Abstract

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.

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