Hierarchical structures are abundant in almost all tissues of the human body. Therefore, it is highly important for tissue engineering approaches to mimic such structures if a gain of function of the new tissue is intended. Here, the hierarchical structures of the so-called enthesis, a gradient tissue located between tendon and bone, were in focus. Bridging the mechanical properties from soft to hard secures a perfect force transmission from the muscle to the skeleton upon locomotion. This study aimed at a novel method of bioprinting to generate gradient biomaterial constructs with a focus on the evaluation of the gradient printing process. First, a numerical approach was used to simulate gradient formation by computational flow as a prerequisite for experimental bioprinting of gradients. Then, hydrogels were printed in a single cartridge printing set-up to transfer the findings to biomedically relevant materials. First, composites of recombinant spider silk hydrogels with fluorapatite rods were used to generate mineralized gradients. Then, fibroblasts were encapsulated in the recombinant spider silk-fluorapatite hydrogels and gradually printed using unloaded spider silk hydrogels as the second component. Thereby, adjustable gradient features were achieved, and multimaterial constructs were generated. The process is suitable for the generation of gradient materials, e.g., for tissue engineering applications such as at the tendon/bone interface.
Purpose
A general first-invariant constitutive model has been derived in literature for incompressible, isotropic hyperelastic materials, known as Marlow model, which reproduces test data exactly without the need of curve-fitting procedures. This paper aims to describe how to extend Marlow’s constitutive model to the more general case of compressible hyperelastic materials.
Design/methodology/approach
The isotropic constitutive model is based on a strain energy function, whose isochoric part is solely dependent on the first modified strain invariant. Based on Marlow’s idea, a principle of energetically equivalent deformation states is derived for the compressible case, which is used to determine the underlying strain energy function directly from measured test data. No particular functional of the strain energy function is assumed. It is shown how to calibrate the volumetric and isochoric strain energy functions uniquely with uniaxial or biaxial test data only. The constitutive model is implemented into a finite element program to demonstrate its applicability.
Findings
The model is well suited for use in finite element analysis. Only one set of test data is required for calibration without any need for curve-fitting procedures. These test data are reproduced exactly, and the model prediction is reasonable for other deformation modes.
Originality/value
Marlow’s basic concept is extended to the compressible case and applied to both the volumetric and isochoric part of the compressible strain energy function. Moreover, a novel approach is described on how both compressive and tensile test data can be used simultaneously to calibrate the model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.