The Dynamic Hygro-Mechanical Behaviour of Wood Panel Paintings under Cyclic Humidity Changes: Response Spectra across Forcing Periods

The mechanical response of wood panel paintings to relative humidity fluctuations depends on how stresses and strains develop within the panel over time. Moisture transport produces dynamic differences in the moisture content profile through the panel thickness, while the initial moisture profile retains the influence of previous environments. Assessing climatic exposure therefore requires a dynamic description linking humidity cycling to the evolving mechanical state of the object. Two hygro-mechanical finite-element models of panel-painting simulacra are presented. These are calibrated against humidity step tests and subsequently validated against independent cyclic experiments to confirm the identified parameters. The panel-painting models are then subjected to sinusoidal and square-wave forcing of equal amplitude across periods from minutes to months. The peak responses — cupping and the stresses in the wood and in the preparation layer — are represented as hygro-mechanical response spectra, providing a framework analogous to response-spectrum assessment in earthquake engineering. Two illustrative initial states are compared: a panel equilibrated with the forcing mean and a panel carrying a moisture offset. The resulting spectra show that period and waveform affect cupping and internal stresses differently. Under sinusoidal forcing, stresses in the preparation layer develop predominantly under long-period cycles, which also induce panel cupping. In contrast, stresses in the wooden substrate reach their maximum under short-period fluctuations, which produce little deformation of the panel. Thus, cupping and preparation-layer stress exhibit low-pass responses, whereas wood stress exhibits a high-pass response. The rapid fluctuations that produce the least visible deformation are those that impose the greatest mechanical load on the substrate. Changing the initial state of the object substantially alters its overall response, resulting in a broad range of elevated stresses in the preparation layer in the offset case. The response magnitudes differ markedly between the two simulacra, even though they are broadly similar in size, construction and materials, differing mainly in the age and grain orientation of their planks and in the presence of a varnish layer. These results support an assessment approach that relates climatic amplitude and temporal structure to the conditioning state and mechanical properties of the individual object. The spectra thus provide a dynamic fingerprint of the individual object, and their regular structure suggests that this strongly dynamic behaviour can be captured by simplified, reduced-order models.