Unified constitutive modeling of anisotropic hyperelastic materials at large strains

2003 ◽  
Vol 105 ◽  
pp. 289-296
Author(s):  
M. Itskov ◽  
N. Aksel
Keyword(s):  
Constitutive Modeling ◽  
Large Strains ◽  
Hyperelastic Materials

scholarly journals Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170858 ◽  
Author(s):  
L. Angela Mihai ◽  
Thomas E. Woolley ◽  
Alain Goriely
Keyword(s):  
Model Selection ◽  
Finite Elasticity ◽  
Experimental Tests ◽  
Mechanical Tests ◽  
Large Strains ◽  
Intrinsic Variability ◽  
Mean Values ◽  
Practical Applications ◽  
Hyperelastic Materials ◽  
Hyperelastic Models

Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress–strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam’s razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

Constitutive modeling of porous hyperelastic materials

2004 ◽  
Vol 36 (4) ◽  
pp. 347-358 ◽  
Author(s):  
M Danielsson ◽  
D.M Parks ◽  
M.C Boyce
Keyword(s):  
Constitutive Modeling ◽  
Hyperelastic Materials

The mensuration of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 216-217
Author(s):  
W.M. Stobbs
Keyword(s):  
Electron Microscopy ◽  
50Th Anniversary ◽  
Numerical Data ◽  
Industrial Applications ◽  
Dynamical Theory ◽  
Large Strains ◽  
Reasonable Approach ◽  
Lattice Resolution ◽  
Analogue To Digital ◽  
The Way

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.

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