Related papers: Surface penalization of self-interpenetration in l…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary…
We present a contact mechanics problem, which we consider to be representative for contacts between nominally flat surfaces. The main ingredients of the mathematically fully defined contact problem are: Self-affine roughness, linear…
Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology and engineering. Often the physical…
When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates…
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…
This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time…
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity…
We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap and the violation of constraints for the solutions to the…
This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…
Extremely compliant elastic materials, such as thin membranes or soft gels, can be deformed when wetted by a liquid drop. It is commonly assumed that the solid capillarity in "soft wetting" can be treated in the same manner as liquid…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
This work focuses on the numerical modelling of confined concretes when subjected to multiaxial loading accounting for a nonlinear material response. Particularly, an improved return mapping procedure is here presented to cope with the…
Understanding surface mechanics of soft solids, such as soft polymeric gels, is crucial in many engineering processes, such as dynamic wetting and adhesive failure. In these situations, a combination of capillary and elastic forces drives…
We report about a mechanism for surface localization, present in finite defect-free polyatomic lattices described by a tight binding model. Numerical diagonalization and degenerated perturbation theory show that there is a minimum number of…
Surface aging phenomena are discussed for semi-infinite systems prepared in a fully disordered initial state and then quenched to or below the critical point. Besides solving exactly the semi-infinite Ising model in the limit of large…
The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an…
A systematic approach for the construction of a density functional for van der Waals interactions that also accounts for saturation effects is described, i.e. one that is applicable at short distances. A very efficient method to calculate…
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving…