Periodic Reporting for period 1 - MULTI-SOFT (Multi-scale and Multi-physics Modelling of Soft Tissues)
Période du rapport: 2024-03-01 au 2026-02-28
Soft biological tissues—such as skin, vessels, and tumors—exhibit highly complex mechanical behavior driven by nonlinear, time-dependent, and multiphysical interactions. Traditional models often treat these effects in isolation, failing to explain critical phenomena like growth-induced instability, delayed buckling, or electro-mediated healing. This modeling gap limits the simulations and predictions required for advances in biomedical applications, including tissue regeneration, cancer diagnostics, and soft robotics.
The MULTI-SOFT project addresses this gap by developing a unified theoretical and computational framework that integrates: multiphysics coupling (chemo-electro-mechanical interactions), multiscale modeling (from cellular microstructure to organ-level behavior), and multi-timescale dynamics (accounting for viscoelastic relaxation and growth). The project’s overall objective is to build predictive tools for morphogenesis and instability in soft materials, validated by both in vivo wound-healing experiments and numerical simulations. Key innovations include: morpho-electroelastic theories predicting the interaction of growth and multiphysics fields, viscoelastic bifurcation frameworks for time-dependent and rate-dependent instability, abd lattice-based models bridging microstructural properties with macroscopic behavior.
The project is designed to deliver impact across multiple dimensions. Scientifically, it advances the theoretical foundations of nonlinear elasticity and develops new modeling paradigms tailored to the complex behavior of living soft tissues. On a societal level, the research contributes to a deeper understanding of healing mechanisms, with potential applications in medical technologies such as electroactive wound dressings. Industrially, the project provides design principles for time-programmable materials and soft robotic systems, paving the way for innovation in adaptive structures and intelligent devices.
While the project concluded earlier than planned due to the fellow’s successful transition to a faculty position via the NSFC Excellent Young Scientists Fund (Overseas), the key scientific results have been achieved, with outcomes disseminated via open-access publications, open-source codes, and conference presentations. This work contributes foundational tools and models for multiple EU priority areas—health innovation and advanced manufacturing—by enabling technologies that respond intelligently to mechanical and bioelectrical stimuli. It sets the stage for further cross-disciplinary research, spanning biomechanics, material science, and soft robotics.
The MULTI-SOFT project addresses this gap by developing a unified theoretical and computational framework that integrates: multiphysics coupling (chemo-electro-mechanical interactions), multiscale modeling (from cellular microstructure to organ-level behavior), and multi-timescale dynamics (accounting for viscoelastic relaxation and growth). The project’s overall objective is to build predictive tools for morphogenesis and instability in soft materials, validated by both in vivo wound-healing experiments and numerical simulations. Key innovations include: morpho-electroelastic theories predicting the interaction of growth and multiphysics fields, viscoelastic bifurcation frameworks for time-dependent and rate-dependent instability, abd lattice-based models bridging microstructural properties with macroscopic behavior.
The project is designed to deliver impact across multiple dimensions. Scientifically, it advances the theoretical foundations of nonlinear elasticity and develops new modeling paradigms tailored to the complex behavior of living soft tissues. On a societal level, the research contributes to a deeper understanding of healing mechanisms, with potential applications in medical technologies such as electroactive wound dressings. Industrially, the project provides design principles for time-programmable materials and soft robotic systems, paving the way for innovation in adaptive structures and intelligent devices.
While the project concluded earlier than planned due to the fellow’s successful transition to a faculty position via the NSFC Excellent Young Scientists Fund (Overseas), the key scientific results have been achieved, with outcomes disseminated via open-access publications, open-source codes, and conference presentations. This work contributes foundational tools and models for multiple EU priority areas—health innovation and advanced manufacturing—by enabling technologies that respond intelligently to mechanical and bioelectrical stimuli. It sets the stage for further cross-disciplinary research, spanning biomechanics, material science, and soft robotics.
The MULTI-SOFT project has delivered significant progress toward modeling complex time-dependent and multiphysical behaviors in soft biological tissues. The project’s work program was structured around three research objectives (RO1–RO3), each addressing a key gap in soft tissue mechanics through a combination of analytical modeling, numerical simulations, and experimental validation.
RO1 – Electro-chemo-mechanical modeling of tissue growth
A theoretical framework was developed coupling differential growth, nonlinear elasticity, and electric stimulation. Analytical bifurcation analysis produced closed-form criteria for growth-induced instability in spherical shells under electric fields. This model was validated through an in vivo wound-healing experiment in a rat model, which demonstrated ~35% faster closure under low-voltage stimulation. The results were published in Journal of the Mechanics and Physics of Solids (2024).
RO2 – Time-delayed instability in viscoelastic materials
The project formulated both finite degree-of-freedom system and continuum models to capture viscoelastic delay effects under mechanical loading. A Kelvin–Voigt beam model revealed the onset and timing of delayed buckling instabilities. Numerical simulations confirmed these predictions and enabled parametric studies of loading rate, geometry, and damping effects. The outcomes support the design of time-programmed materials with controllable deformation sequences.
RO3 – Discrete viscoelastic lattice models
A two-dimensional poroviscoelastic lattice framework was constructed to bridge microscale parameters (e.g. unit-cell stiffness and damping) with macroscopic mechanical instabilities. The governing equations derived from unit-cell analysis quantify how relaxation time and lattice geometry influence critical loads and instability timing. These models lay the foundation for soft robotic or ECM-mimicking materials with tunable morphomechanical response.
Throughout the action, simulation tools were implemented in Mathematica and COMSOL, with code modularity and reproducibility as key priorities. Finalized versions are ready for open-source release. Overall, the MULTI-SOFT project has yielded a set of validated, generalizable models that advance the state of the art in soft matter mechanics and pave the way for bioelectronic and soft robotic applications.
RO1 – Electro-chemo-mechanical modeling of tissue growth
A theoretical framework was developed coupling differential growth, nonlinear elasticity, and electric stimulation. Analytical bifurcation analysis produced closed-form criteria for growth-induced instability in spherical shells under electric fields. This model was validated through an in vivo wound-healing experiment in a rat model, which demonstrated ~35% faster closure under low-voltage stimulation. The results were published in Journal of the Mechanics and Physics of Solids (2024).
RO2 – Time-delayed instability in viscoelastic materials
The project formulated both finite degree-of-freedom system and continuum models to capture viscoelastic delay effects under mechanical loading. A Kelvin–Voigt beam model revealed the onset and timing of delayed buckling instabilities. Numerical simulations confirmed these predictions and enabled parametric studies of loading rate, geometry, and damping effects. The outcomes support the design of time-programmed materials with controllable deformation sequences.
RO3 – Discrete viscoelastic lattice models
A two-dimensional poroviscoelastic lattice framework was constructed to bridge microscale parameters (e.g. unit-cell stiffness and damping) with macroscopic mechanical instabilities. The governing equations derived from unit-cell analysis quantify how relaxation time and lattice geometry influence critical loads and instability timing. These models lay the foundation for soft robotic or ECM-mimicking materials with tunable morphomechanical response.
Throughout the action, simulation tools were implemented in Mathematica and COMSOL, with code modularity and reproducibility as key priorities. Finalized versions are ready for open-source release. Overall, the MULTI-SOFT project has yielded a set of validated, generalizable models that advance the state of the art in soft matter mechanics and pave the way for bioelectronic and soft robotic applications.
The MULTI-SOFT project has generated several results that extend beyond the current state of the art in soft tissue mechanics, viscoelastic instabilities, and bioelectromechanical modeling.
1. Unified electro-growth framework
A novel morpho-electroelastic theory was formulated to couple differential growth, large deformation elasticity, and electric stimulation. This model successfully predicts instability modes and growth thresholds under voltage, with in vivo validation demonstrating accelerated wound healing in animal models. The theoretical formulation and biological confirmation mark a significant advance over existing uncoupled or purely phenomenological models.
2. Time-programmed instability design
The project introduced analytical and computational tools to predict delayed buckling in viscoelastic structures—a phenomenon relevant for adaptive and responsive materials. The derived criteria for time-delayed instability under constant loads offer new pathways for designing smart actuators and deployable systems, where control over when deformation occurs is as important as how it occurs.
3. Multiscale lattice modeling
A 2D poroviscoelastic lattice model was developed to connect microscale unit-cell design (e.g. geometry, stiffness, relaxation) to macroscale behavior. This micro-to-macro bridge has not only theoretical implications but also practical utility for tissue scaffolds, ECM modeling, and reconfigurable metamaterials.
Potential Impact and Future Needs
The developed frameworks have promising applications in:
Soft robotics: Time-controlled deformation and self-actuation mechanisms.
Bioelectronic devices: Electrically tunable materials for wound care or smart implants.
Tissue engineering: Scaffold design informed by microstructural dynamics and delay phenomena.
To ensure successful uptake and translation, the following steps are identified:
Further experimental demonstration: Especially for the 2D lattice-based instabilities and actuator prototypes.
IPR and commercialization: Preliminary evaluation suggests patent potential; further steps require legal and market support via the Technology Transfer Office.
Open-source dissemination: Repositories (Mathematica/COMSOL) will be released under permissive licenses to encourage academic and industrial reuse.
Cross-disciplinary collaboration: Integration with materials science, robotics, and biomedical engineering will be key for broader impact.
Overall, the MULTI-SOFT project lays foundational knowledge and tools that are ready for extension through both academic and industrial pathways.
1. Unified electro-growth framework
A novel morpho-electroelastic theory was formulated to couple differential growth, large deformation elasticity, and electric stimulation. This model successfully predicts instability modes and growth thresholds under voltage, with in vivo validation demonstrating accelerated wound healing in animal models. The theoretical formulation and biological confirmation mark a significant advance over existing uncoupled or purely phenomenological models.
2. Time-programmed instability design
The project introduced analytical and computational tools to predict delayed buckling in viscoelastic structures—a phenomenon relevant for adaptive and responsive materials. The derived criteria for time-delayed instability under constant loads offer new pathways for designing smart actuators and deployable systems, where control over when deformation occurs is as important as how it occurs.
3. Multiscale lattice modeling
A 2D poroviscoelastic lattice model was developed to connect microscale unit-cell design (e.g. geometry, stiffness, relaxation) to macroscale behavior. This micro-to-macro bridge has not only theoretical implications but also practical utility for tissue scaffolds, ECM modeling, and reconfigurable metamaterials.
Potential Impact and Future Needs
The developed frameworks have promising applications in:
Soft robotics: Time-controlled deformation and self-actuation mechanisms.
Bioelectronic devices: Electrically tunable materials for wound care or smart implants.
Tissue engineering: Scaffold design informed by microstructural dynamics and delay phenomena.
To ensure successful uptake and translation, the following steps are identified:
Further experimental demonstration: Especially for the 2D lattice-based instabilities and actuator prototypes.
IPR and commercialization: Preliminary evaluation suggests patent potential; further steps require legal and market support via the Technology Transfer Office.
Open-source dissemination: Repositories (Mathematica/COMSOL) will be released under permissive licenses to encourage academic and industrial reuse.
Cross-disciplinary collaboration: Integration with materials science, robotics, and biomedical engineering will be key for broader impact.
Overall, the MULTI-SOFT project lays foundational knowledge and tools that are ready for extension through both academic and industrial pathways.