Journal ArticleDOI
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids
TLDR
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented in this paper, where a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler-Lagrange equations.Abstract:
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.read more
Citations
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Minimization principles for the coupled problem of Darcy–Biot-type fluid transport in porous media linked to phase field modeling of fracture
TL;DR: In this paper, the authors developed new minimization and saddle point principles for the coupled problem of Darcy-Biot-type fluid transport in porous media at fracture and showed that the quasi-static problem of elastically deforming, fluid-saturated porous media is related to a minimization principle for the evolution problem.
Journal ArticleDOI
On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials
Klaus Hackl,Franz Dieter Fischer +1 more
TL;DR: In this paper, the authors study the evolution of systems described by internal variables and define the dissipation and dissipation potential in a variational formulation, and show that both principles lead to the same evolution equations for the internal variables.
Journal ArticleDOI
Biomechanics of traumatic brain injury
TL;DR: A biomechanical model for traumatic brain injury and soft tissue damage is presented and future directions of this work, relating mechanical damage and physiological brain dysfunction, and application to relevant medical and engineering problems are discussed.
Journal ArticleDOI
An approach for incorporating classical continuum damage models in state-based peridynamics
TL;DR: An approach to incorporate classical continuum damage models in the state-based theory of peridynamics has the advantage of enabling the description of the damage evolution process in perid dynamics according to well-established models.
References
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Book
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Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.
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TL;DR: The Mumford-Shah functional minimiser of free continuity problems as mentioned in this paper is a special function of the Mumfordshah functional and has been shown to be a function of free discontinuity set.
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TL;DR: In this paper, the authors present a method to produce dynamic deformation at high strain rates by using Shear Bands (Thermoplastic Shear Instabilities) and dynamic fracture.
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Elastic-Plastic Deformation at Finite Strains
TL;DR: In this paper, the authors generalize a previous theory to permit arbitrary deformation histories by considering two coupled thermodynamic systems: one comprising thermo- elasticity at finite strain and the other the irreversible process of dissipation and absorption of plastic work.
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