핵심 개념
The authors develop a nonlinear viscoelasticity theory based on the kinematic assumptions of the Green-Naghdi type and the concept of generalized strains within the framework of Hill's hyperelasticity.
초록
The key highlights and insights of the content are:
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Motivation and Background:
- The authors aim to generalize the finite deformation linear viscoelasticity models to the nonlinear regime.
- They observe that the existing finite deformation linear viscoelasticity models, such as the Holzapfel-Simo model, implicitly adopt the kinematic assumption of the Green-Naghdi type.
- The authors discuss the pros and cons of the multiplicative decomposition approach and the additive decomposition approach in modeling inelasticity.
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Kinematic Assumptions and Generalized Strains:
- The authors adopt the kinematic assumptions of the Green-Naghdi type, introducing a viscous deformation-like tensor Γ and the associated viscous strain Ev.
- They utilize the concept of generalized strains, which allows for the description of material nonlinearity within the framework of Hill's hyperelasticity.
- Various generalized strain families, such as the Seth-Hill, Curnier-Rakotomanana, Baˇzant-Itskov, and Curnier-Zysset strains, are presented and discussed.
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Hyperelasticity of Hill's Class:
- The authors construct the hyperelastic strain energy function based on Hill's hyperelasticity framework, which maintains the quadratic functional form while describing nonlinear response using generalized strains.
- They introduce the concept of generalized Hill's hyperelasticity with multiple terms, which allows for improved fitting of experimental data compared to the conventional Hill's hyperelasticity model.
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Constitutive Theory:
- The authors derive the constitutive relations based on the Helmholtz free energy, which consists of an equilibrium part and a non-equilibrium part.
- They show that the non-equilibrium stress vanishes in the equilibrium state, ensuring a well-posed model.
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Computational Aspects:
- The authors address the consistent linearization, constitutive integration, and modular implementation of the proposed nonlinear viscoelasticity theory.
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Numerical Examples:
- The authors provide a suite of numerical examples to demonstrate the capability of the proposed model in characterizing viscoelastic material behaviors at large strains.