A constitutive relation for the tissue composed of type-I collagen fibers under uniaxial tension

On the utility of hierarchical self-healing fiber bundle materials under different environments

Bio-materials use a hierarchical structure to optimize their self-healing mechanical behavior. However, the utility may be restricted by different environments. In this paper, based on the previous work in Ji and Li (J Mater Sci 53:14858-14870, 2018) on the constitutive relation of hierarchical self-healing fiber bundle materials (FBMs), the stability is investigated for the mechanical-environmental interaction system established in Ji and Li (Int J Fract 212:105-112, 2018). With the principle of total potential, the stability criterion is proposed. The critical environment stiffness is derived and the system is therefore classified into the absolutely stable one and the conditionally stable one. For the conditionally stable system, the applied strain of FBMs reduces to be [0,[Formula: see text]], where [Formula: see text] is the cutoff strain. Finally, the toughness of hierarchical self-healing FBMs is studied for different interaction systems. The results show that in the absolutely stable system there exists a critical healing rate across which the toughness benefits from a hierarchical structure. In the conditionally stable system, the toughness is significantly affected by the environment stiffness, i.e., the toughness of a FBM increases with a rising hierarchical level, whereas it decreases with a rising healing rate. Moreover, the critical healing rate for toughness becomes greater compared to that in an absolutely stable system.

On collagen fiber morphoelasticity and homeostatic remodeling tone

A variety of biochemical and physical processes participate in the creation and maintenance of collagen in biological tissue. Under mechanical stimuli these collagen fibers undergo continuous processes of morphoelastic change. The model presented here is motivated by experimental reports of stretch-stabilization of the collagen fibers to enzymatic degradation. The fiber structure is modeled in terms of a fiber density evolution that is regulated by means of a fixed creation rate and a mechano-sensitive dissolution rate. The theory accounts for the possibly different natural configurations of the fiber unit constituents and the ground substance matrix. It also generalizes previous theoretical descriptions so as to account for finite survival times of the individual fiber units. Special consideration is given to steady state fiber-remodeling processes in which fiber creation and dissolution are in balance. Fiber assembly processes that involve prestretching the fiber constituents yield a homeostatic stress response with a characteristic fiber tone. Fiber density returns to homeostasis after mechanical disruption when sufficient time has passed.