Numerical simulation of time-dependent behaviors of self-healing hydrogels based on a generalized recursive algorithm

Self-healing hydrogels exhibit enhanced toughness due to their unique microstructures consisting of an extensible and loose crosslinked polymer network, and a brittle but healable network with tightly connected sacrificial bonds. Due to the time-dependent breaking–healing kinetics of the sacrificial...

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Veröffentlicht in:Computational mechanics Jg. 73; H. 3; S. 449 - 463
Hauptverfasser: Feng, Heng, Jiang, Liying
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Bonding strength
Case studies
Classical and Continuum Physics
Computational Science and Engineering
Computer simulation
Constitutive models
Convolution
Crosslinked polymers
Engineering
Hydrogels
Kinetics
Mathematical analysis
Mathematical models
Numerical analysis
Original Paper
Simulation
Simulation methods
Tensors
Theoretical and Applied Mechanics
Time dependence
Convolution-like constitutive model
Finite element modeling
Recursive integration algorithm
Self-healing hydrogels
ISSN:0178-7675, 1432-0924
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Zusammenfassung:Self-healing hydrogels exhibit enhanced toughness due to their unique microstructures consisting of an extensible and loose crosslinked polymer network, and a brittle but healable network with tightly connected sacrificial bonds. Due to the time-dependent breaking–healing kinetics of the sacrificial network, the constitutive models of self-healing hydrogels are commonly in the form of convolution-like integral, which imposes great challenges to the numerical simulation with intolerable computational cost. In this study, we propose to solve this issue by incorporating a generalized recursive integration algorithm into the finite element (FE) framework for the simulation of the convolution-like constitutive behaviors. With the recursive algorithm, the time-dependent breaking–healing kinetics are numerically solved only based on the results from the previous last time step. The deformation behaviors of one typical self-healing hydrogel with ionic sacrificial bonds are then modeled with the proposed FE framework by adopting the full Newton–Raphson formulation, in which the recursive algorithm is expanded into the tensor space to determine the convolution-like stress and material stiffness tensors. The merits of this numerical framework in simulation capabilities and accuracy are witnessed by different case studies under both transient and equilibrium loading conditions. This proposed FE framework can also be expanded to incorporate different self-healing mechanisms of hydrogels, which is expected to act as a general avenue to numerically simulate the time/history-dependent constitutive behaviors of soft materials.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-023-02375-y