Journal ArticleDOI
Thermodynamics with Internal State Variables
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In this paper, the authors study the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations, and employ a method developed by Coleman and Noll to find the general restrictions which the Clausius-Duhem inequality places on response functions.Abstract:
This is a study of the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations. After employing a method developed by Coleman and Noll to find the general restrictions which the Clausius—Duhem inequality places on response functions, we analyze various types of dynamical stability that can be exhibited by solutions of the internal evolution equations. We also discuss integral dissipation inequalities, conditions under which temperatures can be associated with internal states, and the forms taken by response functions when the material is a fluid.read more
Citations
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Journal ArticleDOI
The concept of physical metric in thermodynamics
TL;DR: In this paper, the authors introduce a new geometric object, the physical metric, for the measurement of distance between material particles in the reference configuration, which is in fact a measure of nonaffine deformation and introduce the concept of the hypercontinuum which allows the existence of multiple velocities in a material neighborhood, thereby leading to a deformation field with multiple metrics.
Journal ArticleDOI
A Strain-Based Formulation for the Coupled Viscoelastic/Damage Behavior
K. Abdel-Tawab,Y. Weitsman +1 more
TL;DR: In this article, a strain-based thermodynamics framework is proposed for modeling the continuum damage behavior of viscoelastic materials, where damage is represented by an internal state variable in the form of a symmetric second rank tensor.
Journal ArticleDOI
Elasto/viscoplastic constitutive equations with memory and internal variables
TL;DR: In this paper, a general elasto/viscoplastic constitutive equation of a material with memory and internal variables is proposed based on the concept of generalized simple body. And the proposed theory can describe not only such rate-dependent behaviours as primary and secondary creep, but also accelerating (teritary) creep, in which strain rate increases under constant stress.
BookDOI
Applied Wave Mathematics
Ewald Quak,Tarmo Soomere +1 more
Abstract: CENS, CMA and the CENS-CMA Project: J.Engelbrecht, R.Winther, E.Quak.- Part I.Waves in Solids.- Overview: A.Berezovski.- Deformation Waves in Solids: J.Engelbrecht.- The Perturbation Technique for Wave Interaction in Prestressed Material: A.Ravasoo.- Waves in Inhomogeneous Solids: A.Berezovski, M.Berezovski, J. Engelbrecht.- Part II. Mesoscopic Theory.- Overview: W.Muschik.- Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids: Ch.Papenfuss.- Towards a Description of Twist Waves in Mesoscopic Continuum Physics: H. Herrmann.- Part III.- Exploiting the Dissipation Inequality.- Overview: W. Muschik.- Weakly Nonlocal Non-equilibrium Thermodynamics - Variational Principles and Second Law: P. Van.- Part IV. Waves in Fluids.- Overview: T.Soomere.- Long Ship Waves in Shallow Water Bodies: T.Soomere.- Modelling of Ship Waves from High-speed Vessels: T. Torsvik.- New Trends in the Analytical Theory of Long Sea Wave Runup: I. Didenkulova.- Part V. Mathematical Methods.- Overview: E. Quak.- The Pseudospectral Method and Discrete Spectral Analysis: A. Salupere.- Foundations of Finite Element Methods for Wave Equations of Maxwell Type: S.H. Christiansen.- An Introduction to the Theory of Scalar Conservation Laws with Spatially Discontinuous Flux Functions: N.H. Risebro.- Index
Journal ArticleDOI
Numerical and experimental investigation of out-of-plane fiber waviness on the mechanical properties of composite materials
Michael Thor,U. Mandel,M. Nagler,Franz Maier,J. Tauchner,Markus G. R. Sause,Roland M. Hinterhölzl +6 more
TL;DR: In this paper, a non-linear 2D material model was implemented in ABAQUS and validated with extensive experimental test data from compression and tensile tests, which was recorded by a stereo camera system for digital image correlation to resolve damage initiation and propagation in detail.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Supersonic flow and shock waves
Richard Courant,Kurt Friedrichs +1 more
TL;DR: In this article, the authors proposed a method to compressible ecoulement for compressible compressible and supersonique and onde de choc Reference Record created on 2005-11-18, modified on 2016-08-08
Book ChapterDOI
The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity
TL;DR: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body as mentioned in this paper, which can be expressed as follows: a body is regarded as a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies.