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We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

A nonlinear continuum theory is advanced for high-rate mechanics and thermodynamics of liver parenchyma. The homogenized continuum is idealized as a solid-fluid mixture of dense viscoelastic tissue and liquid blood. The solid consists of a…

Soft Condensed Matter · Physics 2025-09-30 John D. Clayton

We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.

Analysis of PDEs · Mathematics 2020-04-21 Edoardo Mainini , Danilo Percivale

Bulk rheological properties of viscoelastic fluids have been extensively studied in macroscopic shearing geometries. However, little is known when an active microscopic probe is used to locally perturb them far from the linear-response…

Soft Condensed Matter · Physics 2014-12-17 Juan Ruben Gomez-Solano , Clemens Bechinger

In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a…

Analysis of PDEs · Mathematics 2011-02-16 Josip Tambača , Igor Velčić

The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…

Soft Condensed Matter · Physics 2020-12-15 Daniel Hexner

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…

Analysis of PDEs · Mathematics 2026-01-19 Manuel Friedrich , José Matias , Elvira Zappale

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…

Fluid Dynamics · Physics 2024-09-09 Rossen Ivanov , Vakhtang Putkaradze

A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…

Soft Condensed Matter · Physics 2026-03-17 Nikolas H. Claussen , Fridtjof Brauns , Boris I. Shraiman

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor…

Analysis of PDEs · Mathematics 2015-05-20 Stefan Müller , Stefan Neukamm

This paper is interested in the computation of stresses within jammed packings of rigid polygonal cells. The cells are considered to follow a Tresca friction law. First, a constrained minimization problem is introduced where the friction…

Numerical Analysis · Mathematics 2026-02-05 Frédéric Marazzato , Shankar Venkataramani

Traction force microscopy is a method widely used in biophysics and cell biology to determine forces that biological cells apply to their environment. In the experiment, the cells adhere to a soft elastic substrate, which is then deformed…

The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…

Analysis of PDEs · Mathematics 2010-10-05 Elisa Davoli , Maria Giovanna Mora

The phenomenon of drag reduction by polymer additives had been studied in simulations on the basis of non-Newtonian fluid mechanical models that take into account the field of polymer extension (conformation tensor) and its interaction with…

Fluid Dynamics · Physics 2009-11-10 Roberto Benzi , Emily S. C. Ching , Itamar Procaccia

We study a variational model in nonlinear elasticity allowing for cavitation which penalizes both the volume and the perimeter of the cavities. Specifically, we investigate the approximation (in the sense of {\Gamma}-convergence) of the…

Analysis of PDEs · Mathematics 2025-03-11 Marco Bresciani , Manuel Friedrich

We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic…

Analysis of PDEs · Mathematics 2015-09-02 Pierluigi Cesana , Paul Plucinsky , Kaushik Bhattacharya

A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…

Analysis of PDEs · Mathematics 2013-10-31 Jean-Francois Babadjian , Elvira Zappale , Hamdi Zorgati

Computational simulations have the potential to assist in liver resection surgeries by facilitating surgical planning, optimizing resection strategies, and predicting postoperative outcomes. The modeling of liver tissue across multiple…

Computational Engineering, Finance, and Science · Computer Science 2023-06-14 Adnan Ebrahem , Etienne Jessen , Marco F. P. ten Eikelder , Tarun Gangwar , Michał Mika , Dominik Schillinger

We show convergence of a cell-centered finite volume discretization for linear elasticity. The discretization, termed the MPSA method, was recently proposed in the context of geological applications, where cell-centered variables are often…

Numerical Analysis · Mathematics 2017-05-19 Jan Martin Nordbotten

Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family.…

Analysis of PDEs · Mathematics 2013-08-06 Martin Jesenko , Bernd Schmidt