Abstract
This study presents a peridynamic (PD) constitutive model for visco-hyperelastic materials under homogenous deformation. The constitutive visco-hyperelastic model is developed in terms of Yeoh strain energy density function and Prony series. The material parameters in the model are identified by optimizing the classical stress–strain relation and tension test data for different strain rates. The peridynamic visco-hyperelastic force density function is proposed in terms of the peridynamic integral and the Yeoh strain energy density. The time-dependent behaviour for different strain rates is captured by numerical time integration representing the material parameters. The explicit form of peridynamic equation of motion is then constructed to analyse the deformation of visco-hyperelastic membranes. The numerical results concern the deformation and damage prediction for a polyurea membrane and membrane-type acoustic metamaterial with inclusions under homogenous loading. Different surface defects are considered in the simulation. The peridynamic predictions are verified by comparing with finite element analysis results.
Highlights
Visco-hyperelastic materials have wide applications in aerospace, architecture, bioengineering and marine science, especially when they are loaded under large strain and wide range of strain rate
7 Conclusion The novelty of this study is to develop a PD model for visco-hyperelastic material
The Yeoh strain energy density is expressed by the invariants of Cauchy–Green tensor
Summary
Visco-hyperelastic materials have wide applications in aerospace, architecture, bioengineering and marine science, especially when they are loaded under large strain and wide range of strain rate. The choice for appropriate strain energy function is determined by material parameters identification [3] By using these models, the strain rate dependency can be considered to predict the large deformation behaviour of visco-hyperelastic materials [16]. Madenci and Oterkus [29] proposed the ordinary state-based PD constitutive model for viscoelastic deformation in terms of Prony series They captured the relaxation behaviour of viscoelastic material under mechanical and thermal loads. The hyperelastic part of Cauchy stress captures the quasi-static behaviour using the Yeoh strain energy density, while the viscoelastic part of Cauchy stress represents the rate-dependent behaviour by using hereditary integral This constitutive model is verified by experimental data for high-damping rubber [34] and polyurea [35]. The PD model is used to predict membrane-type acoustic metamaterial morphology
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