Open Access Open Access  Restricted Access Subscription Access

Comprehensive Property Determination for Fiber-Reinforced Polymer Composites in Extrusion Deposition Additive Manufacturing—Bayesian vs Deterministic



This work introduces both deterministic and Bayesian methodologies to simultaneously determine the elastic constants of the constituent polymer and the fiber orientation state in a short fiber-reinforced polymer (SFRP) composite based on a small number of experimental measurements of the composite properties. The ability of the Bayesian approach to calibrate uncertainties makes it a promising tool for enabling a probabilistic framework for composites manufacturing digital twins. The two methods that enable the reverse engineering of the orientation of the fibers and the in-situ polymer properties are compared. For the extrusion deposition additive manufacturing (EDAM) process and other SFRP composites processes (e.g. injection molding), extensive characterization efforts are currently required to develop composites manufacturing digital twins. To circumvent the extensive characterization required, Digimat© provides a suite of tools to reverse engineer material properties of SFRPs. However, Digimat© lacks a methodology to inversely determine the fiber orientation state and the constituent polymer properties simultaneously. To that end, this work presents both a deterministic and hierarchical Bayesian approaches to determine the polymer properties and the fiber orientation state simultaneously. The results indicate that both approaches provide a reliable framework for the reverse engineering process. The deterministic approach provides a more rapid, point estimate methodology, whereas the Bayesian approach provides a more comprehensive methodology that includes uncertainties in the reverse engineering process.


Full Text:



H. C. Tseng, R. Y. Chang, and C. H. Hsu, “Numerical prediction of fiber orientation and

mechanical performance for short/long glass and carbon fiber-reinforced composites,” Compos.

Sci. Technol., vol. 144, pp. 51–56, May 2017, doi: 10.1016/j.compscitech.2017.02.020.

E. Barocio, B. Brenken, A. Favaloro, and R. B. Pipes, “Extrusion deposition additive

manufacturing of composite molds for high-temperature applications,” in International SAMPE

Technical Conference, 2017, pp. 1512–1523.

A. A. Hassen et al., “The durability of large-scale additive manufacturing composite molds,”

S. Advani, “Prediction of fiber orientation during processing of short fiber composites.,” 1989,

Accessed: Jan. 12, 2021. [Online]. Available:

M. Gupta, K. W.-P. Composites, and undefined 1993, “Fiber orientation and mechanical

properties of short‐fiber‐reinforced injection‐molded composites: Simulated and experimental

results,” Wiley Online Libr., Accessed: Jan. 08, 2021. [Online]. Available:



J. Ko and J. R. Youn, “Prediction of fiber orientation in the thickness plane during flow molding

of short fiber composites,” Polym. Compos., vol. 16, no. 2, pp. 114–124, 1995, doi:


E. I. Kurkin, M. O. Spirina, Y. V. Zakhvatkin, and V. O. Chertykovtseva, “The influence of the

weld line location on the mechanical characteristics of lugs from short fibers reinforced composite

material,” in IOP Conference Series: Materials Science and Engineering, Jun. 2020, vol. 868, no.

, p. 012028, doi: 10.1088/1757-899X/868/1/012028.

E. I. Kurkin, M. O. Spirina, V. O. Chertykovtseva, and Y. V. Zakhvatkin, “Mechanical

characteristics of short fiber composite samples located behind circle, rectangle, triangle

obstacles,” in IOP Conference Series: Materials Science and Engineering, Jun. 2020, vol. 868,

no. 1, p. 012024, doi: 10.1088/1757-899X/868/1/012024.

M. L. Landervik and J. Jergeus, “Digimat Material Model for Short Fiber Reinforced Plastics at

Volvo Car Corporation,” 2015.

J. Lindhult, “Fatigue Analysis of Anisotropic Short Fibre Reinforced Polymers-by Use of Digimat

and nCode DesignLife.”

T. R. King, D. M. Blackketter, D. E. Walrath, and D. F. Adams, “Micromechanics Prediction of

the Shear Strength of Carbon Fiber/Epoxy Matrix Composites: The Influence of the Matrix and

Interface Strengths,” J. Compos. Mater., vol. 26, no. 4, pp. 558–573, Apr. 1992, doi:


M. A. Ramirez, “In-silico Tensile Testing of Additively Manufactured Short Fiber Composite,”

Theses Diss. Available from ProQuest, Jan. 2018, Accessed: Jan. 12, 2021. [Online]. Available:

R. F. Gunst, “Response Surface Methodology: Process and Product Optimization Using Designed

Experiments,” Technometrics, vol. 38, no. 3, pp. 284–286, Aug. 1996, doi:


P. S. Yu, S. T. Chen, and I. F. Chang, “Support vector regression for real-time flood stage

forecasting,” J. Hydrol., vol. 328, no. 3–4, pp. 704–716, Sep. 2006, doi:


H. Moon, A. Dean, and T. Santner, “Algorithms for generating maximin latin hypercube and

orthogonal designs,” J. Stat. Theory Pract., vol. 5, no. 1, pp. 81–98, Mar. 2011, doi:


F. Budiman, “SVM-RBF Parameters Testing Optimization Using Cross Validation and Grid

Search to Improve Multiclass Classification,”, vol. 11, no. 1, pp. 80–90, 2019, doi:


P. E. Gill and E. Wong, “Sequential Quadratic Programming Methods,” Springer, New York,

NY, 2012, pp. 147–224.

T. Marwala and S. Sibisi, “Engineering Notes Finite Element Model Updating Using Bayesian

Framework and Modal Properties,” J. Aircr., vol. 42, no. 1, pp. 275–278, 2005, doi:


T. C. Lai and K. H. Ip, “Parameter estimation of orthotropic plates by Bayesian sensitivity

analysis,” Compos. Struct., vol. 34, no. 1, pp. 29–42, Jan. 1996, doi: 10.1016/0263-


F. Daghia, S. de Miranda, F. Ubertini, and E. Viola, “Estimation of elastic constants of thick

laminated plates within a Bayesian framework,” Compos. Struct., vol. 80, no. 3, pp. 461–473,

Oct. 2007, doi: 10.1016/j.compstruct.2006.06.030.

H. Rappel, L. A. A. Beex, L. Noels, and S. P. A. Bordas, “Identifying elastoplastic parameters

with Bayes’ theorem considering output error, input error and model uncertainty,” Probabilistic

Eng. Mech., vol. 55, pp. 28–41, Jan. 2019, doi: 10.1016/j.probengmech.2018.08.004.

C. P. Robert, “The Metropolis-Hastings Algorithm,” Springer, pp. 1–15, Dec. 2014, doi:


M. D. Hoffman and A. Gelman, “The No-U-Turn Sampler: Adaptively Setting Path Lengths in

Hamiltonian Monte Carlo,” 2014. doi: 10.5555/2627435.2638586.

J. Salvatier, T. Wiecki, C. F.-P. C. Science, and undefined 2016, “Probabilistic programming in

Python using PyMC3,”, Accessed: Jun. 17, 2021. [Online]. Available:



A. Gelman, J. Carlin, H. Stern, D. Dunson, and A. Vehtari, Bayesian data analysis. 2013.

C. M. Bishop, Pattern recognition and machine learning. 2006.

T. Lee, A. K. Gosain, I. Bilionis, and A. B. Tepole, “Predicting the effect of aging and defect size

on the stress profiles of skin from advancement, rotation and transposition flap surgeries,” J.

Mech. Phys. Solids, vol. 125, pp. 572–590, Apr. 2019, doi: 10.1016/j.jmps.2019.01.012.


  • There are currently no refbacks.