Strain Stiffening in Synthetic and Biopolymer Networks

Abstract

Strain-stiffening behavior common to biopolymer networks is difficult to reproduce in synthetic networks. Physically associating synthetic polymer networks can be an exception to this rule and can demonstrate strain-stiffening behavior at relatively low values of strain. Here, the stiffening behavior of model elastic networks of physically associating triblock copolymers is characterized by shear rheometry. Experiments demonstrate a clear correlation between network structure and strainstiffening behavior. Stiffening is accurately captured by a constitutive model with a single fitting parameter related to the midblock length. The same model is also effective for describing the stiffening of actin, collagen, and other biopolymer networks. Our synthetic polymer networks could be useful model systems for biological materials due to (1) the observed similarity in strain-stiffening behavior, which can be quantified and related to network structure, and (2) the tunable structure of the physically associating network, which can be manipulated to yield a desired response.

Soft wearable motion sensing suit for lower limb biomechanics measurements

“…At lower extension values the rubber is fairly compliant, with a spring constant of 88.4 N/m, but after 60 mm of extension (corresponding to 200% strain) it stiffens considerably to 499 N/m. This strain-stiffening effect is more commonly seen in biopolymers than in synthetics, and is due to the constitutive polymer network strands reaching their finite maximum extensions at the molecular scale, resulting in the increase in stiffness at the macro-scale [22]. The sensor eventually fractures at an extension of 109 mm (364% strain) which required a force of 22 N. The change in the stiffness of the elastic sensor indicates that it is an important design consideration for future optimization, since it would be restricting to have a wearable sensor that suddenly stiffens at certain ranges of motion.…”

Rate-Dependent Stiffening and Strain Localization in Physically Associating Solutions

“…This critical strain was found previously to increase with the molecular weight of the midblock segment, implying that strain stiffening was ultimately controlled by the finite extensibility, and thus the overall length, of a compliant strand in the macromolecular network. 14 The dashed and dotted lines in Figure 3 show the elastic stiffening response predicted for 20°C, 25°C, and 28°C solutions by Eq. (2) with G 0 from Table 1 and γ* = 3.7, the characteristic critical strain for the triblock copolymer network investigated here.…”

“…At larger strains, the finite extensibility of the network strands and the subsequent strain-stiffening behavior is accurately described by a single fitting parameter, J*. This expression has been employed previously to describe the large strain behavior of elastic, self-assembled triblock copolymer gels deformed in uniaxial compression 1 and shear 14 and equivalent functions have been applied to describe the non-linear elasticity of biological systems 33 and recently stiff polymer networks. 34 The physically associating solution is assumed to deform affinely, so that the local extension ratios We assume that strain energy is stored in deformed 'network strands' or 'bonds', which in our case correspond to bridging midblocks that span different endblock aggregates.…”

Stepped Moduli in Layered Composites

“…Liquid crystals [22] or carbon nanotubes [23] embedded in elastomers show a permanent self-stiffening response when subjected to recurring elastic stress; this response is superficially similar (although based on an entirely different mechanism) to the adaptive strengthening of bones that improves their strength due to repeated mechanical loading. [24] A few crystalline solids (Fe 3 C and Al 3 BC 3 ) [25] and physically-associating synthetic polymer networks [26,27] also change their mechanical strength in response to mechanical stimuli. This change is, however, different from the self-stiffening behavior of liquid crystals in elastomers, as these materials have an increasing modulus with applied strain (called strain stiffening), and the change is reversible.…”