Evaluation of Moisture-Induced Stresses in Wood Cross-Sections Determined with a Time-Dependent, Plastic Material Model during Long-Time Exposure
Abstract
:1. Introduction
2. Materials and Methods
2.1. Hygrothermal Multi-Fickian Transport Model
2.2. Rheological Model for Wood
2.2.1. Elastic Strain
2.2.2. Hygroscopic Expansion
2.2.3. Irrecoverable Mechanosorption
2.2.4. Viscoelasticity
2.2.5. Mechanosorption
2.2.6. Multisurface Plasticity—Return-Mapping Algorithm
2.3. Geometries, Initial and Boundary Conditions
3. Results and Discussion
3.1. Performance of the Mechanical Material Model
3.2. Effect of Uniform Moisture Field Variations
- The presented rheological model;
- The presented rheological model without irrecoverable mechanosorption;
- A material model not considering viscoelasticity and mechanosorption and;
- A material model not considering viscoelasticity and mechanosorption, with a constant compliance tensor.
3.3. Effect with Non-Uniform Moisture Field Variations
3.4. Effects under Realistic Long-Term Loading
4. Conclusions
- A moisture-dependent compliance tensor results in smaller absolute stresses during wetting periods and larger absolute stresses during drying periods, as compared to a constant stiffness tensor (Figure 4).
- The irrecoverable part of mechanosorption increases only during wetting periods, which are accompanied by compression, e.g., in the boundary region of the cross-section. During wetting periods, therefore, mechanosorption and irrecoverable mechanosorption add up. However, during drying periods, mechanosorption develops in the opposite direction, up to a value close to the irrecoverable mechanosorption, thus, significantly reducing the total mechanosorptive strains (Figure 5).
- The consideration of realistic sorption hysteresis affects the moisture content field and, consequently, the stresses under changing climatic conditions. This leads to a step-wise increase in moisture content under cyclic humidity changes, thus resulting in larger moisture-induced loading (Figure 5).
- During a 14-month climatic cycle, the resulting stresses were found to be significantly more affected during the wetting period (with moisture content being greater at the edge than in the center) than during the drying period.
- During the wetting period, stress relaxation at the edge of the cross-section reduces the stress levels in the center of the cross-section, bringing them below the threshold where cracks could potentially form. This finding validates the empirical understanding that cracks are more likely to occur on the surface under drying conditions, rather than inside a cross-section due to wetting.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
MC | Moisture content |
GLT | Glued laminated timber |
FSP | Fiber saturation point |
ST | Solid timber |
Appendix A
Appendix A.1. Algorithm and Implementation of the Rheological Material Model
- Compute the strains and the MC at the end of the increment.
- Initialize the strain components of each additively combined viscoelastic element i and each mechanosorptive Kelvin–Voigt element j, as well as the irrecoverable mechanosorptive strain and plastic strains with the last increment’s values (initial values for the first increment are set to 0).
- Determine the hygroexpansion (Equation (6)) and irrecoverable mechanosorptive strain (Equation (7)).
- Determine the compliance tensor (Equation (3)).
- Begin loop, set
- (a)
- Determine and using the return-mapping algorithm.
- (b)
- Determine ((Equation (2))
- (c)
- Determine total algorithmic tangent operator:
- (d)
- Determine residual vectors (Equation (A1)), and their sum
- (e)
- Compute the change of the total stress
- (f)
- Recompute the strain components of each additively combined viscoelastic element i and each mechanosorptive Kelvin-Voigt element j.
- (g)
- Recompute (based on Equation (A1))
- (h)
- If fulfills the convergence criterion exit the loop, otherwise set and go to (a).
- Store final values of , , , .
Appendix A.2. Residuals
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Pech, S.; Autengruber, M.; Lukacevic, M.; Lackner, R.; Füssl, J. Evaluation of Moisture-Induced Stresses in Wood Cross-Sections Determined with a Time-Dependent, Plastic Material Model during Long-Time Exposure. Buildings 2024, 14, 937. https://doi.org/10.3390/buildings14040937
Pech S, Autengruber M, Lukacevic M, Lackner R, Füssl J. Evaluation of Moisture-Induced Stresses in Wood Cross-Sections Determined with a Time-Dependent, Plastic Material Model during Long-Time Exposure. Buildings. 2024; 14(4):937. https://doi.org/10.3390/buildings14040937
Chicago/Turabian StylePech, Sebastian, Maximilian Autengruber, Markus Lukacevic, Roman Lackner, and Josef Füssl. 2024. "Evaluation of Moisture-Induced Stresses in Wood Cross-Sections Determined with a Time-Dependent, Plastic Material Model during Long-Time Exposure" Buildings 14, no. 4: 937. https://doi.org/10.3390/buildings14040937