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Multi-material problems often exhibit complex geometries along with physicalresponses presenting large spatial gradients or discontinuities. In thesecases, providing high-quality body-fitted finite element analysis meshes andobtaining accurate solutions remain challenging. Immersed boundary techniquesprovide elegant solutions for such problems. Enrichment methods alleviate theneed for generating conforming analysis grids by capturing discontinuitieswithin mesh elements. Additionally, increased accuracy of physical responsesand geometry description can be achieved with higher-order approximation bases.In particular, using B-splines has become popular with the development ofIsoGeometric Analysis. In this work, an eXtended IsoGeometric Analysis (XIGA)approach is proposed for multi-material problems. The computational domaingeometry is described implicitly by level set functions. A novel generalizedHeaviside enrichment strategy is employed to accommodate an arbitrary number ofmaterials without artificially stiffening the physical response. Higher-orderB-spline functions are used for both geometry representation and analysis.Boundary and interface conditions are enforced weakly via Nitsche's method, anda new face-oriented ghost stabilization methodology is used to mitigatenumerical instabilities arising from small material integration subdomains.Two- and three-dimensional heat transfer and elasticity problems are solved tovalidate the approach. Numerical studies provide insight into the ability tohandle multiple materials considering sharp-edged and curved interfaces, aswell as the impact of higher-order bases and stabilization on the solutionaccuracy and conditioning.

XIGA: An eXtended IsoGeometric Analysis approach for multi-material problems