Nonlinear material identification of heterogeneous isogeometric Kirchhoff–Love shells

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

“…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). Similar to the present study, thickness values were included as design variables in some test problems of [38].…”

“…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). Similar to the present study, thickness values were included as design variables in some test problems of [38]. However, target properties in [38] either were defined analytically or some level of noise was artificially added to the analytical fields.…”

“…Besides the novelty introduced by the proposed projection moiré model and the hybrid HS-JAYA optimization formulation, the present identification framework also accounts for structural inhomogeneity of tested specimens, an aspect not very often considered in the literature on mechanical characterization of hyperelastic materials (see discussions in [37,38] and references cited therein). For this purpose, the inverse problem variants formulated in this study include up to 324 design variables, an unusually large number of unknown parameters in the mechanical characterization of soft matter.…”

An isogeometric finite element formulation for surface and shell viscoelasticity based on a multiplicative surface deformation split

“…Isogeometric analysis has been used within several applications for shell structures, e.g. it has been applied in fracture (Ambati and De Lorenzis, 2016;Kiendl et al, 2016;Paul et al, 2020b;Proserpio et al, 2020):, shape and topology optimization (Nagy et al, 2013;Kiendl et al, 2014;Hirschler et al, 2019), elasto-plasticity (Ambati et al, 2018;Huynh et al, 2020), composite shells (Thai et al, 2012;Deng et al, 2015;Roohbakhshan and Sauer, 2016;Schulte et al, 2020), inverse analysis (Vu-Bac et al, 2018Borzeszkowski et al, 2022), Cahn-Hilliard phase separations (Valizadeh and Rabczuk, 2019;Zimmermann et al, 2019), biological shells (Tepole et al, 2015;Roohbakhshan and Sauer, 2017), and surfactants (Roohbakhshan and Sauer, 2019).…”

An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split

“…The continuity of such discretizations is not preserved at patch interfaces and needs to be restored, see Paul et al 12 for a recent review on patch enforcement techniques in isogeometric analysis. Isogeometric analysis has been used within several shell and membrane applications, such as laminated composite shells, 13,14 anisotropic shells, 15,16 shape optimization of shells, 17,18 liquid membranes, 19,20 biological tissues, 21,22 topology optimization of shells, 23,24 shell fracture, 25,26 lipid bilayers, 27,28 2D materials, 29,30 shell elastoplasticity, 31,32 inverse analysis of shells, 33,34 Cahn-Hilliard phase separations on deforming surfaces, 35,36 adaptive surface refinement, 37,38 and fiber-reinforced shells. 39,40 The rigorous treatment of linear viscoelasticity dates back to the works by Coleman and Noll 41 and Crochet and Naghdi.…”