TY  - JOUR
AU  - Ouardi, Ayoub
AU  - Boukamel, Adnane
AU  - Damil, Noureddine
PY  - 2026
DA  - 2026/06/08
TI  - Extended Micromechanical Model for the Hyperelastic Behavior of Elastomers and Identification of Material Parameters Using the Particle Swarm Optimization (PSO) Algorithm
JO  - Journal of Carbon Neutrality
T2  - Journal of Carbon Neutrality
JF  - Journal of Carbon Neutrality
VL  - 1
IS  - 1
SP  - 38
EP  - 63
DO  - 10.62762/JCN.2026.518617
UR  - https://www.icck.org/article/abs/JCN.2026.518617
KW  - micromechanical model
KW  - macro-molecular polymer chains
KW  - rubber-like materials
KW  - parameter identification
KW  - Particle Swarm Optimization (PSO)
KW  - hyperelastic
KW  - Asymptotic Numerical Method (ANM)
AB  - In this work, we propose a new four-parameter micromechanical model to describe the hyperelastic behavior of elastomeric materials. The proposed model extends and improves a previously developed three-parameter micromechanical approach. As in earlier studies, the constitutive behavior is obtained by minimizing the potential energy of a Representative Volume Element (RVE) composed of multiple macromolecular chains. Each chain segment is modeled as a linear spring with stiffness $K$, acting in both tension and compression. To account for rotational flexibility between consecutive segments, nonlinear torsional springs are introduced, whose behavior is described as the sum of two contributions: a sigmoidal function characterized by a limiting moment $M_0$ and a parameter $a$, and a linear term with stiffness $b$ representing resistance during segment unfolding. This four-parameter formulation ($a$, $b$, $M_0$, and $K$) provides greater flexibility for parameter identification and improves the accuracy of the predicted mechanical response. Two identification strategies are considered: a physically motivated approach and an optimization-based method using the Particle Swarm Optimization (PSO) algorithm, which minimizes the discrepancy between numerical predictions and experimental data without requiring gradient information, making it particularly suitable for implicit numerical models. Numerical simulations are carried out on a two-dimensional RVE composed of four chains, and results are compared with Treloar's (1943) experimental data and selected statistical models under uniaxial tension, pure shear, and equibiaxial tension.
SN  - pending
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Ouardi2026Extended,
  author = {Ayoub Ouardi and Adnane Boukamel and Noureddine Damil},
  title = {Extended Micromechanical Model for the Hyperelastic Behavior of Elastomers and Identification of Material Parameters Using the Particle Swarm Optimization (PSO) Algorithm},
  journal = {Journal of Carbon Neutrality},
  year = {2026},
  volume = {1},
  number = {1},
  pages = {38-63},
  doi = {10.62762/JCN.2026.518617},
  url = {https://www.icck.org/article/abs/JCN.2026.518617},
  abstract = {In this work, we propose a new four-parameter micromechanical model to describe the hyperelastic behavior of elastomeric materials. The proposed model extends and improves a previously developed three-parameter micromechanical approach. As in earlier studies, the constitutive behavior is obtained by minimizing the potential energy of a Representative Volume Element (RVE) composed of multiple macromolecular chains. Each chain segment is modeled as a linear spring with stiffness \$K\$, acting in both tension and compression. To account for rotational flexibility between consecutive segments, nonlinear torsional springs are introduced, whose behavior is described as the sum of two contributions: a sigmoidal function characterized by a limiting moment \$M\_0\$ and a parameter \$a\$, and a linear term with stiffness \$b\$ representing resistance during segment unfolding. This four-parameter formulation (\$a\$, \$b\$, \$M\_0\$, and \$K\$) provides greater flexibility for parameter identification and improves the accuracy of the predicted mechanical response. Two identification strategies are considered: a physically motivated approach and an optimization-based method using the Particle Swarm Optimization (PSO) algorithm, which minimizes the discrepancy between numerical predictions and experimental data without requiring gradient information, making it particularly suitable for implicit numerical models. Numerical simulations are carried out on a two-dimensional RVE composed of four chains, and results are compared with Treloar's (1943) experimental data and selected statistical models under uniaxial tension, pure shear, and equibiaxial tension.},
  keywords = {micromechanical model, macro-molecular polymer chains, rubber-like materials, parameter identification, Particle Swarm Optimization (PSO), hyperelastic, Asymptotic Numerical Method (ANM)},
  issn = {pending},
  publisher = {Institute of Central Computation and Knowledge}
}