Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

Heuristic molecular modelling of quasi-isotropic auxetic metamaterials under large deformations

“…To reproduce such behaviour, multi-scale methods [59,60,68] and analytical phenomenological models, such as the Blatz-Ko [52] and related hyperelastic constitutive models [54], are generally pursued. Data-driven procedures seem also a valid alternative when analytical models fail to be accurate [69,70] and have been also…”

Mechanical Characterization of Soft Membranes with One-Shot Projection Moiré and Metaheuristic Optimization

“…The observed residual errors in the hybrid numerical-experimental identification process hence were fully consistent with the level of uncertainty normally entailed by FEMU-based characterization. Optically measured (d) Remarkably, HS-JAYA solved variants 1 and 2 of the identification problem including, respectively, 324 and 110 unknown material/structural parameters, a significantly larger number of unknowns than those usually reported in the literature for elastomers and rubberlike materials [66][67][68][69][70][71][72] (from two to six unknown material parameters or neural networks depending on three input characteristics), visco-hyperelastic materials [73][74][75] (from six to nine unknown material parameters including tangent modulus and softening index, Prony constants and relaxation times), biological tissues [76][77][78][79][80][81] (from five to sixteen unknowns accounting also for visco-elastic effects and stochastic variation of material properties), non-homogeneous hyperelastic structures [37,63,[82][83][84] (from four to sixteen unknown material parameters for the global model, or two unknown material parameters for each local inverse problem at the element level) or anisotropic hyperelastic materials modeled with much more complicated constitutive equations [27,34,[84][85][86] (from three to seventeen unknown material parameters). A very recent study by Borzeszkowski et al [38] considered identification problems of nonlinear shells subject to various loading conditions (i.e., uniaxial tension, pure bending, sheet inflation and abdominal wall pressurization).…”

Auxetic orthotropic materials: Numerical determination of a phenomenological spline-based stored density energy and its implementation for finite element analysis

“…One option is an analytical phenomenological approach, which obtains an approximate solution of the stored energy density functions that defines their behavior. When these analytical functions do not give accurate predictions, some data-driven procedures may be employed both to compute material parameters [20,21] and to select the best approximate functions/model (e.g. Bayesian methods [22,23,24,25], Neural Networks [26,27]); and for corrections for these models [28].…”