DOI: 10.25338/b87914
title: Age affects strain-rate dependence of the mechanical properties of kelp tissue

description: Premise:  The resistance of macroalgae to hydrodynamic forces
 imposed by ambient water motion depends in part on the mechanical
 properties of their tissues.  In wave-swept habitats, tissues are
 stretched (strained) at different rates as hydrodynamic forces constantly
 change.  Kelp have tissues of different ages, and mechanical
 properties of kelp tissue change with age.  However, the effects
 of age on the strain-rate dependence of the mechanical behavior of kelp
 tissues is unknown.  Methods:  Using the kelp Egregia
 menziesii, we measured how high strain rate (simulating wave impingement)
 vs. lower strain rate (simulating wave surge) affected mechanical
 properties of frond tissues of various ages.   Results: 
 Stiffness of tissues of all ages increased with strain rate, whereas
 extensibility was unaffected.  Strength and toughness of old
 tissue were unaffected by strain rate but increased with strain rate for
 young tissue.   Conclusions:  Young tissue is weaker
 than old tissue, and therefore the most susceptible to breakage from
 hydrodynamic forces.  The increased strength of young tissue at
 high strain rates can help the whole frond resist breaking when pulled
 rapidly during wave impingement.  Because breakage of young
 tissue can remove a frond’s meristem and negatively impact the survival of
 the whole kelp, strain-rate dependence of young tissue’s strength can
 enhance kelp’s survival.
description: <b><i>Field site and
 collection</i></b><i> –
 </i>Fronds of
 <i>Egregia menziesii
 </i>were collected from two
 sites in northern California: 20 fronds were collected from Miwok Beach
 (38° 21’25” N, 123° 4’2” W) near Bodega, CA and 12 fronds were collected
 from McClures Beach (38° 11’3”N, 122° 58’2”W) in the Point Reyes National
 Seashore.  In a concurrent study, material properties of
 <em>E. menziesii
 </em>were compared between sites
 and found to be similar (Burnett and Koehl, 2019).  At each site, fronds
 were collected by walking along a transect parallel to the shoreline and
 haphazardly removing a frond from every third
 <i>E. menziesii
 </i>encountered.  Fronds were
 only collected if they were ≥ 40 cm long, unwounded (i.e., no damage from
 herbivores), and had their intercalary meristem (Burnett and Koehl,
 2019).  Fronds were stored in a cooler between 11 and 15 ℃ with just the
 water that was trapped on the fronds and transported to UC Berkeley. 
 Material properties were measured within 12 hours.
 <b><i>Measuring material
 properties</i></b><i> –
 </i>We measured the material
 properties of rachis tissue by conducting tensile stress-strain tests
 (details in Koehl and Wainwright, 1985).  An Instron materials-testing
 machine (Model 5544, Norwood, MA, USA) was used to pull on a section of
 rachis at a defined strain rate until it broke, while simultaneously
 measuring the specimen extension and the force with which it resisted the
 deformation.  We define "strain rate" as the change in length
 per time of a sample divided by the sample’s original length.  We use
 engineering stress-strain definitions, which are common in studies of
 macroalgal mechanics, where “engineering stress”  is defined as the force
 acting on a sample divided by the sample’s original cross-sectional area,
 and “engineering strain” is the total change in the sample’s length
 divided by the sample’s original length.  In studies of macroalgal
 mechanics, engineering strain is often reported as extension ratio, which
 is the total length of the sample divided by the sample’s original length
 (i.e., engineering strain + 1), and we follow this convention here.  We
 also consider the true stress-strain definitions, which are appropriate
 for materials that are highly deformable, including macroalgal tissue: 
 “true stress” is the instantaneous force acting on a sample divided by the
 sample’s instantaneous cross-sectional area, and “true strain” is the
 instantaneous extension of the sample relative to the previous
 instantaneous length, which is calculated as the ln(1 + engineering
 strain) (Vincent 2012).  We calculate the instantaneous cross-sectional
 area of the sample by dividing the sample’s volume, which remains
 constant) by its instantaneous length.  A variety of material properties
 can be calculated from the resulting stress-strain curve, whether
 represented as engineering stress-strain or true stress-strain (Fig. 2). 
 <i> </i> <i>            </i>We measured material properties of <i>E. menziesii</i> rachis tissue of different ages.  For each frond, we cut sections (10 cm in length) of the intact rachis at specific distances from the intercalary meristem, where distance from meristem indicates tissue age (Burnett and Koehl, 2019): 0 to 10 cm, 20 to 30 cm, 40 to 50 cm, and 60 to 70 cm.  For simplicity, we will hereafter refer to these rachis regions by the mean distance of each sample from the intercalary meristem (i.e., 5, 25, 45, and 65, respectively).  Some fronds were not long enough to provide tissue at each region.  The ends of each sample were wrapped with pieces of paper towel that were affixed to the specimen by cyanoacrylate glue to prevent slipping in the grips of the Instron.  Each sample was then secured in the grips of the Instron and strain was applied at a fixed rate (see below) until the sample failed.  The force with which the sample resisted the strain was measured at 10 Hz to the nearest 0.1 N, and the extension of the sample was based on the distance between the Instron’s clamps.  The cross-section of the sample next to the break location was then photographed, and its area (<i>A</i>) was measured using ImageJ software v1.52g (US National Institutes of Health, Bethesda, MD, USA).               We used the measurements of force (<i>F</i>) and change in sample length Δ<i>L</i>, along with the sample’s cross-sectional area (<i>A</i>) and original length (<i>L</i><sub>o</sub>), to construct an engineering stress-strain curve and true stress-strain curve for each sample (Fig. 2).  We then calculated four pairs of material properties for each sample, with one set based on engineering stress-strain curves and the other set based on the true stress-strain curves:  (1) Tensile strength, σ<sub>max</sub> is the stress (<i>F</i>/<i>A</i>) at which the sample broke; (2) extensibility, λ<sub>max</sub>, is the strain at which the sample broke; (3) elastic modulus, <i>E</i>, is the slope of the initial linear portion of the stress-strain curve between strains 0.0 and 0.1; (4) yield stress, σ<sub>yield</sub>, is the stress at which the sample exhibited plastic deformation after it was extended beyond the range of its elastic behavior.  Yield stress was identified by fitting a cubic spline regression model to the stress-strain curve and finding the stress at which the rate of change in stress per change in strain was lowest (i.e., where the sample suddenly started deforming without a proportional increase in stress).  We also calculated (5) work per volume to fracture, <i>W/V</i>, which is the mechanical work to fracture the sample normalized by the sample’s volume (<i>A L</i><sub>o</sub>), as the total area under the stress-strain curve (i.e., it is independent of whether the curve is presented as engineering vs. true stress-strain). <b><i>Strain rates</i></b><i> –</i>  Material properties were measured at one of two strain rates that were chosen to represent strain rates that may be encountered by <i>E. menziesii </i>exposed to breaking waves:  a high strain rate that could occur during wave impingement and a lower strain rate that could occur during wave surge.  Each frond was randomly assigned a strain rate and all samples from that frond were measured at the same strain rate.  <i>In situ </i>measurements of hydrodynamic forces on whole <i>E. menziesii </i>showed that loads during the surge portion of waves can increase at rates of approximately 10 N/s (Gaylord et al., 2008).  From preliminary stress-strain measurements of <i>E. menziesii </i>rachis tissue, we found that a loading rate of 10 N/s corresponds to a strain rate of approximately 3.33 x 10<sup>-3</sup>/s.  <i>In situ </i>measurements of water accelerations during complete wave cycles showed that water accelerates on the order of 100 m/s<sup>2</sup> during wave impingement and on the order of 1 m/s<sup>2</sup> during wave surge (Gaylord 1999).  We estimate that the water accelerations during impingement that are 100-fold higher than during wave surge could produce loading and strain rates in <i>E. menziesii </i>that are 100-times greater than the rates experienced during wave surge.  Therefore, to simulate strain that could occur during wave impingement, we used a strain rate of 3.33 x 10<sup>-1</sup>/s during stress-strain tests on <i>E. menziesii </i>rachis tissue.  It is important to note that these two strain rates, 3.33 x 10<sup>-3</sup>/s and 3.33 x10<sup>-1</sup>/s, are not the only strain rates that may occur during wave surge and wave impingement, respectively, because waves are highly variable across space and time (O’Donnell and Denny, 2008), and many factors influence the specific strain rates that occur in different regions of the kelp’s tissues (e.g., the kelp’s position in the water, the length of the kelp) (Koehl, 1986, 1999).  Instead, these two strain rates represent a range of strain rates that could occur as a wave passes over the kelp, but which has not been examined for its effects on the kelp’s material properties.
description: This dataset contains the following data: 
 Date collected: (m/dd/yyyy) Site: Miwok
 Beach, McClures Beach Specimen label: Fronds 1 to
 32 Distance from meristem: distance of the measured
 rachis tissue from the frond's intercalary meristem (units =
 cm) Strain rate: units = s<sup>-1</sup>
 Initial sample length: Starting distance between the
 Instron clamps (units = mm) Cross-sectional area of
 sample at breakage location (units = m<sup>2</sup>)
 Maximum extension ratio of sample (units =
 dimensionless) Maximum engineering stress of sample
 (units = MPa) Engineering modulus (units =
 MPa) Engineering yield stress (units =
 MPa) Maximum true strain (units =
 dimensionless) Maximum true stress (units =
 MPa) True modulus (units = MPa)
 True yield stress (units = MPa)