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We use a differential constitutive equation to model the flow of a viscoelastic flow in a cross-slot geometry, which is known to exhibit bistability above a critical flow rate. The novelty lies in two asymmetric modifications to the…

Fluid Dynamics · Physics 2018-02-19 Kristian Ejlebjerg Jensen , Peter Szabo , Fridolin Okkels

We study the solution of the system of equations describing the dynamical evolution of spontaneous ruptures generated in a prestressed elastic-gravitational deforming body and governed by rate and state friction laws. We propose an…

Computational Physics · Physics 2019-08-26 Maarten V. de Hoop , Kundan Kumar , Ruichao Ye

The problem of the sudden growth and coalescence of voids in elastic media is considered. The Dirichlet energy is minimized among incompressible and invertible Sobolev deformations of a two-dimensional domain having $n$ microvoids of radius…

Analysis of PDEs · Mathematics 2019-06-26 Victor Cañulef-Aguilar , Duvan Henao

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the…

Materials Science · Physics 2009-11-10 Itai Afek , Eran Bouchbinder , Eytan Katzav , Joachim Mathiesen , Itamar Procaccia

The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a…

Disordered Systems and Neural Networks · Physics 2023-09-11 Freya Behrens , Barbora Hudcová , Lenka Zdeborová

We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in $D$ dimensions coupled to a $q$-form field and positive cosmological constant. We show that…

High Energy Physics - Theory · Physics 2021-09-13 Maxence Corman , William E. East , Matthew C. Johnson

The nonconservative elastic responses of active solids have driven a recent explosion of interest in two-dimensional "odd" elasticity: small, linear deformations of these Cauchy elastic solids enable new behaviour absent from classical,…

Soft Condensed Matter · Physics 2026-05-05 Shiheng Zhao , Pierre A. Haas

The nucleation of cavities in a homogenous polymer under tensile strain is investigated in a coarse-grained molecular dynamics simulation. In order to establish a causal relation between local microstructure and the onset of cavitation, a…

Materials Science · Physics 2012-04-20 Ali Makke , Michel Perez , Joerg Rottler , Olivier Lame , Jean-Louis Barrat

Using a matched asymptotic expansion we analyze the two-dimensional, near- critical reflection of a weakly nonlinear, internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the…

patt-sol · Physics 2017-05-17 T. Dauxois , W. R. Young

A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…

Analysis of PDEs · Mathematics 2020-06-24 Shokhrukh Yu. Kholmatov , Paolo Piovano

The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the constitutive parameters are characterised by probability density…

Classical Physics · Physics 2020-03-17 L. Angela Mihai , Thomas E. Woolley , Alain Goriely

Inertial cavitation in soft matter is an important phenomenon featured in a wide array of biological and engineering processes. Recent advances in experimental, theoretical, and numerical techniques have provided access into a world full of…

Soft Condensed Matter · Physics 2022-03-21 Jin Yang , Anastasia Tzoumaka , Kazuya Murakami , Eric Johnsen , David L. Henann , Christian Franck

We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow…

Materials Science · Physics 2009-10-31 Alexander E. Lobkovsky , J. S. Langer

A fundamental open problem in the theory of the multidimensional compressible Navier-Stokes equations is whether smooth solutions can develop singularities in finite time. For constant viscosity coefficients, recent remarkable results show…

Analysis of PDEs · Mathematics 2026-03-25 Gui-Qiang G. Chen , Lihui Liu , Shengguo Zhu

The dynamics of defect excitations in crystalline solids is necessary to understand the macroscopic low-energy properties of elastic media. We use fracton-elasticity duality to systematically study the defect dynamics and interactions in…

Materials Science · Physics 2024-05-07 Lazaros Tsaloukidis , Piotr Surówka

We study the time evolution of non-linear viscoelastic solids in the presence of inertia and (self-)contact. For this problem we prove the existence of weak solutions for arbitrary times and initial data, thereby solving an open problem in…

Analysis of PDEs · Mathematics 2023-12-04 Antonín Češík , Giovanni Gravina , Malte Kampschulte

We consider a system of evolutionary equations that is capable of describing certain viscoelastic effects in linearized yet nonlinear models of solid mechanics. The essence of the paper is that the constitutive relation, involving the…

Analysis of PDEs · Mathematics 2020-11-25 Miroslav Bulíček , Victoria Patel , Yasemin Şengül , Endre Süli

Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progres- sively cavitating plastic solid with two…

We propose a model for quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only…

Analysis of PDEs · Mathematics 2025-07-22 Marco Bresciani , Manuel Friedrich

The two-dimensional thermoelastic problem of an adiabatic cavity in an infinite isotropic homogeneous medium subjected to uniform heat flux is studied, where the shape of the cavity is characterized by the Laurent polynomial. By virtue of a…

Applied Physics · Physics 2021-03-03 Zhaohang Lee , Yu Tang , Wennan Zou