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Moreno-Corrales L, Sanz-Gómez MÁ, Benítez JM, Saucedo-Mora L, Montáns FJ. Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers. Materials (Basel) 2024; 17:1098. [PMID: 38473570 DOI: 10.3390/ma17051098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 02/10/2024] [Accepted: 02/14/2024] [Indexed: 03/14/2024]
Abstract
The formulation of the entropic statistical theory and the related neo-Hookean model has been a major advance in the modeling of rubber-like materials, but the failure to explain some experimental observations such as the slope in Mooney plots resulted in hundreds of micromechanical and phenomenological models. The origin of the difficulties, the reason for the apparent need for the second invariant, and the reason for the relative success of models based on the Valanis-Landel decomposition have been recently explained. From that insight, a new micro-macro chain stretch connection using the stretch tensor (instead of the right Cauchy-Green deformation tensor) has been proposed and supported both theoretically and from experimental data. A simple three-parameter model using this connection has been suggested. The purpose of this work is to provide further insight into the model, to provide an analytical expression for the Gaussian contribution, and to provide a simple procedure to obtain the parameters from a tensile test using the Mooney space or the Mooney-Rivlin constants. From different papers, a wide variety of experimental tests on different materials and loading conditions have been selected to demonstrate that the simple model calibrated only from a tensile test provides accurate predictions for a wide variety of elastomers under different deformation levels and multiaxial patterns.
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Affiliation(s)
- Laura Moreno-Corrales
- ETS de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza Cardenal Cisneros 3, 28040 Madrid, Spain
| | - Miguel Ángel Sanz-Gómez
- ETS de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza Cardenal Cisneros 3, 28040 Madrid, Spain
| | - José María Benítez
- ETS de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza Cardenal Cisneros 3, 28040 Madrid, Spain
| | - Luis Saucedo-Mora
- ETS de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza Cardenal Cisneros 3, 28040 Madrid, Spain
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Francisco J Montáns
- ETS de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza Cardenal Cisneros 3, 28040 Madrid, Spain
- Department of Mechanical and Aerospace Engineering, Herbert Wertheim College of Engineering, University of Florida, Gainesville, FL 32611, USA
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Irastorza-Valera L, Benítez JM, Montáns FJ, Saucedo-Mora L. An Agent-Based Model to Reproduce the Boolean Logic Behaviour of Neuronal Self-Organised Communities through Pulse Delay Modulation and Generation of Logic Gates. Biomimetics (Basel) 2024; 9:101. [PMID: 38392147 PMCID: PMC10886514 DOI: 10.3390/biomimetics9020101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2023] [Revised: 01/16/2024] [Accepted: 02/04/2024] [Indexed: 02/24/2024] Open
Abstract
The human brain is arguably the most complex "machine" to ever exist. Its detailed functioning is yet to be fully understood, let alone modelled. Neurological processes have logical signal-processing and biophysical aspects, and both affect the brain's structure, functioning and adaptation. Mathematical approaches based on both information and graph theory have been extensively used in an attempt to approximate its biological functioning, along with Artificial Intelligence frameworks inspired by its logical functioning. In this article, an approach to model some aspects of the brain learning and signal processing is presented, mimicking the metastability and backpropagation found in the real brain while also accounting for neuroplasticity. Several simulations are carried out with this model to demonstrate how dynamic neuroplasticity, neural inhibition and neuron migration can reshape the brain's logical connectivity to synchronise signal processing and obtain certain target latencies. This work showcases the importance of dynamic logical and biophysical remodelling in brain plasticity. Combining mathematical (agents, graph theory, topology and backpropagation) and biomedical ingredients (metastability, neuroplasticity and migration), these preliminary results prove complex brain phenomena can be reproduced-under pertinent simplifications-via affordable computations, which can be construed as a starting point for more ambitiously accurate simulations.
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Affiliation(s)
- Luis Irastorza-Valera
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
- PIMM Laboratory, Arts et Métiers Institute of Technology, 151 Bd de l'Hôpital, 75013 Paris, France
| | - José María Benítez
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
| | - Francisco J Montáns
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
- Department of Mechanical and Aerospace Engineering, Herbert Wertheim College of Engineering, University of Florida, Gainesville, FL 32611, USA
| | - Luis Saucedo-Mora
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Moreno S, Amores VJ, Benítez JM, Montáns FJ. Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure. J Mech Behav Biomed Mater 2020; 110:103877. [PMID: 32957187 DOI: 10.1016/j.jmbbm.2020.103877] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Revised: 05/05/2020] [Accepted: 05/19/2020] [Indexed: 10/23/2022]
Abstract
In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.
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Affiliation(s)
- Sonsoles Moreno
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040, Madrid, Spain
| | - Víctor Jesús Amores
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040, Madrid, Spain
| | - José Ma Benítez
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040, Madrid, Spain
| | - Francisco J Montáns
- E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, 28040, Madrid, Spain.
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Latorre M, Mohammadkhah M, Simms CK, Montáns FJ. A continuum model for tension-compression asymmetry in skeletal muscle. J Mech Behav Biomed Mater 2018; 77:455-460. [DOI: 10.1016/j.jmbbm.2017.09.012] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Revised: 06/19/2017] [Accepted: 09/06/2017] [Indexed: 02/03/2023]
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Latorre M, Montáns FJ. Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle. J Biomech Eng 2017; 139:2646922. [PMID: 28753687 DOI: 10.1115/1.4037405] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Indexed: 11/08/2022]
Abstract
Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.
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Affiliation(s)
- Marcos Latorre
- Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, Madrid 28040, Spain e-mail:
| | - Francisco J Montáns
- Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, Madrid 28040, Spain e-mail:
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Latorre M, Peña E, Montáns FJ. Determination and Finite Element Validation of the WYPIWYG Strain Energy of Superficial Fascia from Experimental Data. Ann Biomed Eng 2016; 45:799-810. [PMID: 27600686 DOI: 10.1007/s10439-016-1723-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2016] [Accepted: 08/26/2016] [Indexed: 11/30/2022]
Abstract
What-You-Prescribe-Is-What-You-Get (WYPIWYG) procedures are a novel and general phenomenological approach to modelling the behavior of soft materials, applicable to biological tissues in particular. For the hyperelastic case, these procedures solve numerically the nonlinear elastic material determination problem. In this paper we show that they can be applied to determine the stored energy density of superficial fascia. In contrast to the usual approach, in such determination no user-prescribed material parameters and no optimization algorithms are employed. The strain energy densities are computed solving the equilibrium equations of the set of experiments. For the case of superficial fascia it is shown that the mechanical behavior derived from such strain energies is capable of reproducing simultaneously the measured load-displacement curves of three experiments to a high accuracy.
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Affiliation(s)
- Marcos Latorre
- Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, 28040, Madrid, Spain
| | - Estefanía Peña
- Aragón Institute of Engineering Research (I3A), Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain.,CIBER de Bioingeniera, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain
| | - Francisco J Montáns
- Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, 28040, Madrid, Spain.
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Latorre M, Montáns FJ. On the tension-compression switch of the Gasser–Ogden–Holzapfel model: Analysis and a new pre-integrated proposal. J Mech Behav Biomed Mater 2016; 57:175-89. [DOI: 10.1016/j.jmbbm.2015.11.018] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2015] [Accepted: 11/17/2015] [Indexed: 10/22/2022]
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