Confined particulate systems, particularly powder compacts, are widely used in various applications in industries such as pharmaceutical, automotive, agriculture, and energy production. Due to their extensive applications, characterization of these materials is of great importance for optimizing their performance and manufacturing processes. Modeling approaches capable of capturing the heterogeneity and complex behavior are effective at predicting the macroscopic behavior of granular systems. These modeling approaches utilize information about the microstructure evolution of these materials during compaction processes at the mesoscale (particle-scale). Using these types of modeling depend on accurate contact formulation between inter-particle contacts. The challenge comes in formulating these contact models that accurately predict force-area-deformation relationships. In this work, contact laws are presented for elastic-ideally plastic particles and plastic particles with power-law hardening under unconfined (simple compression) and confined (die and hydrostatic compaction) compression. First, material properties for a set of finite element simulations are obtained using space-filling design. The finite element simulations are used for verification and building an analytical framework of the contact radius and contact pressure which allows for efficient determination of the contact force. Semi-mechanistic contact laws are built for elastic-ideally plastic spherical particles that depend on material properties and loading configuration. Then, rigid-plastic assumption is used to modify the contact laws to consider power-law hardening effects while keeping loading configuration dependency. Finally, after building and verifying the contact laws, they are used to estimate hardening properties, contact radius evolution, and stress response of micro-crystalline cellulose particles under different loading configurations using experimental data from simple compression.