Versatile data-adaptive hyperelastic energy functions for soft materials - Wiesheier, Simon; Moreno Mateos, Miguel Angel; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2024)
Download full issue Search ScienceDirect Search ScienceDirect Outline Abstract Keywords 1. Introduction 2. Hyperelasticity based on a approximation of the strain energy function 3. Inverse identification of the parameters of the approximated strain energy function 4. Experimental insights: threefold application and validation of the model 5. Conclusion and outlook CRediT authorship contribution statement Declaration of competing interest Acknowledgment Appendix A. Normalized error plots of forces and vertical displacement fields Appendix B. Sensitivity matrix Data availability References Show full outline Figures (10) Fig. 1. Graphical comparison of linear basis functions (above, k=2) and cubic basis… Fig. 2. Sampled invariants Ī1 at the quadrature points (c) across all load steps of a… Fig. 3. Deformed samples featuring holes of different dimensions for three elastomers Fig. 4. Identification of the strain energy function W̄(I,Ī1) for the material… Fig. 5. Identification of the strain energy function W̄(I,Ī1) for the material DOWSIL Fig. 6. Identification of the strain energy function W̄(I,Ī1)+W̄(I,Ī2) for the… Show 4 more figures Elsevier Computer Methods in Applied Mechanics and Engineering Volume 430, 1 October 2024, 117208 Computer Methods in Applied Mechanics and Engineering Versatile data-adaptive hyperelastic energy functions for soft materials Author links open overlay panelSimon Wiesheier a, Miguel Angel Moreno-Mateos a, Paul Steinmann a b a Institute of Applied Mechanics, Friedrich-Alexander-Universität Erlangen–Nürnberg, Egerlandstr. 5, 91058, Erlangen, Germany b Glasgow Computational Engineering Centre, School of Engineering, University of Glasgow, G12 8QQ, United Kingdom Received 21 May 2024, Revised 25 June 2024, Accepted 30 June 2024, Available online 11 July 2024, Version of Record 11 July 2024. What do these dates mean? crossmark-logo Show less Add to Mendeley Share Cite https://doi.org/10.1016/j.cma.2024.117208 Get rights and content Under a Creative Commons license open access Abstract Applications of soft materials are customarily linked to complex deformation scenarios and material nonlinearities. In the bioengineering field, soft materials typically mimic the low stiffness of biological matter subjected to extreme deformations. Computational frameworks surge as a versatile tool to assist the design of functional applications. The constitutive model lies at the core of such frameworks. In this regard, the customary extreme non-linear behavior of elastomers poses an additional challenge to thoroughly capture the material behavior. Here, data-driven methodologies hold considerable promise for enhancing constitutive modeling when contrasted with phenomenological approaches. In this investigation, we introduce a versatile data-adaptive method tailored to the modeling of hyperelastic soft materials at finite strains. Specifically, our method substitutes an a priori chosen model for the strain energy function by a flexible interpolant defined on a discretized invariant space. Within this framework, the interpolation values assume the role of material parameters and are determined through finite element model updating to conform to measured experimental data — comprising full-field displacements coming from Digital-Image-Correlation and global reaction forces. We validate the method on uniaxial experimental tests of soft elastomers, encompassing , , and . Overall, we aim to establish a new route for the construction of hyperelastic energy functions, untethered from any predefined existing models or assumptions regarding the shape of the energ
Keywords: Data-driven; Parameter identification; Soft materials; Finite-element-method; Finite strains; Experimental mechanics