Stochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible case

DOI10.1002/zamm.201500255OpenAlexW2529952079MaRDI QIDQ6065111

Johann Guilleminot, Unnamed Author

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)

Full work available at URL: https://doi.org/10.1002/zamm.201500255

zbMATH Keywords

stochastic modelingmaximum entropy principleuncertaintiespolyconvexityhyperelasticity

Mathematics Subject Classification ID

Numerical and other methods in solid mechanics (74Sxx) Generalities, axiomatics, foundations of continuum mechanics of solids (74Axx) Elastic materials (74Bxx)

Related Items

Stochastic hyperelastic modeling considering dependency of material parameters ⋮ Stochastic isotropic hyperelastic materials: constitutive calibration and model selection ⋮ Likely cavitation and radial motion of stochastic elastic spheres ⋮ Likely equilibria of stochastic hyperelastic spherical shells and tubes

Cites Work

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• The efficient evaluation of the hypergeometric function of a matrix argument
• A Mathematical Theory of Communication
• On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties
• Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials
• The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains
• Convexity conditions and existence theorems in nonlinear elasticity
• Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations
• Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction.
• On a new class of elastic deformations not allowing for cavitation
• Hyperelastic energy densities for soft biological tissues: a review
• Fitting hyperelastic models to experimental data
• Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media
• Some Open Problems in Elasticity
• Information Theory and Statistical Mechanics
• Spectral Methods for Uncertainty Quantification
• Fourth-rank tensors of the thirty-two crystal classes: multiplication tables
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• AN OVERVIEW OF NONINTRUSIVE CHARACTERIZATION, PROPAGATION, AND SENSITIVITY ANALYSIS OF UNCERTAINTIES IN COMPUTATIONAL MECHANICS
• Itô SDE--based Generator for a Class of Non-Gaussian Vector-valued Random Fields in Uncertainty Quantification
• Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids
• Matrix variate Kummer-Dirichlet distributions