This work presents a new Updated Reference Lagrangian Smoothed Particle Hydrodynamics (SPH) algorithm [1] for analysing large deformations. It introduces a novel system of first-order conservation laws and considers both isothermal [2] and thermally-coupled [3] scenarios in elasticity and elasto-plasticity. Specifically, the usual linear momentum conservation equation is solved in conjunction with a set of geometric conservation laws describing the motion of a continuum. The geometric conservation laws are re-formulated based on a multiplicative decomposition strategy. The key feature of this formulation is the multiplicative decomposition of the deformation tensor into an internal state variable and an incremental deformation. This is achieved by considering that the original configuration deforms into the current configuration through a series of intermediate configurations. Taking advantage of this formalism, an entropy-stable upwiding stabilisation method derived by means of Rankine Hugoniot jump conditions is introduced. No ad-hoc algorithmic regularisation procedures are needed. Finally, to demonstrate the robustness and applicability of the methodology, a wide spectrum of challenging problems are presented and compared. The overall methodology is shown to be capable of handling problems in hyperelasticity, elasto-plasticity, and dynamic fracture. [1] Refachinho de Campos, P. R. A New Updated Reference Lagrangian Smooth Particle Hydrodynamics framework for large strain solid dynamics and its extension to dynamic fracture. PhD Thesis. Swansea University. (2023) [2] Refachinho de Campos, P. R., Gil, A. J., Hean Lee, C., Giacomini, M., Bonet, J. A New Updated Reference Lagrangian Smooth Particle Hydrodynamics algorithm for isothermal elasticity and elasto-plasticity. Comput. Methods Appl. Mech. Engrg. (2022) 392:114680. [3] Hean Lee, C., Refachinho de Campos, P. R., Gil, A. J., Giacomini, M., Bonet, J. An entropy-stable Updated Reference Lagrangian Smoothed Particle Hydrodynamics algorithm for thermo-elasticity and thermo-visco-plasticity. Comp. Part. Mech. (2023) 10:1493-1531.