Related papers: Linear constrained Cosserat-shell models including…
The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
We consider a class of single-director Cosserat shell models accounting for both curvature and finite mid-plane strains. We assume a polyconvexity condition for the stored-energy function that reduces to a physically correct membrane model…
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…
A coarse-grained simulation model eliminates microscopic degrees of freedom and represents a polymer by a simplified structure. A priori, two classes of coarse-grained models may be distinguished: those which are designed for a specific…
In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly…
A new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four prominently used bending models. Through an essential set of elementary nonlinear bending test cases, the stresses…
In a geometrically non-linear Cosserat model for micro-polar elastic solids, we insert dipole pairs of singularities into smooth maps and control the amount of Cosserat energy needed to do so. We use this method to force an arbitrary number…
We consider Riesz' fractional gradient and a truncated version of it. The equations of nonlocal nonlinear elasticity based on those gradients are known. We perform a formal linearization and arrive at the equations of linear elasticity…
We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces to obtain $L^2$ regularity solutions. Then the rigidity results on the strain tensor of the middle surface are implied by the $L^2$…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
This paper deals with $\varepsilon$-efficient and $\varepsilon$-properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the paper, we establish a new nonlinear separation theorem for…
Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…
We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces. We prove that if the surface is a smooth noncharacteristic region, any first order infinitesimal isometry can be matched to an…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structured problems, these global constants can…
Recent developments in lipid membrane models for simulations are reviewed. To reduce computational costs, various coarse-grained molecular models have been proposed. Among them, implicit solvent (solvent-free) molecular models are…