Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger
From MaRDI portal
Publication:6064307
DOI10.1002/zamm.201700112MaRDI QIDQ6064307
Francesco dell'Isola, Simon R. Eugster
Publication date: 12 December 2023
Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)
Thermodynamics and heat transfer (80Axx) History of mathematics and mathematicians (01Axx) Generalities, axiomatics, foundations of continuum mechanics of solids (74Axx)
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Cites Work
- A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model
- A virtual power format for thermomechanics
- The complete works of Gabrio Piola: Volume I. Commented English translation of the original Italian works, published between 1825 and 1856
- A second gradient formulation for a 2D fabric sheet with inextensible fibres
- A review on 2D models for the description of pantographic fabrics
- Non-standard coupled extensional and bending bias tests for planar pantographic lattices. I: Numerical simulations
- Non-standard coupled extensional and bending bias tests for planar pantographic lattices. II: Comparison with experimental evidence
- Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures
- On the derivation of thermomechanical balance equations for continuous systems with a nonmaterial interface
- Continuum description of the dynamics and thermodynamics of phase boundaries between ice and water. III: Thermostatics and its consequences
- Continuum description of the dynamics and thermodynamics of phase boundaries between ice and water. IV: On thermostatic stability and well- posedness
- Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales
- Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof
- On phase transition in classical fluid mixtures with surface adsorption
- On a principle of virtual work for thermoelastic bodies
- Hypertractions and hyperstresses convey the same mechanical information
- A phenomenological approach to phase transition in classical field theory
- On a general balance law for continua with an interface
- Continuum description of the dynamics and thermodynamics of phase boundaries between ice and water. I. Surface balance laws and their interpretation in terms of three-dimensional balance laws averaged over the phase change boundary layer. II. Thermodynamics
- Elastic materials with couple-stresses
- The method of virtual power in continuum mechanics: Application to coupled fields
- A justification of the von Kármán equations
- A phase-field theory for solidification based on a general anisotropic sharp-interface theory with interfacial energy and entropy
- Revisiting brittle fracture as an energy minimization problem
- Introduction to relativistic continuum mechanics
- A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
- A principle of objectivity for relativistic continuum mechanics
- A variational approach for a nonlinear 1-dimensional second gradient continuum damage model
- A model for elastic flexoelectric materials including strain gradient effects
- Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids
- Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
- Mechanical and Thermodynamical Modeling of Fluid Interfaces
- The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure
- General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids
- Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives
- Euclidean Geometry and Minkowskian Chronometry
- 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
- Nonlinear problems of elasticity
- Exegesis of Sect. II and III.A from “Fundamentals of the Mechanics of Continua” by E. Hellinger
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