GUIDELINES TO SIMULATE LINEAR VISCOELASTIC MATERIALS WITH AN ARBITRARY NUMBER OF CHARACTERISTIC TIMES IN THE CONTEXT OF ATOMIC FORCE MISCROSCOPY

We provide guidelines for modeling linear viscoelastic materials containing an arbitrary number of characteristic times, under atomic force microscopy (AFM) characterization. Instructions are provided to set up the governing equations that rule the deformation of the material by the AFM tip. Procedures are described in detail in the spirit of providing a simple handbook, which is accompanied by open-access code and workbook (Excel) sheets. These guidelines seek to complement the existing literature and reach out to a larger audience in the awareness of the interdisciplinary nature of science. Examples are given in the context of force-distance curves characterization within AFM, but they can be easily extrapolated to other types of contact characterization techniques at different length scales. Despite the simplified approach of this document, the algorithms described herein are built upon rigorous classical linear viscoelastic theory.

Viscoelasticity in simple indentation-cycle experiments: a computational study

Instrumented indentation has become an indispensable tool for quantitative analysis of the mechanical properties of soft polymers and biological samples at different length scales. These types of samples are known for their prominent viscoelastic behavior, and attempts to calculate such properties from the indentation data are constantly made. The simplest indentation experiment presents a cycle of approach (deepening into the sample) and retraction of the indenter, with the output of the force and indentation depth as functions of time and a force versus indentation dependency (force curve). The linear viscoelastic theory based on the elastic-viscoelastic correspondence principle might predict the shape of force curves based on the experimental conditions and underlying relaxation function of the sample. Here, we conducted a computational analysis based on this theory and studied how the force curves were affected by the indenter geometry, type of indentation (triangular or sinusoidal ramp), and the relaxation functions. The relaxation functions of both traditional and fractional viscoelastic models were considered. The curves obtained from the analytical solutions, numerical algorithm and finite element simulations matched each other well. Common trends for the curve-related parameters (apparent Young’s modulus, normalized hysteresis area, and curve exponent) were revealed. Importantly, the apparent Young’s modulus, obtained by fitting the approach curve to the elastic model, demonstrated a direct relation to the relaxation function for all the tested cases. The study will help researchers to verify which model is more appropriate for the sample description without extensive calculations from the basic curve parameters and their dependency on the indentation rate.

FINITE ELEMENT SIMULATION OF BIOFILM VISCOELASTIC BEHAVIOR UNDER VARIOUS LOADINGS

Experiments showed that biofilms exhibit viscoelasticity under both displacement and stress loadings, irrespective of pellicles at liquid–air interface or biofilms at solid–liquid interface. However, the general theoretical models are lacking inuniformly and quantitatively describing biofilms’ viscoelastic behavior under various loading conditions. We use the linear viscoelastic theory — Generalized Maxwell model to describe the viscoelastic mechanical properties of biofilms, and study the responses of biofilms under different loadings, including various strain/stress loading rates and cyclic loadings, by finite element method. The results can capture the typical viscoelastic characteristics of biofilms, such as creep, hysteresis, energy dissipation and loading rate-dependent behavior. Our work provides a simple viscoelastic model not only for bacterial biofilms but also for other biological materials.

THE EFFECT OF PREGNANCY AND POSTPARTUM RECOVERY ON THE VISCOELASTIC BEHAVIOR OF THE RAT CERVIX

The objective of this study was to elucidate the normal functional adaptations of the cervix in pregnancy. Utilizing a Long-Evans rodent model, the cervix was divided into distal and proximal portions for virgin, mid-pregnant, and four weeks postpartum animals. The quasi-linear viscoelastic theory describes the elastic and viscous behavior of the cervix. A hydroxyproline assay was used to measure collagen content. The nonlinearity of the elastic response significantly increased throughout the entire cervix during pregnancy when compared to virgin samples (p < 0.05) and was similar to virgin samples postpartum. All viscous behavior, except for the short-term relaxation of the proximal cervix, significantly differed for pregnant specimens (p < 0.05) and remained similar to pregnant samples postpartum. Collagen content was found to increase by mid-pregnancy only in the proximal cervix when compared to virgin. Distal and proximal portions, however, were found to differ in collagen content at all time points (p < 0.05). This study finds that the cervix becomes elastically stiffer with increasing strain and exhibits increased viscous behavior during pregnancy, with incomplete recovery postpartum. These alterations allow for quick dissipation of loads, and are likely related to altered matrix organization and porosity reported by others.

Dynamic, Regional Mechanical Properties of the Porcine Brain: Indentation in the Coronal Plane

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ∼10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.

Quasi-Linear Viscoelastic Theory is Insufficient to Comprehensively Describe the Time-Dependent Behavior of Human Cervical Spine Ligaments

Stress relaxation experiments were conducted on cervical spine ligaments at multiple strain magnitudes to determine the validity and applicability of the quasi-linear viscoelastic (QLV) theory to model their dynamic behavior. The results indicate that the shape of the stress relaxation curve is dependent upon the magnitude of the applied strain. Thus, a more general, nonlinear formulation is required to model these ligaments within the physiological strain range.