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Related papers: Linear viscoelasticity: Mechanics, analysis and ap…

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A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…

Analysis of PDEs · Mathematics 2024-08-28 Willem J. M. van Oosterhout

Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel,…

Disordered Systems and Neural Networks · Physics 2011-12-06 Xiaoming Mao , Paul M. Goldbart , Xiangjun Xing , Annette Zippelius

This paper proves that the linear elastic behavior of the material with inhomogeneous pre-stresses can be described by the Willis equations. In this case, the additional terms in the Willis equations, compared with the classical linear…

Classical Physics · Physics 2015-11-10 Zhihai Xiang , Ruiwen Yao

We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of…

High Energy Physics - Theory · Physics 2021-09-16 Jay Armas , Akash Jain

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…

Materials Science · Physics 2020-02-17 Snarskii Andrei , Shamonin Mikhail , Yuskevich Pavel

Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…

General Relativity and Quantum Cosmology · Physics 2017-08-23 Robert Beig , Bernd G. Schmidt

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

This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite…

Mathematical Physics · Physics 2011-02-08 Ivana Bochicchio , Elena Vuk

In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…

Mathematical Physics · Physics 2014-03-17 Patrizio Neff , Ionel-Dumitrel Ghiba , Markus Lazar , Angela Madeo

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…

High Energy Physics - Phenomenology · Physics 2024-11-08 Alessio Zaccone

Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Understanding the origins of such rheologic behaviors is crucial to find proper technological applications. Using an elastic…

Soft Condensed Matter · Physics 2023-03-14 A. E. O. Ferreira , J. L. B. de Araújo , W. P. Ferreira , J. S. de Sousa , C. L. N. Oliveira

An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with…

Computational Engineering, Finance, and Science · Computer Science 2025-06-27 Stephen T. Castonguay , Joshua B. Fernandes , Michael A. Puso , Sylvie Aubry

Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…

Mathematical Physics · Physics 2026-05-14 Rohan Abeyaratne , Roberto Paroni , Marco Picchi Scardaoni

A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…

Soft Condensed Matter · Physics 2023-02-28 P. J. Atzberger

A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…

Analysis of PDEs · Mathematics 2019-10-16 Maria Deliyianni , Varun Gudibanda , Jason Howell , Justin T. Webster

The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…

Analysis of PDEs · Mathematics 2023-09-14 Tomáš Roubíček

For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…

Materials Science · Physics 2007-05-23 Petr Lazar , Raimund Podloucky , Walter Wolf

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…

Dynamical Systems · Mathematics 2014-03-05 Robert Szalai

A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…

Classical Physics · Physics 2025-06-26 D. Bigoni , S. G. Mogilevskaya , A. Piccolroaz , M. Gaibotti

We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…

Numerical Analysis · Mathematics 2024-10-22 Wietse Marijn Boon , Omar Duran , Jan Martin Nordbotten