The invention provides a heat pump system and method comprising a first Shape-Memory Alloy (SMA) or Negative Thermal Expansion (NTE) elastocaloric core positioned in a housing and adapted to absorb heat and store energy in response to a first fluid inputted at a first temperature. The housing is configured to receive the first fluid at a first temperature via an inlet to cause the first SMA or NTE elastocaloric core to change state. A device is configured to apply stress on the first SMA or NTE core in the housing to cause the SMA or NTE elastocaloric core to change state, releasing heat/energy and causing the SMA/NTE to heat up. A second fluid at a higher temperature is inputted and then subsequently heated further as a result of heat transfer. A second Shape-Memory Alloy (SMA) or Negative Thermal Expansion (NTE) or elastocaloric core is positioned in a cascade arrangement with the first core, but exhibiting a higher activation temperature. The higher temperature fluid leaving core 1 is inputted into core 2, resulting in a larger net temperature lift than could be achieved with a single core. In the alternative, in a cooling system, to achieve a lower temperature drop, the second core in the cascade can exhibit a lower activation temperatures than the first core. The cycle focus is on the endothermic stress release component where the SMA/NTE/elastocaloric core absorbs energy from the fluid. The first core results in a fluid stream drop and that then enters the second core with lower activation temperatures, resulting in a further drop of the output fluid during the cooling half of the cycle.