Second-gradient continua: from Lagrangian to Eulerian and back (Q6644345)

scientific article; zbMATH DE number 7950201

Language	Label	Description	Also known as
English	Second-gradient continua: from Lagrangian to Eulerian and back	scientific article; zbMATH DE number 7950201

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instance of

scholarly article

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title

Second-gradient continua: from Lagrangian to Eulerian and back (English)

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Mathematics and Mechanics of Solids

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publication date

27 November 2024

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zbMATH Keywords

continuum mechanics

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second-gradient continua

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piola transformation

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principle of virtual work

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Lagrangian formulation

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Eulerian formulation

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The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure

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The method of virtual power in the mechanics of continuous media. I. Second-gradient theory

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Elastic materials with couple-stresses

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The complete works of Gabrio Piola: Volume I. Commented English translation of the original Italian works, published between 1825 and 1856

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Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives

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How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert''

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An introduction to continuum mechanics

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The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results

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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

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Cauchy tetrahedron argument applied to higher contact interactions

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Edge contact forces and quasi-balanced power

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An appreciation and discussion of Paul Germain's ``The method of virtual power in the mechanics of continuous media. I.: second-gradient theory''

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Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger

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Exegesis of Sect. II and III.A from “Fundamentals of the Mechanics of Continua” by E. Hellinger

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Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger

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Q5729748

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The complete works of Gabrio Piola: Volume II. Commented English translation of the original Italian works

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Variational principles are a powerful tool also for formulating field theories

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Q4340096

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Q5528072

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Q3909512

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The effect of a pre-existing nanovoid on martensite formation and interface propagation: a phase field study

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Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids

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Continuum mechanics through the eighteenth and nineteenth centuries. Historical perspectives from John Bernoulli (1727) to Ernst Hellinger (1914)

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Cauchy and the modern mechanics of continua

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Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales

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Equilibrium of a second-gradient fluid and an elastic solid with surface stresses

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Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional \textit{Elastica}

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On the notion of stress in classical continuum mechanics

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In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

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On the Direct Approach in the Theory of Second Gradient Plates

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Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field

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Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics

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Linear pantographic sheets: asymptotic micro-macro models identification

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Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations

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Linear Boltzmann dynamics in a strip with large reflective obstacles: stationary state and residence time

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Numerical investigation of a particle system compared with first and second gradient continua: Deformation and fracture phenomena*

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A homogenized theory for functionally graded Euler-Bernoulli and Timoshenko beams

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Semi-inverse method à la Saint-Venant for two-dimensional linear isotropic homogeneous second-gradient elasticity

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A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling

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Equilibrium paths of Hencky pantographic beams in a three-point bending problem

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An unconstrained dynamic approach for the generalised beam theory

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Stepwise analysis of pantographic beams subjected to impulsive loads

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Finite element formulations for constrained spatial nonlinear beam theories

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Reformulation of elasticity theory for discontinuities and long-range forces

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Fluid-elastic structure interaction simulation by using ordinary state-based peridynamics and peridynamic differential operator

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A review on 2D models for the description of pantographic fabrics

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Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

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Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model

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B-spline interpolation of Kirchhoff-Love space rods

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A variational model based on isogeometric interpolation for the analysis of cracked bodies

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A nonsmooth generalized-alpha method for mechanical systems with frictional contact

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Two new triangular \(\operatorname{G}^1\)-conforming finite elements with cubic edge rotation for the analysis of Kirchhoff plates

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A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results

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Two-dimensional strain gradient damage modeling: a variational approach

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On the dependence of standard and gradient elastic material constants on a field of defects

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Energy approach to brittle fracture in strain-gradient modelling

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Stiffness optimization in nonlinear pantographic structures

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Q5560249

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Q4133227

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Continuum theory for mechanical metamaterials with a cubic lattice substructure

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On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continua

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Identifiers

DOI

10.1177/10812865221078822

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Mathematics Subject Classification ID

74-XX

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zbMATH DE Number

7950201

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Sitelinks

Mathematics(1 entry)

mardi Publication:6644345