Related papers: Optimal control of plate shape with incompatible s…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…
In this paper, the growth-induced bending deformation of a thin hyperelastic plate is studied. For a plane-strain problem, the governing PDE system is formulated, which is composed of the mechanical equilibrium equations, the constraint…
In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain…
We study the fluid-mediated approach of a deformable axisymmetric object towards a rigid substrate, focusing on how its shape influences contact formation. For low approach velocities and large Stokes numbers, we show that sharper profiles…
In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational…
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
In this paper, we propose a multi-layered hyperelastic plate theory of growth within the framework of nonlinear elasticity. First, the 3D governing system for a general multi-layered hyperelastic plate is established, which incorporates the…
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 introduce a new class of thin flexible structures that morph from a flat shape into prescribed 3D shapes without an external stimulus such as mechanical loads or heat. To achieve control over the target shape, two different concepts are…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In…
Inspired by biological systems, we introduce a general framework for quasi-static shape control of human-scale structures under slowly varying external actions or requirements. In this setting, shape control aims to traverse the stable…
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…