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We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…

Analysis of PDEs · Mathematics 2018-06-13 Manuel Friedrich , Martin Kruzik

This work presents a Virtual Element Method (VEM) formulation tailored for two-dimensional axisymmetric problems in linear elasticity. By exploiting the rotational symmetry of the geometry and loading conditions, the problem is reduced to a…

Numerical Analysis · Mathematics 2025-05-20 Paulo Akira F. Enabe , Rodrigo Provasi

The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…

Computational Engineering, Finance, and Science · Computer Science 2022-10-06 Martin Horák , Emma La Malfa Ribolla , Milan Jirásek

We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral…

Numerical Analysis · Mathematics 2024-09-23 Daobo Zhang , Josef Kiendl

We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in…

Analysis of PDEs · Mathematics 2016-01-26 Seonghak Kim , Youngwoo Koh

The first super-convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is…

Numerical Analysis · Mathematics 2019-08-16 Ruben Sevilla , Matteo Giacomini , Alexandros Karkoulias , Antonio Huerta

A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the…

Analysis of PDEs · Mathematics 2023-06-27 Willem J. M. van Oosterhout , Matthias Liero

An extension of the Sequence of Physical Processes using geometrical corrections of the Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor is addressed. More precisely, the usual Sequence of Physical Processes omits some…

Soft Condensed Matter · Physics 2025-03-14 Louis-Vincent Bouthier , Romain Castellani , Rudy Valette

In this paper we propose a new mixed virtual element formulation for the numerical approximation of viscoelasticity equations with weakly imposed stress symmetry. The governing equations use the Zener model and are expressed in terms of the…

Numerical Analysis · Mathematics 2025-10-23 Sarvesh Kumar , Utkarsh Rajput , Ricardo Ruiz-Baier

A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…

Analysis of PDEs · Mathematics 2011-02-15 Jean-Luc Akian , Radjesvarane Alexandre , Salma Bougacha

A stress equilibration procedure for hyperelastic material models is proposed andanalyzed in this paper. Based on the displacement-pressure approximation computed with a stable finite element pair, it constructs, in a vertex-patch-wise…

Numerical Analysis · Mathematics 2019-05-07 Fleurianne Bertrand , Marcel Moldenhauer , Gerhard Starke

We continue our investigation of viscoelasticity by extending the Holzapfel-Simo approach discussed in Part I to the fully nonlinear regime. By scrutinizing the relaxation property for the non-equilibrium stresses, it is revealed that a…

Numerical Analysis · Mathematics 2024-08-22 Ju Liu , Jiashen Guan , Chongran Zhao , Jiawei Luo

We extend the Euler-Bernoulli beam problem, formulated as a matrix string equation with a matrix-valued density, to a setting where the density takes values in a Clifford algebra, and we analyze its isospectral deformations. For discrete…

Exactly Solvable and Integrable Systems · Physics 2025-09-19 Richard Beals , Jacek Szmigielski

The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…

Numerical Analysis · Mathematics 2023-10-06 L. L. Yaw

Point by point strain scanning is often used to map the residual stress (strain) in engineering materials and components. However, the gauge volume and hence spatial resolution is limited by the beam defining apertures and can be…

Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture…

Computational Engineering, Finance, and Science · Computer Science 2024-08-13 Sai Kubair Kota , Siddhant Kumar , Bianca Giovanardi

Network models are used as efficient representation of materials with complex, interconnected locally one-dimensional structures. They typically accurately capture the mechanical properties of a material, while substantially reducing…

Numerical Analysis · Mathematics 2025-12-16 Morgan Görtz , Moritz Hauck , Axel Målqvist , Andreas Rupp , Lucia Swoboda

Isothermal visco-elastodynamics in the Kelvin-Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted.…

Analysis of PDEs · Mathematics 2022-04-13 Tomáš Roubíček

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

Applications · Statistics 2015-11-02 Isabell M. Franck , P. S. Koutsourelakis

We present a novel formulation for the dynamics of geometrically exact Timoshenko beams and beam structures made of viscoelastic material featuring complex, arbitrarily curved initial geometries. An $\textrm{SO}(3)$-consistent and…

Computational Engineering, Finance, and Science · Computer Science 2024-12-02 Giulio Ferri , Enzo Marino