ON THE METHOD OF VIRTUAL POWER IN CONTINUUM MECHANICS

By G. Piero. 2009

209 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a6efa9ed01c2bdc0948cb461a837d533d2f022c9

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In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert” (2012, background): “[59], [60], [61], [62], [110], [29], [30], [84], [87], [88] ) who follow the ideas of D’Alembert and Lagrange as the basic concept in mechanics.”
A limit analysis approach based on Cosserat continuum for the evaluation of the in-plane strength of discrete media: Application to masonry (2017, unknown): “Cosserat (or micropolar) continuum is a special case of a micromorphic continuum of ﬁrst order (Eringen, 1999; Germain, 1973; Godio et al., 2015).”
Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger (2017, background): “The reader should remark that the extended kinematics considered here includes micro-rotations, but does not consider micro-deformations: a clear variational treatment of continua with micro-stretch is presented in [42], where the ideas presented by Hellinger are fully developed.”
Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua (2010, background): “Coupling with other phenomena can be performed in a systematic way by means of the method of virtual power and of continuum thermomechanics, e.g. (Maugin, 1980).”
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 (2013, background): “…in Russo [2, 3] the author clearly analyses the consequences of the existence of those linguistic ideological and cultural barriers which did not permit the Latin-speaking scholars to understand the depth of Hellenistic science: the beginning of the economical and social processes leading to the…”
Linear pantographic sheets: Asymptotic micro-macro models identification (2017, background): “A phenomenological approach can applied at the macroscopic scale: it gives a general framework and in general it is based on variational principles and methods ([70, 90, 50, 53, 22, 41, 38, 64]); however, using this approach it is not possible to make the influence of microstructure on macrophenomen”
Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua (2012, unknown): “[63], [64], [65], [23], [24], [40] and [41].”
On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush (2016, background): “The relation between the Cauchy-like stress and constitutive stress indeed involve the volume simple double and triple forces (see [6] in French, first part on the classical theory).”
Generalized continua and non‐homogeneous boundary conditions in homogenisation methods (2011, methodology): “1 Definition of the micromorphic degrees of freedom A kinematic view of the micromorphic model has been proposed by Germain [26] that we rephrase here.”
Granular micromechanics based micromorphic model predicts frequency band gaps (2015, methodology): “Since the second rank tensor γi j (xk) is independent of coordinates x ′ k (homogeneous within the material point), the fluctuations modeled this way are taken as linear within the material point, which leads to a micromorphic theory of degree 1 in the terminology introduced by Germain [6].”
A Geometrically Exact Micromorphic Model for Elastic Metallic Foams Accounting for Affine Microstructure. Modelling, Existence of Minimizers, Identification of Moduli and Computational Results (2007, methodology): “The strain measures used in [32] are retained for the computational part of this work:”
Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics (2018, background): “Two branches of generalized continuum theories can be distinguished: ”higher-order” theories in which the number of degrees of freedom increases [5, 6, 7, 8, 9], and ”higher-grade/gradient” theories in which the higher gradients of displacements (or strains) are included [10, 6, 11, 12].”
A unifying perspective: the relaxed linear micromorphic continuum (2013, unknown): “Let us consider the general energy from the isotropic strain gradient model [3,38,42,62,63,114,161] E(∇u, D2u) = μ ‖ sym ∇u‖2 + λ 2 [tr(sym ∇u)]2 + Wcurv(∇ sym ∇u).”