A constitutive model for amorphous thermoplastics from low to high strain rates: Formulation and computational aspects

In this paper, a recently proposed finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is extended to predict the nonlinear response of amorphous polymers from low to high strain rates. The model accounts for the influence of distinct molecular mechanisms, which become a...

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Published in:International journal of plasticity Vol. 169; p. 103712
Main Authors: Carvalho Alves, A. Francisca, Ferreira, Bernardo P., Andrade Pires, F.M.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.10.2023
Subjects:
Amorphous polymers
Calibration
Finite Element Analysis
Implicit integration algorithm
Poly(methyl methacrylate)
Polycarbonate
Strain-rate
Visco-elasticity
Visco-plasticity
Visco-plasticity
Strain-rate
Amorphous polymers
Implicit integration algorithm
Finite Element Analysis
Poly(methyl methacrylate)
Calibration
Polycarbonate
Visco-elasticity
ISSN:0749-6419
Online Access:Get full text
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Abstract In this paper, a recently proposed finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is extended to predict the nonlinear response of amorphous polymers from low to high strain rates. The model accounts for the influence of distinct molecular mechanisms, which become active at different deformation rates. Therefore, the constitutive equations include two relaxation phenomena to describe the strain rate sensitivity of amorphous polymers. Well-established rheological elements are adopted to define visco-elasticity (generalized Maxwell elements) and visco-plasticity (Eyring dashpots). In addition, strain hardening is modeled with a plasticity-induced (nonlinear) hardening element which is extended to distinguish between the contribution of the two transitions. From a computational viewpoint, a fully implicit integration algorithm is derived, and a highly efficient implementation is obtained. It is shown that it is possible to reduce the return mapping system of equations to only two independent (scalar) nonlinear equations. A four-stage optimization-based calibration procedure is proposed to identify the model’s material parameters in a completely unsupervised way. The predictive capability of the constitutive model is validated against literature results for polycarbonate and poly(methyl methacrylate), accounting for temperature and strain rate dependencies under different loading conditions. The results show that the model can capture the transition in the yield behavior and predict the post-yield large strain behavior over a wide range of strain rates. The efficiency of the calibration procedure and the overall numerical strategy is also demonstrated. Despite the adiabatic conditions observed under high strain rates, the model replicates the associated effect of temperature through strain rate dependency. •A visco-elastic visco-plastic constitutive model is formulated from low to high strain rates.•Two molecular mobility mechanisms are modeled with known rheological elements.•A fully implicit formulation is derived leading to an efficient implementation.•A four-stage optimization-based calibration procedure is proposed.•Excellent agreement with experimental and numerical results for two thermoplastics.
AbstractList In this paper, a recently proposed finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is extended to predict the nonlinear response of amorphous polymers from low to high strain rates. The model accounts for the influence of distinct molecular mechanisms, which become active at different deformation rates. Therefore, the constitutive equations include two relaxation phenomena to describe the strain rate sensitivity of amorphous polymers. Well-established rheological elements are adopted to define visco-elasticity (generalized Maxwell elements) and visco-plasticity (Eyring dashpots). In addition, strain hardening is modeled with a plasticity-induced (nonlinear) hardening element which is extended to distinguish between the contribution of the two transitions. From a computational viewpoint, a fully implicit integration algorithm is derived, and a highly efficient implementation is obtained. It is shown that it is possible to reduce the return mapping system of equations to only two independent (scalar) nonlinear equations. A four-stage optimization-based calibration procedure is proposed to identify the model’s material parameters in a completely unsupervised way. The predictive capability of the constitutive model is validated against literature results for polycarbonate and poly(methyl methacrylate), accounting for temperature and strain rate dependencies under different loading conditions. The results show that the model can capture the transition in the yield behavior and predict the post-yield large strain behavior over a wide range of strain rates. The efficiency of the calibration procedure and the overall numerical strategy is also demonstrated. Despite the adiabatic conditions observed under high strain rates, the model replicates the associated effect of temperature through strain rate dependency. •A visco-elastic visco-plastic constitutive model is formulated from low to high strain rates.•Two molecular mobility mechanisms are modeled with known rheological elements.•A fully implicit formulation is derived leading to an efficient implementation.•A four-stage optimization-based calibration procedure is proposed.•Excellent agreement with experimental and numerical results for two thermoplastics.
ArticleNumber 103712
Author Andrade Pires, F.M.
Carvalho Alves, A. Francisca
Ferreira, Bernardo P.
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  organization: DEMec - Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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Keywords Visco-plasticity
Strain-rate
Amorphous polymers
Implicit integration algorithm
Finite Element Analysis
Poly(methyl methacrylate)
Calibration
Polycarbonate
Visco-elasticity
Language English
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Snippet In this paper, a recently proposed finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is extended to predict the nonlinear...
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StartPage 103712
SubjectTerms Amorphous polymers
Calibration
Finite Element Analysis
Implicit integration algorithm
Poly(methyl methacrylate)
Polycarbonate
Strain-rate
Visco-elasticity
Visco-plasticity
Title A constitutive model for amorphous thermoplastics from low to high strain rates: Formulation and computational aspects
URI https://dx.doi.org/10.1016/j.ijplas.2023.103712
Volume 169
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