A stochastic multiscale formulation for isogeometric composite Kirchhoff–Love shells

• Published in: Computer methods in applied mechanics and engineering Vol. 373; p. 113541
• Main Authors: Tsapetis, Dimitrios, Sotiropoulos, Gerasimos, Stavroulakis, George, Papadopoulos, Vissarion, Papadrakakis, Manolis
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2021; Elsevier BV
• Subjects: Composite materials; Graphene reinforced composites; Heterogeneity; Inclusions; Isogeometric analysis; Kirchhoff–Love shells; Mathematical analysis; Multiscale analysis; Shells (structural forms); Stochastic processes; Thickness; Thin walled shells; Topology; Isogeometric analysis; Graphene reinforced composites; Kirchhoff–Love shells; Multiscale analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113541

This work extends isogeometric thin shell formulations to incorporate constitutive laws generated by stochastic multiscale analyses. The integration of the constitutive law is performed through the thickness of the shell, in order to account for material heterogeneity. At each thickness integration point, a corresponding representative volume element is assigned, defining the microstructural topology of a composite material comprised of a matrix with arbitrary volumetric inclusions. With the aid of stochastic processes, the impact of material and inclusion variability on the structural response is demonstrated in benchmark and real-scale numerical examples. Spatial material variability is considered in both surface and through thickness coordinates of the shell. As a result, the elimination of geometric error, together with the realistic material descriptions, renders this formulation an ideal candidate for the simulation of shell structures made of composite materials. •An isogeometric Kirchhoff–Love formulation is extended to multiscale analyses.•Plane-stress constitutive law is extracted via a nested IGA-FEM framework.•Plane stress conditions are imposed as displacements on the microstructure.•Demonstrated sensitivity of structural performance to micromechanics modelling.