flexible polymers with explicit thickness. The thickness constraint, which is introduced geometrically via the global…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial…