Abradable coatings are part of dynamic seals used in aircraft engines to reduce inter-stage leakages. However, during running, severe interactions may occur between the rotating blades and the coating of the casing leading to these parts getting damaged. Numerical approaches simulating these interactions could be a way to prevent these contact risks but they require both a characterization of the thermomechanical behavior of the abradable material and of the blade. This paper presents a quasi-static compression behavior study of a heterogeneous and porous AlSi-PE abradable used in the low-pressure compressor of aircraft engines. Combined with the results obtained for tests conducted at high compression strain-rates and extreme temperatures recently published in a previous paper (Skiba et al., in Dyn Behav Mater 6:213–223, 2020. 10.1007/s40870-020-00242-y), a thermoelastoviscoplastic bilinear constitutive law is proposed. This formulation allows the prediction of the macroscopic behavior of a heterogeneous and porous AlSi-PE abradable material from room temperature to 360 °C and with strain-rates ranging from 10–3 to 103 s−1.