Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites

Abstract

In this paper, we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites. Here, the material is modeled as a random hyperelastic medium characterized by a spatially dependent, stochastic and anisotropic strain energy function. The latter is parametrized by a set of material parameters, modeled as non-Gaussian random fields. From a probabilistic standpoint, the construction is first achieved by invoking information theory and the principle of maximum entropy. Constraints related to existence theorems in finite elasticity are, in particular, accounted for in the formulation. The identification of the parameters defining the random fields is subsequently addressed. This issue is attacked as a two-step problem where the mean model is calibrated in a first step, by imposing a match between the linearized model and nominal values proposed in the literature. The remaining parameters controlling the fluctuations are next estimated by solving an inverse problem in which principal component analysis and the maximum likelihood method are combined. The whole framework is illustrated considering an experimental database where multi-axial measurements are performed on a carbonepoxy laminate. This work constitutes a first step towards the development of an integrated framework that will support decision making under uncertainty for the design, certification and qualification of composite materials and structures.

Likely oscillatory motions of stochastic hyperelastic solids

“…The finite dynamic analysis presented here can be extended (albeit numerically) to other stochastic homogeneous hyperelastic materials (for example, using the stochastic strain-energy functions derived from experimental data in [66]), or to inhomogeneous incompressible bodies similar to those considered deterministically in [30]. For incompressible bodies with inhomogeneous material parameters, the constitutive parameters of the stochastic hyperelastic models can be treated as random fields, as described in [99,100]. Clearly, the combination of knowledge from elasticity, statistics, and probability theories offers a richer set of tools compared to the elastic framework alone, and would logically open the way to further considerations of this type.…”

Likely chirality of stochastic anisotropic hyperelastic tubes

“…where Ψ m is the magic angle given by (52), then A 31 > 0, i.e., there is right-handed (anti-clockwise) twist;…”

“…In addition, for many solid materials, a crucial part in assessing their physical properties is to quantify the uncertainties in their mechanical responses, which cannot be ignored [18,38,40]. In finite elasticity, the use of the variability in observational data and information about uncertainties [11,53] were proposed in [48][49][50] and [33], where stochastic isotropic hyperelastic models are described by a strain-energy function, with the parameters defined as random variables characterised by probability distributions, while anisotropic stochastic models, where the parameters are spatially-dependent random fields, were discussed in [51,52]. These are phenomenological models, based on the notion of entropy (or uncertainty) [43] (see also [46]) and the maximum entropy principle for a discrete probability distribution [19][20][21], which can also be embedded in Bayesian methodologies [4] (see also [26]) for model selection and updates [33,38,42].…”

Extreme Learning Machine Based Prediction of Soil Shear Strength: A Sensitivity Analysis Using Monte Carlo Simulations and Feature Backward Elimination

“…A concept of using the Monte Carlo method is presented in Figure 4, involving a two-dimensional input space with a typical probability distribution. In this work, the statistical convergence of Monte Carlo simulations has been investigated using the following equation [18,32,39,40]: In this work, the statistical convergence of Monte Carlo simulations has been investigated using the following equation [18,32,39,40]:…”