This thesis presents a novel general energy approach for adhesive contact mechanics of viscoelastic materials. The proposed formulation relies on the virtual work formalism: virtual variations of the contact domain must imply the precise balance between the work of the (external) adhesive forces and the work of internal stresses. Importantly, the latter cannot be simply derived as the variation of a potential energy: the intrinsic non-conservative behavior of viscoelastic materials must be properly considered. For this reason, the mathematical and physical aspects of the energy formulation significantly deviate from equivalent elastic cases. Moving from the assumption of infinitely short-range adhesive forces, the proposed approach, in fact, generalizes the Griffith's fracture criterion to hysteretic materials. The closure equation of the steady or unsteady contact problem is derived by enforcing the energy balance at the boundary of the contact area and exploiting boundary formulations based on the Green's function approach. This allows to correctly model the viscoelastic dissipation involving the entire volume of the material, thus overcoming limitations of many previous studies that approached viscoelastic adhesive contacts by assuming that viscoelastic losses are localized at the contact edges and vanish in the bulk of the material. The proposed theory provides results in solid agreement with experimental evidence and insights into the underlying physical mechanisms responsible for the experimentally observed phenomena. The first part of the thesis focuses on steady-state sliding contacts between rough surfaces. Depending on the sliding velocity, the effective adhesive strength of the system in terms of pull-off force, toughness, and contact area size is found highly enhanced compared to corresponding purely elastic cases, in agreement with experimental evidence. This is ascribable to viscoelastic losses localized at the contact trailing edge, where the energy release rate is increased. This phenomenon also highly affects the frictional response: the velocity-dependent friction coefficient is found significantly increased compared to corresponding adhesiveless conditions. At low velocity values, this behavior depends on local small-scale viscoelastic losses. At intermediate velocity, it reflects a complex interplay between bulk viscoelasticity, small-scale viscoelasticity, and adhesion. Importantly, summing up independent estimations of small-scale and large-scale viscoelastic losses does not provide a correct estimation of the friction coefficient. This is a key result, confirmed by existing experimental studies. The proposed energy formulation is then extended to general unsteady conditions and applied to analyze the dynamic approach-retraction motion of a rigid sphere in adhesive contact with a viscoelastic half-space. In this case, besides correctly predicting the effects of local viscoelastic losses, the proposed theory identifies a different fundamental mechanism, also experimentally observed, responsible for adhesion enhancement. Specifically, when the retraction of the indenter begins from a fully relaxed state, the enhancement of the pull-off force depends on a sort of "frozen" state, triggered by the material's glassy response, during which the contact area is almost constant. The different physical mechanisms responsible for the increase of adhesion strength in unsteady conditions are investigated in detail for different loading time-histories and by exploiting a novel approach to correctly calculate the energy release rate for viscoelastic materials under general unsteady conditions. Results clearly indicate that neglecting the viscoelastic response of the bulk material while modeling adhesive contacts might lead to significative errors. In the last part of the thesis, the proposed theory is applied to investigate crack propagation and healing in viscoelastic solids. When steady-state conditions are assumed, the approach provides results in perfect agreement with previous studies. If this assumption is relaxed, the theory is able to correctly tackle complex unsteady phenomena, as the so called delayed-fracture: under a given applied load, the fracture of a viscoelastic solid may occur after a certain delay-time, whose order of magnitude corresponds to that of the material’s relaxation time. Overall, the proposed energy formulation might be of interest in several engineering application, in which the effects of the interplay between viscoelasticity and adhesion on the contact behavior must be properly controlled and designed, such as, for instance, structural adhesives, pressure-sensitive adhesives, protective coatings, bio-inspired adhesives, orthopedic applications, micro-electro-mechanical systems, micro-manipulations and micro-assembly.
Questa tesi presenta un’innovativa formulazione di natura energetica per lo studio della meccanica del contatto adesivo di materiali viscoelastici. La formulazione proposta si basa sul formalismo del principio dei lavori virtuali: variazioni virtuali del dominio di contatto implicano il bilancio tra il lavoro delle forze (esterne) adesive e il lavoro delle tensioni interne. Quest'ultimo non può essere semplicemente derivato come variazione di energia potenziale: il comportamento intrinsecamente non-conservativo dei materiali viscoelastici deve essere adeguatamente considerato. Di conseguenza, gli aspetti matematici e fisici della formulazione energetica si discostano significativamente da equivalenti casi puramente elastici. A partire dall'assunzione range di interazione adesiva infinitamente corto, l'approccio proposto generalizza, di fatto, il criterio di frattura di Griffith ai materiali non-conservativi. L'equazione di chiusura del problema di contatto stazionario o non-stazionario è derivata imponendo il bilancio energetico al contorno dell'area di contatto, sfruttando formulazioni di tipo Boundary-Element basate sulle opportune funzioni di Green. Dunque, la presenza di dissipazione viscoelastica nell'intero volume del materiale è modellata correttamente. Di conseguenza, sono superate le limitazioni di molti studi precedenti che hanno approcciato il contatto adesivo viscoelastico assumendo che le perdite viscoelastiche siano localizzate al contorno dell’area di contatto e si annullino nella maggior parte del volume del sistema. La teoria proposta fornisce risultati supportati da evidenze sperimentali nel campo e offre approfondimenti sui meccanismi fisici responsabili di fenomeni osservati sperimentalmente. La prima parte della tesi si concentra sul contatto tra superfici rugose con moto relativo laterale in regime stazionario. A seconda del regime di velocità relativa, le performance adesive del sistema, in termini di forza di distacco, tenacità e dimensione dell'area di contatto, risultano notevolmente incrementata rispetto ai corrispondenti casi puramente elastici, in accordo con esistenti evidenze sperimentali. Questo fenomeno è attribuibile alle perdite viscoelastiche localizzate al trailing ege del contatto, dove l’energy release rate è incrementato. Tale fenomeno influisce significativamente anche sull’attrito: il coefficiente di attrito, dipendente dalla velocità, risulta notevolmente incrementato rispetto a condizioni di contatto prive di adesione. A basse velocità, questo comportamento dipende dalle perdite viscoelastiche localizzate al bordo del contatto. A velocità intermedie, riflette una complessa interazione tra viscoelasticità macroscopica, viscoelasticità locale, e adesione. I risultati evidenziano che le perdite viscoelastiche locali e macroscopiche non possono essere separate linearmente. Questo è un risultato chiave, confermato da studi sperimentali esistenti. La formulazione energetica è successivamente estesa a generiche condizioni non-stazionarie e applicata per analizzare il moto dinamico di indentazione e retrazione di una sfera rigida in contatto adesivo con un semi-spazio viscoelastico. In questo caso, oltre a prevedere correttamente gli effetti delle perdite viscoelastiche locali, la teoria identifica un differente fondamentale meccanismo, osservato anche sperimentalmente, responsabile dell'incremento dell'adesione effettiva indotto dalla viscoelasticità. In particolare, quando la retrazione del rigido inizia da uno stato completamente rilassato, l'aumento della forza di distacco dipende da una sorta di "stato congelato", innescato dalla risposta elastica (di alta frequenza) del materiale, durante il quale l'area di contatto rimane quasi costante. I diversi meccanismi fisici responsabili dell'incremento della forza adesiva effettiva in condizioni non stazionarie sono analizzati in dettaglio per differenti storie di carico temporali, sfruttando un nuovo approccio sviluppato per calcolare correttamente l’energy release rate per materiali viscoelastici in condizioni non-stazionarie generali. I risultati indicano chiaramente che trascurare la risposta viscoelastica macroscopica del materiale e assumere che la dissipazione sia localmente confinata potrebbe generare errori significativi. Nell'ultimo capitolo, la teoria oggetto della tesi è applicata allo studio della meccanica della frattura in solidi viscoelastici. Nel momento in cui le condizioni di propagazione stazionaria di una cricca sono assunte, l'approccio fornisce risultati perfettamente in accordo con studi precedenti. Se questa ipotesi è rilassata, la teoria è in grado di predire correttamente complessi fenomeni non stazionari, come la cosiddetta delayed fracture: quando un solido viscoelastico è sottoposto ad un certo carico, applicato in maniera discontinua, la sua frattura può avvenire dopo un certo tempo di ritardo, il cui ordine di grandezza corrisponde a quello del tempo di rilassamento del materiale. Nel complesso, la formulazione energetica proposta è di interesse in diverse applicazioni ingegneristiche, in cui gli effetti dell'interazione tra viscoelasticità e adesione sul comportamento meccanico del contatto devono essere adeguatamente controllati e progettati, come ad esempio adesivi strutturali, adesivi sensibili alla pressione, rivestimenti protettivi, adesivi ispirati a sistemi biologici, applicazioni ortopediche, sistemi micro-elettro-meccanici, micro-manipolazione e micro-assemblaggio.
Adhesion and friction in steady and unsteady viscoelastic contacts / Mandriota, Cosimo. - ELETTRONICO. - (2025).
Adhesion and friction in steady and unsteady viscoelastic contacts
Mandriota, Cosimo
2025-01-01
Abstract
This thesis presents a novel general energy approach for adhesive contact mechanics of viscoelastic materials. The proposed formulation relies on the virtual work formalism: virtual variations of the contact domain must imply the precise balance between the work of the (external) adhesive forces and the work of internal stresses. Importantly, the latter cannot be simply derived as the variation of a potential energy: the intrinsic non-conservative behavior of viscoelastic materials must be properly considered. For this reason, the mathematical and physical aspects of the energy formulation significantly deviate from equivalent elastic cases. Moving from the assumption of infinitely short-range adhesive forces, the proposed approach, in fact, generalizes the Griffith's fracture criterion to hysteretic materials. The closure equation of the steady or unsteady contact problem is derived by enforcing the energy balance at the boundary of the contact area and exploiting boundary formulations based on the Green's function approach. This allows to correctly model the viscoelastic dissipation involving the entire volume of the material, thus overcoming limitations of many previous studies that approached viscoelastic adhesive contacts by assuming that viscoelastic losses are localized at the contact edges and vanish in the bulk of the material. The proposed theory provides results in solid agreement with experimental evidence and insights into the underlying physical mechanisms responsible for the experimentally observed phenomena. The first part of the thesis focuses on steady-state sliding contacts between rough surfaces. Depending on the sliding velocity, the effective adhesive strength of the system in terms of pull-off force, toughness, and contact area size is found highly enhanced compared to corresponding purely elastic cases, in agreement with experimental evidence. This is ascribable to viscoelastic losses localized at the contact trailing edge, where the energy release rate is increased. This phenomenon also highly affects the frictional response: the velocity-dependent friction coefficient is found significantly increased compared to corresponding adhesiveless conditions. At low velocity values, this behavior depends on local small-scale viscoelastic losses. At intermediate velocity, it reflects a complex interplay between bulk viscoelasticity, small-scale viscoelasticity, and adhesion. Importantly, summing up independent estimations of small-scale and large-scale viscoelastic losses does not provide a correct estimation of the friction coefficient. This is a key result, confirmed by existing experimental studies. The proposed energy formulation is then extended to general unsteady conditions and applied to analyze the dynamic approach-retraction motion of a rigid sphere in adhesive contact with a viscoelastic half-space. In this case, besides correctly predicting the effects of local viscoelastic losses, the proposed theory identifies a different fundamental mechanism, also experimentally observed, responsible for adhesion enhancement. Specifically, when the retraction of the indenter begins from a fully relaxed state, the enhancement of the pull-off force depends on a sort of "frozen" state, triggered by the material's glassy response, during which the contact area is almost constant. The different physical mechanisms responsible for the increase of adhesion strength in unsteady conditions are investigated in detail for different loading time-histories and by exploiting a novel approach to correctly calculate the energy release rate for viscoelastic materials under general unsteady conditions. Results clearly indicate that neglecting the viscoelastic response of the bulk material while modeling adhesive contacts might lead to significative errors. In the last part of the thesis, the proposed theory is applied to investigate crack propagation and healing in viscoelastic solids. When steady-state conditions are assumed, the approach provides results in perfect agreement with previous studies. If this assumption is relaxed, the theory is able to correctly tackle complex unsteady phenomena, as the so called delayed-fracture: under a given applied load, the fracture of a viscoelastic solid may occur after a certain delay-time, whose order of magnitude corresponds to that of the material’s relaxation time. Overall, the proposed energy formulation might be of interest in several engineering application, in which the effects of the interplay between viscoelasticity and adhesion on the contact behavior must be properly controlled and designed, such as, for instance, structural adhesives, pressure-sensitive adhesives, protective coatings, bio-inspired adhesives, orthopedic applications, micro-electro-mechanical systems, micro-manipulations and micro-assembly.File | Dimensione | Formato | |
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