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