In previous works, we introduced a discrete particle model in which positions are
updated according to a specific algorithm to describe the behaviour of materials
under deformation. This paper presents a novel definition of stress within this
kinematic discrete model, allowing us to reproduce the stress-strain curves of a tensile
specimen. Our findings suggest that the model can simulate various material
behaviours (e.g., ductile, plastic, polymeric) by adjusting its parameters. A key
advantage of the swarm-based approach is its computational efficiency, its
ability to handle fracture naturally, and its independence from differential
equations. However, being discrete, it lacks conventional energy and stress
concepts, requiring alternative definitions. The closest equivalent to energy
was already introduced in previous papers; in this work, we introduce the
closest equivalent to stress, which is crucial for interpreting fracture and
damage effects in the obtained stress-strain curves. This study highlights the
model’s potential as a computationally efficient tool for simulating material
behaviour.