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Toward fractional gradient elasticity [PDF]
Journal of the Mechanical Behavior of Materials, 2014 The use of an extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe the power law type of non-locality is discussed. Two phenomenological possibilities are explored. The first is based on the Caputo
Tarasov Vasily E., Aifantis Elias C.
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On gradient field theories: gradient magnetostatics and gradient elasticity [PDF]
Philosophical Magazine, 2014 In this work the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared.
Lazar, Markus
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Non-Conventional Thermodynamics and Models of Gradient Elasticity [PDF]
Entropy, 2018 We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange ...
Hans-Dieter Alber +3 more
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Thermodynamically consistent gradient elasticity with an internal variable [PDF]
Theoretical and Applied Mechanics, 2020 The role of thermodynamics in continuum mechanics and the derivation of proper constitutive relations is a topic discussed in Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical of the
Ván Peter
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Gradient elasticity solutions of 2D nano-beams
Applications in Engineering Science, 2023 In this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered.
Teoman Özer
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A Proposition for a "Self-Consistent" Gradient Elasticity [PDF]
Journal of the Mechanical Behavior of Materials, 2009 The notion of “self-consistent” boundary conditions in gradient elasticity is explored. They are introduced in the place of the “standard” boundary conditions commonly used in the formulation of gradient elasticity problems derived through corresponding variational principles.
Efremidis, G. +2 more
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The Green tensor of Mindlin’s anisotropic first strain gradient elasticity
Materials Theory, 2019 We derive the Green tensor of Mindlin’s anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of triclinic media.
Giacomo Po +2 more
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Gradient-enriched linear-elastic tip stresses to perform the highcycle fatigue assessment of notched plain concrete [PDF]
Fracture and Structural Integrity, 2015 Gradient Elasticity (GE) allows the stress analysis to be performed by taking into account the size of the dominant source of microstructural heterogeneity via a suitable length scale parameter.
C. Bagni, H. Askes, L. Susmel
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity [PDF]
Lobachevskii Journal of Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eremeyev V. A., dell'Isola F.
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Materials & Design, 2023 Functionally graded polymer foams are advanced materials that exhibit great potential for applications in energy absorption, electromagnetic interference shielding, and high-elasticity due to the graded cellular structure for mechanical performance and ...
Lijun Zhu +5 more
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