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Fougeron N, Oddes Z, Ashkenazi A, Solav D. Identification of constitutive materials of bi-layer soft tissues from multimodal indentations. J Mech Behav Biomed Mater 2024; 155:106572. [PMID: 38754153 DOI: 10.1016/j.jmbbm.2024.106572] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2024] [Revised: 04/19/2024] [Accepted: 05/08/2024] [Indexed: 05/18/2024]
Abstract
The personalisation of finite element models is an important problem in the biomechanical fields where subject-specific analyses are fundamental, particularly in studying soft tissue mechanics. The personalisation includes the choice of the constitutive law of the model's material, as well as the choice of the material parameters. In vivo identification of the material properties of soft tissues is challenging considering the complex behaviour of soft tissues that are, among other things, non-linear hyperelastic and heterogeneous. Hybrid experimental-numerical methods combining in vivo indentations and inverse finite element analyses are common to identify these material parameters. Yet, the uniqueness and the uncertainty of the multi-material hyperelastic model have not been evaluated. This study presents a sensitivity analysis performed on synthetic indentation data to investigate the identification uncertainties of the material parameters in a bi-material thigh phantom. Synthetic numerical data, used to replace experimental measurements, considered several measurement modalities: indenter force and displacement, stereo-camera 3D digital image correlation of the indented surface, and ultrasound B-mode images. A finite element model of the indentation was designed with either Ogden-Moerman or Mooney-Rivlin constitutive laws for both materials. The parameters' identifiability (i.e. the possibility of converging to a unique parameter set within an acceptable margin of error) was assessed with various cost functions formulated using the different synthetic data sets. The results underline the need for multiple experimental modalities to reduce the uncertainty of the identified parameters. Additionally, the experimental error can impede the identification of a unique parameter set, and the cost function depends on the constitutive law. This study highlights the need for sensitivity analyses before the design of the experimental protocol. Such studies can also be used to define the acceptable range of errors in the experimental measurement. Eventually, the impact of the evaluated uncertainty of the identified parameters should be further investigated according to the purpose of the finite element modelling.
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Affiliation(s)
- Nolwenn Fougeron
- Faculty of Mechanical Engineering, Technion Institute of Technology, Haifa, Israel.
| | - Zohar Oddes
- Faculty of Mechanical Engineering, Technion Institute of Technology, Haifa, Israel
| | - Amit Ashkenazi
- Faculty of Mechanical Engineering, Technion Institute of Technology, Haifa, Israel
| | - Dana Solav
- Faculty of Mechanical Engineering, Technion Institute of Technology, Haifa, Israel
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Moreno-Guerra MR, Martínez-Romero O, Palacios-Pineda LM, Olvera-Trejo D, Diaz-Elizondo JA, Flores-Villalba E, da Silva JVL, Elías-Zúñiga A, Rodriguez CA. Soft Tissue Hybrid Model for Real-Time Simulations. Polymers (Basel) 2022; 14:polym14071407. [PMID: 35406279 PMCID: PMC9003246 DOI: 10.3390/polym14071407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Revised: 03/09/2022] [Accepted: 03/16/2022] [Indexed: 12/07/2022] Open
Abstract
In this article, a recent formulation for real-time simulation is developed combining the strain energy density of the Spring Mass Model (SMM) with the equivalent representation of the Strain Energy Density Function (SEDF). The resulting Equivalent Energy Spring Model (EESM) is expected to provide information in real-time about the mechanical response of soft tissue when subjected to uniaxial deformations. The proposed model represents a variation of the SMM and can be used to predict the mechanical behavior of biological tissues not only during loading but also during unloading deformation states. To assess the accuracy achieved by the EESM, experimental data was collected from liver porcine samples via uniaxial loading and unloading tensile tests. Validation of the model through numerical predictions achieved a refresh rate of 31 fps (31.49 ms of computation time for each frame), achieving a coefficient of determination R2 from 93.23% to 99.94% when compared to experimental data. The proposed hybrid formulation to characterize soft tissue mechanical behavior is fast enough for real-time simulation and captures the soft material nonlinear virgin and stress-softened effects with high accuracy.
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Affiliation(s)
- Mario R. Moreno-Guerra
- Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico; (M.R.M.-G.); (O.M.-R.); (D.O.-T.)
| | - Oscar Martínez-Romero
- Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico; (M.R.M.-G.); (O.M.-R.); (D.O.-T.)
- Laboratorio Nacional de Manufactura Aditiva y Digital MADIT, Apodaca 66629, NL, Mexico
| | - Luis Manuel Palacios-Pineda
- Tecnológico Nacional de Mexico, Instituto Tecnológico de Pachuca, Carr. México-Pachuca Km 87.5, Pachuca de Soto 42080, HG, Mexico;
| | - Daniel Olvera-Trejo
- Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico; (M.R.M.-G.); (O.M.-R.); (D.O.-T.)
- Laboratorio Nacional de Manufactura Aditiva y Digital MADIT, Apodaca 66629, NL, Mexico
| | - José A. Diaz-Elizondo
- Escuela de Medicina y Ciencias de la Salud, Tecnológico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico; (J.A.D.-E.); (E.F.-V.)
| | - Eduardo Flores-Villalba
- Escuela de Medicina y Ciencias de la Salud, Tecnológico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico; (J.A.D.-E.); (E.F.-V.)
| | - Jorge V. L. da Silva
- DT3D/CTI, Rodovia Dom Pedro I (SP-65), Km 143,6-Amarais-Campinas, Campinas 13069-901, SP, Brazil;
| | - Alex Elías-Zúñiga
- Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico; (M.R.M.-G.); (O.M.-R.); (D.O.-T.)
- Laboratorio Nacional de Manufactura Aditiva y Digital MADIT, Apodaca 66629, NL, Mexico
- Correspondence: (A.E.-Z.); (C.A.R.)
| | - Ciro A. Rodriguez
- Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501 Sur, Monterrey 64849, NL, Mexico; (M.R.M.-G.); (O.M.-R.); (D.O.-T.)
- Laboratorio Nacional de Manufactura Aditiva y Digital MADIT, Apodaca 66629, NL, Mexico
- Correspondence: (A.E.-Z.); (C.A.R.)
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Serra-Aguila A, Puigoriol-Forcada JM, Reyes G, Menacho J. Estimation of Tensile Modulus of a Thermoplastic Material from Dynamic Mechanical Analysis: Application to Polyamide 66. Polymers (Basel) 2022; 14:polym14061210. [PMID: 35335539 PMCID: PMC8949491 DOI: 10.3390/polym14061210] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 03/09/2022] [Accepted: 03/11/2022] [Indexed: 02/04/2023] Open
Abstract
The mechanical properties of thermoplastic materials depend on temperature and strain rate. This study examined the development of a procedure to predict tensile moduli at different strain rates and temperatures, using experimental data from three-point-bending dynamic mechanical analysis (DMA). The method integrated different classical concepts of rheology to establish a closed formulation that will allow researchers save an important amount of time. Furthermore, it implied a significant decrease in the number of tests when compared to the commonly used procedure with a universal testing machine (UTM). The method was validated by means of a prediction of tensile moduli of polyamide PA66 in the linear elastic range, over a temperature range that included the glass-transition temperature. The method was applicable to thermo-rheologically simple materials under the hypotheses of isotropy, homogeneity, small deformations, and linear viscoelasticity. This method could be applicable to other thermoplastic materials, although it must be tested using these other materials to determine to what extent it can be applied reliably.
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Affiliation(s)
- Albert Serra-Aguila
- Passive Safety Department, Applus + IDIADA HQ, Santa Oliva, L’Albornar, P.O. Box 20, 43710 Tarragona, Spain;
| | | | - Guillermo Reyes
- IQS School of Engineering, Universitat Ramon Llull, Via Augusta 390, 08017 Barcelona, Spain; (J.M.P.-F.); (G.R.)
| | - Joaquin Menacho
- IQS School of Engineering, Universitat Ramon Llull, Via Augusta 390, 08017 Barcelona, Spain; (J.M.P.-F.); (G.R.)
- Correspondence:
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