Abstract
The increasing use of soft materials in industrial, commercial and military applications has necessitated a more thorough understanding of their visco-hyperelastic, reactive, and other non-linear properties. Additionally, testing and design methods for components that employ these materials have required innovation. Large-scale computational modeling has become an effective tool to mitigate the increased cost that accompanies the added complexity in testing and design, but modeling error in the forms of inaccuracy and uncertainty must be appropriately accounted for to effectively reduce both design-stage and validation-stage testing costs.
In this work, several models were built to simulate the split Hopkison pressure bar (SHPB) compression of plasticized polyvinyl chloride (PVC), butyl rubber (BR) and vulcanized rubber (VR) samples across a range of medium- to high-strain rates. Using these analyses, hyper-viscoelastic constitutive models were fit to experimental data for a number of samples at each strain rate, and effective material properties were determined for each curve. The model calibration values were also used to generate statistics to compare the utility of different fitting methods for soft materials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- A :
-
Visco-hyperelastic energy calibration value
- α :
-
Ogden strain energy calibration value
- E :
-
Green strain tensor
- \( \dot{E} \) :
-
Green strain rate tensor
- f :
-
Weighting parameter in Blatz–Ko strain energy
- F :
-
Deformation gradient tensor
- G i :
-
Prony-series calibration modulus
- G el :
-
Elastic/tangent shear modulus
- G ve :
-
Viscoelastic shear modulus
- I :
-
Invariant of the Cauchy–Green tensor
- J :
-
Jacobian
- λ :
-
Stretch
- μ :
-
Ogden strain energy calibration value
- ν :
-
Poisson’s ratio
- σ :
-
Cauchy stress
- t, Ï„ :
-
Time variable
- T :
-
Prony-series relaxation time
- ψ :
-
Strain energy function
- ω :
-
Prony-series relaxation frequency
References
Li C, Lua J (2009) A hyper-viscoelastic constitutive model for polyurea. Mater Lett 63(11):877–880
Marques SPC, Creus GJ (2012) Computational viscoelasticity. Springer, New York
Doman DA, Cronin DS, Salisbury CP (2006) Characterization of polyurethane rubber at high deformation rates. Exp Mech 46(3):367–376
Chen WW, Song B (2011) Split Hopkinson (Kolsky) bar – design, testing and applications. Springer
Crisfield MA (1991) Non-linear finite element analysis of solids and structures. Wiley, Chichester
Ogden RW (1972) Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond Math Phys Sci 326(1567):565–584
Blatz PJ, Ko WL (1962) Application of finite elastic theory to the deformation of rubbery materials. J Rheol 6(1):223
Ko WL (1963) Application of finite elastic theory to the behavior of rubber-like materials. PhD, California Institute of Technology
Martins PALS, Natal Jorge RM, Ferreira AJM (2006) A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues. Strain 42:132–147
Onat ET (1970) Representation of inelastic mechanical behavior by means of state variables. In: Boley BA (ed) Thermoinelasticity. Springer, Vienna, pp 213–225
Onat ET (1968) The notion of state and its implications in thermodynamics of inelastic solids. In: Parkus PH, Sedov PLI (eds) Irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluids. Springer, Vienna, pp 292–314
Song B, Chen W (2003) One-dimensional dynamic compressive behavior of EPDM rubber. J Eng Mater Technol 125(3):294–301
Amin AFMS, Alam MS, Okui Y (2002) An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification. Mech Mater 34(2):75–95
Ogden RW, Saccomandi G, Sgura I (2004) Fitting hyperelastic models to experimental data. Comput Mech 34(6):484–502
Treloar LRG (1944) Stress–strain data for vulcanised rubber under various types of deformation. Trans Faraday Soc 40:59–70
Acknowledgment
The authors would like to thank Anne Purtell at USMC Program Executive Office – Land Systems for funding this research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Czech, C., Ward, A.J., Liao, H., Chen, W.W. (2015). Investigating Uncertainty in SHPB Modeling and Characterization of Soft Materials. In: Qi, H., et al. Challenges in Mechanics of Time-Dependent Materials, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-06980-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-06980-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06979-1
Online ISBN: 978-3-319-06980-7
eBook Packages: EngineeringEngineering (R0)