Identifying Second-Gradient Continuum Models in Particle-Based Materials with Pairwise Interactions Using Acoustic Tensor Methodology

This paper discusses wave propagation in unbounded particle-based materials described by a second-gradient continuum model, recently introduced by the authors, to provide an identification technique. The term particle-based materials denotes materials modeled as assemblies of particles, disregarding...

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Veröffentlicht in:Journal of elasticity 2024, Vol.156 (2), p.623-639
Hauptverfasser: La Valle, Gabriele, Soize, Christian
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description This paper discusses wave propagation in unbounded particle-based materials described by a second-gradient continuum model, recently introduced by the authors, to provide an identification technique. The term particle-based materials denotes materials modeled as assemblies of particles, disregarding typical granular material properties such as contact topology, granulometry, grain sizes, and shapes. This work introduces a center-symmetric second-gradient continuum resulting from pairwise interactions. The corresponding Euler-Lagrange equations (equilibrium equations) are derived using the least action principle. This approach unveils non-classical interactions within subdomains. A novel, symmetric, and positive-definite acoustic tensor is constructed, allowing for an exploration of wave propagation through perturbation techniques. The properties of this acoustic tensor enable the extension of an identification procedure from Cauchy (classical) elasticity to the proposed second-gradient continuum model. Potential applications concern polymers, composite materials, and liquid crystals.
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subjects Acoustic propagation
Biomechanics
Classical and Continuum Physics
Classical Mechanics
Composite materials
Continuum modeling
Engineering
Engineering Sciences
Equilibrium equations
Euler-Lagrange equation
Grain size
Granular materials
Liquid crystals
Material properties
Materials Science
Mathematical Applications in the Physical Sciences
Mechanics
Perturbation methods
Principle of least action
Tensors
Theoretical and Applied Mechanics
Topology
Wave propagation
title Identifying Second-Gradient Continuum Models in Particle-Based Materials with Pairwise Interactions Using Acoustic Tensor Methodology
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