A multiscale approach to investigate the impact of thermal fluctuations on crack propagation in fracture and decohesion
Résumé
In various physical, biological and technological systems, fracture propagation and decohesion phenomena are widespread. Understanding these processes has broad applications, ranging from classical solid mechanics (e.g., crack propagation) to emerging fields such as advanced materials, nanotechnology, and soft materials like rubber-like substances and biomaterials (e.g., cell adhesion and de-adhesion, DNA denaturation). Experimental findings have already highlighted the important role that thermal fluctuations can play on these phenomena. However, a theoretical investigation of temperature effects remains challenging due to the complexity of the involved physical processes. Thus, despite extensive experimental studies and numerical simulations investigating the interplay between thermal fluctuations and mechanical properties, a comprehensive theoretical framework fully integrating temperature effects is still lacking. In this study we present a first step in this direction, based on a simplified model for the Griffith energy criterion for mode I fracture, extending the classical approach to include thermal fluctuations. The key step in this direction lies in replacing the total mechanical energy by including entropicterms and referring to the free energies. Thuss, by employing tools from equilibrium statistical mechanics, we incorporate entropic effects into the overall energy balance. Furthermore, we adopt a multiscale paradigm by developing both discrete and continuum models. Although intentionally simplified, these models allow for analytical solutions and provide deeper insights into the underlying physics. Our approach effectively captures the energetic competition between elastic deformation, external loading, fracture energy, and entropic contributions. The proposed framework describes not only the scenario where fracture or decohesion propagates from one end but also cases where the broken region forms inside the system, including configurations with multiple fracture bubbles (e.g., multiple bubbles in DNA). In the latter case, we identify solutions where these bubbles merge before complete failure occurs. Finally, our model reveals a classical critical behaviour: the critical load decreases as temperature increases, following the law (1 − T /Tc)^(1/2) . As a direct consequence of temperature effects, we demonstrate that, at the critical temperature Tc , the system undergoes a phase transition, leading to complete rupture without any applied mechanical load.
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