Materialica+ is an international scientific group focusing on boundary value problems and their applications in the elasticity of composites, porous media, and biological structures. We employ symbolic-numerical computations to develop new formulas essential for engineers and researchers. Our research includes the study of dispersed composites randomly embedded in matrices, with a special focus on critical regimes related to optimal packing of inclusions and extremal physical constants. We investigate regular and random structures using the representative volume element (RVE) approach and e-sums, systematically documented in our publications. Additionally, we have developed an effective algorithm for computing structural sums as discrete multiple convolutions, leveraging image analysis and machine learning methods for heterogeneous structures.
Scope:
- Boundary value problems in elasticity of composites
- Symbolic-numerical computations
- Dispersed composites and optimal packing of inclusions
- Extremal physical constants (rigid and soft inclusions)
- Representative volume element (RVE) approach
- Structural sums and multiple convolutions
- Image analysis and machine learning for heterogeneous structures
