The performance gap between CPU and memory widens continuously. Choosing the best memory layout for each hardware architecture is increasingly important as more and more programs become memory bound. For portable codes that run across heterogeneous hardware architectures, the choice of the memory layout for data structures is therefore ideally decoupled from the rest of a program. This can be accomplished via a zero-runtime-overhead abstraction layer, underneath which memory layouts can be freely exchanged. We present the C++ library LLAMA, which provides such a data structure abstraction layer with example implementations for multidimensional arrays of nested, structured data. LLAMA provides fully C++ compliant methods for defining and switching custom memory layouts for user-defined data types. Providing two close-to-life examples, we show that the LLAMA-generated AoS (Array of Struct) and SoA (Struct of Array) layouts produce identical code with the same performance characteristics as manually written data structures. LLAMA's layout-aware copy routines can significantly speed up transfer and reshuffling of data between layouts compared with naive element-wise copying. The library is fully extensible with third-party allocators and allows users to support their own memory layouts with custom mappings.