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A finite element discretization is developed for the Cai-Hu model, describing the formation of biological networks. The model consists of a non linear elliptic equation for the pressure $p$ and a non linear reaction-diffusion equation for…

Numerical Analysis · Mathematics 2025-03-28 Clarissa Astuto , Daniele Boffi , Fabio Credali

This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on…

Numerical Analysis · Mathematics 2026-03-10 De-Han Chen , Yi-Hsuan Lin , Irwin Yousept

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Gerard Awanou , Ragnar Winther

This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…

Numerical Analysis · Mathematics 2025-07-02 Ram Manohar , S. M. Mallikarjunaiah

We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion.…

Numerical Analysis · Mathematics 2020-06-03 Erik Burman , Peter Hansbo , Mats G. Larson

This work concerns the continuum basis and numerical formulation for deformable materials with viscous dissipative mechanisms. We derive a viscohyperelastic modeling framework based on fundamental thermomechanical principles. Since most…

Numerical Analysis · Mathematics 2021-08-12 Ju Liu , Marcos Latorre , Alison L. Marsden

In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…

Numerical Analysis · Mathematics 2020-08-21 Tingting Hao , Manman Ma , Xuejun Xu

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

Numerical Analysis · Mathematics 2026-04-28 Andrea Bonito , Vivette Girault , Diane Guignard

The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven…

Soft Condensed Matter · Physics 2025-09-19 Denisa Martonová , Alain Goriely , Ellen Kuhl

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

Computational Engineering, Finance, and Science · Computer Science 2020-05-20 Reza Behrou , Maroun Abi Ghanem , Brianna C. Macnider , Vimarsh Verma , Ryan Alvey , Jinho Hong , Ashley F. Emery , Hyunsun Alicia Kim , Nicholas Boechler

This paper models stress softening during cyclic loading and unloading of an elastomer. The paper begins by remodelling the primary loading curve to include a softening function and goes on to derive non-linear transversely isotropic…

Soft Condensed Matter · Physics 2020-05-19 S. R. Rickaby , N. H. Scott

We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the present…

Analysis of PDEs · Mathematics 2020-09-09 Husnu A. Erbay , Yasemin Sengul

We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The…

Numerical Analysis · Mathematics 2009-06-26 Kenneth H. Karlsen , Trygve K. Karper

Constitutive equations are derived for the viscoelastic behavior of filled elastomers at isothermal loading with finite strains. A particle-reinforced rubber is thought of as a composite where regions with low concentrations of junctions…

Materials Science · Physics 2009-11-07 Aleksey D. Drozdov , Al Dorfmann

Understanding the role played by the microstructure of materials on their macroscopic failure properties is an important challenge in solid mechanics. Indeed, when a crack propagates at a heterogeneous brittle interface, the front is…

Materials Science · Physics 2015-11-09 Sylvain Patinet , L Alzate , E Barthel , D Dalmas , D Vandembroucq , V Lazarus

In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with…

Numerical Analysis · Mathematics 2023-08-08 Jeonghun J. Lee , Jacob Moore

In this paper, we develop an elasto-viscoplastic (EVP) model for clay using the non-associated flow rule. This is accomplished by using a modified form of the Perzyna's overstressed EVP theory, the critical state soil mechanics, and the…

Geophysics · Physics 2019-11-27 M. N. Islam , C. T. Gnanendran , M. Massoudi

In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…

Numerical Analysis · Mathematics 2013-09-04 Sundararajan Natarajan , Chongmin Song

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…

Soft Condensed Matter · Physics 2015-06-16 Nishant Kumar , Stefan Luding , Vanessa Magnanimo

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while…

Materials Science · Physics 2022-04-22 Vishnu Raghuraman , Michael Widom , Michael C. Gao