Journal ArticleDOI
Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage
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In this paper, a unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years.Abstract:
A unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years . It is based on the introduction of the micromorphic counterpart ϕχ of a selected state or internal variable ϕ in a standard constitutive model. In addition to the classical balance of momentum equation, a balance of micromorphic momentum is derived that involves generalized stress tensors. The corresponding additional boundary conditions are also deduced from the procedure. The power of generalized forces is assumed to contribute to the energy balance equation. The free energy density function is then chosen to depend on a relative generalized strain, typically ϕ- ϕχ , and the microstrain gradient ∇ ϕχ . When applied to the deformation gradient itself, ϕ≡ F , the method yields the micromorphic theory of Eringen and Mindlin together with its extension to finite deformation elastoviscoplasticity by Forest and Sievert. If...read more
Citations
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Journal ArticleDOI
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola
TL;DR: Gabrio Piola's scientific papers have been underestimated in mathematical physics literature as mentioned in this paper, but a careful reading of them proves that they are original, deep and far-reaching, and even even...
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At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola
TL;DR: In this paper, the authors show that non-local and higher gradient continuum mechanics was conceived already in Piola's works and explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of Piola contribution.
Journal ArticleDOI
Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium
TL;DR: In this article, the authors considered a discrete spring model for extensible beams and proposed a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model.
Journal ArticleDOI
Mechanical metamaterials: a state of the art:
TL;DR: A review of the state of the art in the study of mechanical metamaterials is given in this article, where the very attractive property of having a microstructure capable of determining exotic and specific properties is discussed.
Journal ArticleDOI
Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory
TL;DR: In this paper, a variational-based framework for the phase field modeling of ductile fracture in elastic-plastic solids undergoing large strains is presented, which includes two independent length scales which regularize both the plastic response and the crack discontinuities.
References
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Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Book
Mechanics of Solid Materials
TL;DR: In this article, the physical mechanisms of deformation and fracture are discussed, including linear elasticity, thermo-elasticity, and viscoelastic properties of real solids.
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.