The paper discusses various approaches for parameter identification and model discovery in computational solid mechanics. It starts by providing an overview of the fundamental equations in solid mechanics, the experimental possibilities for obtaining stress and strain data, and the parameter identification challenges for different classes of constitutive models (e.g., elasticity, hyperelasticity, viscoelasticity, elastoplasticity, viscoplasticity).
The paper then presents computational approaches for parameter identification, including:
The authors propose a unified framework based on the "all-at-once" approach from the inverse problems community, which can cover both traditional parameter estimation and novel model discovery methods. This framework allows the authors to structure a large portion of the literature on parameter estimation in computational mechanics and identify combinations of methods that have not yet been addressed.
The paper also discusses statistical approaches to quantify the uncertainty in the estimated parameters, including identifiability analysis and a novel two-step procedure for identifying complex material models using both frequentist and Bayesian principles.
Finally, the authors illustrate and compare several of the discussed methods using mechanical benchmarks with synthetic and real data.
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