Many brittle and quasi-brittle materials such as ceramics and geomaterials exhibit complex mechanical response under dynamic multiaxial loading conditions. In this work, a constitutive model framework is proposed to capture their behaviors triggered by multiple mechanisms. In particular, the statistics of pre-existing flaws, identifiable through sophisticated microstructural characterization techniques, play a crucial role in damage initiation, evolution, and post-failure behaviors of materials. On the other hand, contrasting deformation and failure mechanisms can be triggered under different multiaxial stress states. For instance, under low confinement compression, brittle cracking and frictional sliding along closed cracks are the dominant mechanisms, whereas at sufficiently high confinement, crack growth can be suppressed, and crystal-plasticity mechanisms such as dislocation and twinning may be triggered and become dominant. Another level of complexity arises from capturing the inertial and rate effect, which is essential to understand the rate-dependent behavior of materials such as dynamic strength increment, fragmentation, and failure mode transition. We seek to develop a thermodynamically consistent framework to enable the integration of the models for the specific mechanisms into a global modeling approach. Model calibration has been performed against a wide range of experimental data for engineering ceramics.