Limit analysis of debonding states in multi-body systems of stochastic hyperelastic material

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The aim of this project is to establish effective mathematical formulations and construct reliable numerical solution procedures for the debonding analysis of multi-body systems of stochastic hyperelastic material subject to large strain deformations. The theoretical and computational challenges raised by these systems range from the large deformation of individual bodies, to the detection of contact and openings between them, to the estimation of the probability distribution for the critical load such that debonding through loss of contact can or cannot occur. Even though debonding through loss of contact is a mechanism for damage initiation and crack propagation in many natural and engineered materials, it has been insufficiently investigated. For these materials, deterministic approaches, which are based on average data values, can greatly underestimate or overestimate the damage, and stochastic representations accounting also for data dispersion are needed. In recent years, there has been a growing interest in stochastic modelling techniques for engineering and biomedical applications, where uncertainties in the material parameters calibrated to sparse and approximate observational data cannot be ignored. In the quest for estimating material uncertainties, stochastic finite elasticity introduces stochastic features into the finite elasticity theory in order to characterise the variability in the elastic responses of materials, which are rarely deterministic. Within this framework, stochastic hyperelastic materials are advanced phenomenological models described by a strain-energy function where the parameters are random variables characterised by probability density functions. These models rely on the notion of entropy (or uncertainty) and on the maximum entropy principle for a discrete probability distribution, and are able to propagate uncertainties from input data to output quantities. In this context, the proposed investigation is novel and will contribute to the development of many associated research areas in engineering, biomechanics, and materials science. Specific applications include soft biological materials (e.g., plants, articular cartilages, arterial walls, brain tissue) and engineering structures (e.g., soft actuators, 3D printing composites) at large strains.