Related papers: Stable numerics for finite-strain elasticity
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…
Amorphous solids, such as glasses, have complex responses to deformations, with significant consequences in material design and applications. In this respect two intertwined aspects are important: stability and reversibility. It is crucial…
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for which a "good" macroscopic description in the form of…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Disordered solids distort and fail as particle contacts become unstable and rearrange under sufficiently large shear strains. Such instabilities can occur at different locations and, because of their proximity, can interact with one…
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit finite difference schemes for the one-dimensional advection equation with an inflow boundary condition. The strong…
This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and…
In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both problems are related through the Herrmann pressure. Employing the…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
In this paper, we discuss the dynamic modeling of fluid-filled straw-like elements consisting of serially interconnected elastic frusta with both axisymmetric and antisymmetric degrees of freedom, assuming planar motion. Under appropriate…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…