Institut Charles Sadron Event

Characterizing the time-dependent mechanical properties of surfaces is a major scientific challenge. Micromechanical techniques are the only methods capable of characterizing the mechanical behaviour of confined interfaces, thin films, and functionalized surfaces. For more than twenty years, elastoplastic constitutive laws have formed the basis of analytical models. Although these models are well suited to the study of instantaneous responses, they reach their limits when describing time-dependent creep and relaxation behaviour. A further challenge in the study of polymer surfaces arises from the heterogeneity of the stress and strain fields, as well as from their complex rheological behaviour at both small and large strains. Analysing the viscoelastic and viscoplastic behaviour of polymers and soft matter therefore requires improvements in instrumentation and a fundamental reassessment of the mechanical behaviour of an object in contact with a surface. This work proposes an approach for characterizing and modelling PMMA, selected as a model material because it exhibits time-dependent behaviour at room temperature and has been extensively studied, particularly by the MIM team. The proposed approach combines multiscale, time-dependent mechanical testing with finite element simulations. A constitutive model coupling nonlinear viscoelasticity with an enhanced viscoplastic formulation was developed and implemented through user subroutines. The main contribution lies in the enhancement of the viscoplastic flow law: multiple nonlinear dependencies on stress and the Odqvist parameter make it possible to capture the experimentally observed behaviour, which cannot be reproduced using conventional Norton-type formulations. Validation under uniaxial compression demonstrates satisfactory qualitative and quantitative agreement over a wide range of strain levels (1-20%) and strain rates (10>''' s-3 × 10>¹ s>¹). Beyond these homogeneous configurations, uniaxial tests involving heterogeneous deformation fields and instrumented indentation tests reveal complex material movements within the bulk and beneath the surface, characterized using digital image correlation (DIC). Simulations involving heterogeneous fields qualitatively reproduce these deformation mechanisms at both the bulk and local scales. These results pave the way for the numerical analysis of time-dependent mechanical contact in glassy polymers, offering promising perspectives for understanding and predicting surface deformation, recovery, wear, friction, and scratching. They also provide a new perspective on tribological behaviour under complex loading conditions while accounting for its time-dependent evolution. Keywords: Contact mechanics, glassy polymers, PMMA, relaxation, hardening law, indentation, loading, nonlinear behaviour, finite element method (FEM), numerical modelling, time-temperature superposition (TTS).