P. Mast, G. Nash, J. G. Michopoulos, R. Thomas, I. Wolock et al., Characterization of strain-induced damage in composites based on the dissipated energy density part iii. general material constitutive relation, Theoretical and Applied Fracture Mechanics, vol.22, issue.2, pp.115-125, 1995.

J. Michopoulos, J. Hermanson, and T. Furukawa, Towards the robotic characterization of the constitutive response of composite materials, Composite Structures, vol.86, issue.1-3, pp.154-164, 2008.

J. Michopoulos, J. Hermanson, A. Iliopoulos, S. Lambrakos, and T. Furukawa, Data-driven design optimization for composite material characterization, Journal of Computing and Information Science in Engineering, vol.11, issue.2, p.21009, 2011.

J. Michopoulos, J. Hermanson, and A. Iliopoulos, Advances on the constitutive characterization of composites via multiaxial robotic testing and design optimization, Advances in computers and information in engineering research, vol.1, pp.73-95, 2014.

C. Soize, Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial derivative operators, Comput. Methods Appl. Mech. Engrg, vol.195, pp.26-64, 2006.

J. Guilleminot and C. Soize, Stochastic model and generator for random fields with symmetry properties: Application to the mesoscopic modeling of elastic random media, SIAM Multiscale Modeling & Simulation, vol.11, pp.840-870, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00854121

B. Staber and J. Guilleminot, Stochastic modeling and generation of random fields of elasticity tensors: a unified information-theoretic approach, Compte rendus Mécanique, vol.345, pp.299-416, 2017.

J. Guilleminot and C. Soize, On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties, Journal of Elasticity, vol.111, pp.109-130, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00724048

B. Staber and J. Guilleminot, Stochastic modeling of a class of stored energy functions for incompressible hyperelastic materials with uncertainties, Compte rendus Mécanique, vol.349, pp.503-514, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01223820

B. Staber and J. Guilleminot, Stochastic modeling of the ogden class of stored energy functions for hyperelastic materials: the compressible case, ZAMM -Journal of Applied Mathematics and Mechanics, vol.97, pp.273-295, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01359703

L. A. Mihai, T. E. Woolley, and A. Goriely, Stochastic isotropic hyperelastic materials: constitutive calibration and model selection, Proceedings of the Royal Society A, vol.474, 2018.
DOI : 10.1098/rspa.2017.0858

URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5897763

B. Staber and J. Guilleminot, A random field model for anisotropic strain energy functions and its application for uncertainty quantification in vascular mechanics, Computer Methods in Applied Mechanics and Engineering, vol.333, pp.94-113, 2018.

B. Staber and J. Guilleminot, Stochastic hyperelastic constitutive laws and identification procedure for soft biological tissues with intrinsic variability, Journal of the Mechanical Behavior of Biomedical Materials, vol.65, pp.743-752, 2017.
DOI : 10.1016/j.jmbbm.2016.09.022

URL : https://hal.archives-ouvertes.fr/hal-01367381

P. T. Brewick and K. Teferra, Uncertainty quantification for constitutive model calibration of brain tissue, Journal of the Mechanical Behavior of Biomedical Materials, vol.85, pp.237-255, 2018.

J. Michopoulos, J. Hermanson, A. Iliopoulos, A. Lambrakos, and T. Furukawa, Overview of constitutive response characterization for composite materials via data-driven design optimization, Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, 2011.

A. Iliopoulos and J. Michopoulos, Direct strain imaging for full field measurements, ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, vol.2, pp.1021-1031, 2012.
DOI : 10.1115/detc2012-71109

A. P. Iliopoulos and J. G. Michopoulos, Direct strain tensor approximation for full-field strain measurement methods, International Journal for Numerical Methods in Engineering, vol.95, issue.4, pp.313-330, 2013.
DOI : 10.1002/nme.4509

A. P. Iliopoulos and J. G. Michopoulos, Meshless methods for full field displacement and strain measurement, Advances in Computers and Information in Engineering Research, vol.1, pp.97-124, 2014.
DOI : 10.1115/1.860328_ch5

P. G. Ciarlet, Three-Dimensional Elasticity, Mathematical Elasticity, vol.I, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01077590

R. W. Ogden, Non-Linear Elastic Deformations, 1997.
DOI : 10.1016/0264-682x(84)90061-3

J. Schröder, P. Neff, and V. Ebbing, Anisotropic polyconvex energies on the basis of crystallographic motivated structural tensors, Journal of the Mechanics and Physics of Solids, vol.56, issue.12, pp.3486-3506, 2008.

J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Ration. Mech. Anal, vol.3, pp.337-403, 1977.
DOI : 10.1007/bf00279992

S. Müller, T. Qi, and B. S. Yan, On a new class of elastic deformations not allowing for cavitation, Ann. Inst. Henri Poincaré, Analyse Nonlinéaire, vol.11, issue.2, pp.217-243, 1994.

, Handbook of Uncertainty Quantification, 2017.

C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, vol.27, pp.379-423, 1948.

E. T. Jaynes, Information theory and statistical mechanics i, Physical Review, vol.106, issue.4, pp.620-630, 1957.
DOI : 10.1103/physrev.106.620

E. T. Jaynes, Information theory and stastitical mechanics ii, Physical Review, vol.108, issue.2, pp.171-190, 1957.

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, vol.15, issue.3, pp.277-294, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00686293

M. Shinozuka and G. Deodatis, Simulation of stochastic processes by spectral representation, Applied Mechanics Reviews, vol.44, issue.4, pp.191-204, 1991.

F. Poirion and C. Soize, Numerical methods and mathematical aspects for simulation of homogeneous and non homogeneous gaussian vector fields, Probabilistic methods in applied physics, pp.17-53, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00770416

A. Iliopoulos, J. G. Michopoulos, and J. C. Hermanson, Loading subspace selection for multidimensional characterization tests via computational experiments, ASME, editor, Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2010, 2010.

B. Dacorogna, Direct methods in the calculus of variations, 2007.

J. Schröder and P. Neff, Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions, International journal of solids and structures, vol.40, issue.2, pp.401-445, 2003.