A series of numerical models are presented for two-dimensional thermal convection in a fluid with viscosity that nonlinearly depends on degree of damage ω as well as temperature and pressure; ω increases and viscosity decreases with time when the convection induces strong viscous dissipation. The convecting fluid recovers from the damage with a characteristic time that depends on temperature. The ω dependence of viscosity induces a stress-viscosity relationship that consists of two branches, the intact branch at low stress and the damaged branch at high stress, with a hysteresis between the two branches; ω is small (large) and viscosity is high (low) on the intact (damaged) branch. The hysteresis lets the viscosity depend on stress history. The dependence of viscosity on stress history due to the hysteresis induces a regime where the numerically modeled lithosphere along the surface boundary is fragmented into smaller pieces that are on the intact branch and rigidly move. The pieces of lithosphere are separated by narrow mechanically weak zones that are on the damaged branch. Each piece of lithosphere is further fragmented and mechanically weak zones are newly formed only when the piece is tapped by particularly strong hot uprising plumes. This plate-like regime is the only regime, among the convective regimes searched here, where each piece of lithosphere rigidly moves and still is not ruptured by the forces that drive the piece. The Earth's mantle is suggested to be on the plate-like regime.