Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger
From MaRDI portal
Publication:6065129
DOI10.1002/zamm.201600108MaRDI QIDQ6065129
Simon R. Eugster, Francesco dell'Isola
Publication date: 11 December 2023
Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)
Thin bodies, structures (74Kxx) History of mathematics and mathematicians (01Axx) Generalities, axiomatics, foundations of continuum mechanics of solids (74Axx)
Related Items
To Francesco dell’Isola ⋮ Maestro and his pupils: History of a scientific production ⋮ Third-gradient continua: nonstandard equilibrium equations and selection of work conjugate variables ⋮ From fluid mechanics backgrounds to modern field theory ⋮ Asymmetric lipid bilayers from the perspective of three-dimensional liquid crystal theory ⋮ The contribution of Gustav R. Kirchhoff to the dynamics of tapered beams ⋮ On the notion of stress in classical continuum mechanics ⋮ The «materialization» of forces: Why confounding mathematical concept and physical entity makes the design of metamaterials arduous ⋮ Energy based methods applied in mechanics by using the extended Noether's formalism ⋮ Extended granular micromechanics approach: a micromorphic theory of degreen ⋮ Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis ⋮ Linear pantographic sheets: existence and uniqueness of weak solutions ⋮ A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams ⋮ Continuum theory for mechanical metamaterials with a cubic lattice substructure ⋮ Commented translation of Erwin Schrödinger’s paper ‘On the dynamics of elastically coupled point systems’ (Zur Dynamik elastisch gekoppelter Punktsysteme) ⋮ Lagrangian descriptions of dissipative systems: a review ⋮ Dynamics of pantographic sheet around the clamping region: experimental and numerical analysis
Cites Work
- Buckling of an elastic hemispherical shell with an obstacle
- Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations
- The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids
- Granular micromechanics based micromorphic model predicts frequency band gaps
- A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings
- Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks
- Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales
- Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials
- Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics
- Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof
- Hypertractions and hyperstresses convey the same mechanical information
- Elastic materials with couple-stresses
- Functional concepts in continuum mechanics
- Edge contact forces and quasi-balanced power
- How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert
- Equilibrium of a second-gradient fluid and an elastic solid with surface stresses
- On generalized Cosserat-type theories of plates and shells: a short review and bibliography
- Multipolar continuum mechanics
- An unconstrained dynamic approach for the generalised beam theory
- A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis
- Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations
- Cosserat-Type Rods
- A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials
- A 2-D continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution under load slowly variable in time
- Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids
- Existence theorems in the linear theory of micropolar shells
- Continuum Thermodynamics
- On the linear theory of micropolar plates
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- Continuum Limits of Discrete Systems without Convexity Hypotheses
- The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure
- Euromech 563 Cisterna di Latina 17–21 March 2014 Generalized continua and their applications to the design of composites and metamaterials: A review of presentations and discussions
- The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results
- ADVANCED ENGINEERING ANALYSIS
- 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
- A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations
- Cauchy tetrahedron argument applied to higher contact interactions
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item