Research paper
Compressive behavior of a turtle’s shell: Experiment, modeling, and simulation

https://doi.org/10.1016/j.jmbbm.2011.10.011Get rights and content

Abstract

The turtle’s shell acts as a protective armor for the animal. By analyzing a turtle shell via finite element analysis, one can obtain the strength and stiffness attributes to help design man-made armor. As such, finite element analysis was performed on a Terrapene carolina box turtle shell. Experimental data from compression tests were generated to provide insight into the scute through-thickness behavior of the turtle shell. Three regimes can be classified in terms of constitutive modeling: linear elastic, perfectly inelastic, and densification regions, where hardening occurs. For each regime, we developed a model that comprises elasticity and densification theory for porous materials and obtained all the material parameters by correlating the model with experimental data. The different constitutive responses arise as the deformation proceeded through three distinctive layers of the turtle shell carapace. Overall, the phenomenological stress–strain behavior is similar to that of metallic foams.

Highlights

► Experiments, modeling, and simulation were performed on a box turtle shell. ► Experimental data provided insight into the through-thickness behavior of turtle scute. ► A model comprising elasticity and densification theory was developed. ► Finite element analyses were performed to understand structure–property relations. ► The simulation results showed good agreement between experiments and simulations.

Introduction

Biological structural materials have gained tremendous attention in recent years, because they exhibit mechanical properties that are far beyond those of their synthetic counterparts (Lin et al., 2006, Menig et al., 2000, Menig et al., 2001, Meyers et al., 2006). These exceptional mechanical properties are the result of their organization in terms of composition and structure. They contain both organic and inorganic components woven into complex structures that are hierarchically organized at the nanoscale, microscale, and mesoscale levels (Meyers et al., 2006). Studying biological materials and systems enables material scientists and engineers to develop biologically inspired designs. This field of study is also known as biomimetics, which is one of the new frontiers in materials science (Meyers et al., 2008). Many studies have been performed to discover the structure and mechanical properties of biological skeletons. For example, sea shells (Katti et al., 2001, Katti et al., 2004, Katti et al., 2005a, Katti et al., 2005b, Katti et al., 2006, Katti and Katti, 2006, Lin et al., 2006, Menig et al., 2000, Menig et al., 2001, Meyers et al., 2006, Meyers et al., 2008, Mohanty et al., 2006), bird beaks (Seki et al., 2006, Vecchio, 2005), crustacean exoskeletons (Raabe et al., 2005, Raabe et al., 2006, Sachs et al., 2006), bones (Meyers et al., 2008), and teeth (Meyers et al., 2008) have been extensively studied. In addition, the structure of the soft suture between adjacent bone segments of the red-eared slider turtle shell and its supposed mechanical function have been discussed in a recent publication (Krauss et al., 2009). The authors concluded that the convoluted structure of the suture permits easy deformation at small loads while it provides stiffening upon larger deformations as a composite material with interlocking elements. However, studies on the turtle’s armor system have not been undertaken to the best of our knowledge, particularly with respect to finite element analysis.

The primary function of the turtle shell is for armor defense against environmental penetration events. The shell has two sections: the upper or dorsal section is called the carapace and the lower or ventral section is called the plastron (Alderton, 1988), as shown in Fig. 1. The carapace and the plastron are connected by bridges that are located between the front and hind limbs on either side of the body. The carapace and the plastron comprise individual horny shields called scutes. The pattern in which they are assembled on the shell enhances the overall strength of the shell. The details of the structure of the turtle shell in different length scales will be discussed in Section 3.

The aim of this study is to understand the constitutive behavior of the turtle shell, develop a material model, and run finite element simulations of the through-thickness behavior. By studying the relationship between the microstructure of the turtle shell and its mechanical properties, one can hopefully understand new venues for designing man-made armor. In order to accomplish this task, experiments and modeling were performed that were focused on the upper shell (carapace) of a box turtle (Terrapene carolina). Rhee et al. (2009) reported the hierarchical structure and mechanical behavior of the turtle shell carapace. Based on previously reported experimental results, computational modeling and simulation on the mechanical behavior of the turtle shell carapace were carried out. The findings from the present study could aid in identifying the pathway to design bio-inspired synthetic composite materials.

Section snippets

Material and methods

In order to model and simulate the mechanical behavior of the turtle shell, multiscale structure and mechanical properties were quantified under different length scales by using such biological structural material obtained after the natural death of a box turtle. The structure of the turtle shell carapace was investigated by using an optical microscope. Also included for modeling and simulation efforts, but not presented here, was the structure obtained from a scanning electron microscope

Structure and micromechanical properties of turtle shell

Microstructural observations revealed that the turtle shell is a multiphase composite material that is arranged in a multiscale hierarchy (Rhee et al., 2009). The turtle shell carapace is made of a sandwich composite structure, and such functionally graded material (FGM) is comprised of a relatively denser exterior that covers a network of fibrous foam interior, as shown in Fig. 2(a). These fibrous structures can be seen inside the cell upon closer observation.

The dimensions and porosities of

Conclusions

For the first time, finite element analyses have been performed on a Terrapene carolina box turtle shell in order to understand the strength, stress–strain behavior, and overall stiffness. Finite element simulations were combined with compression experimental results to illustrate the gradients of porosity in the microstructure of the three-layered shell system. Compression test results showed a typical nonlinear deformation behavior similar to that of man-made foams. A three-phase constitutive

Acknowledgments

The authors would like to acknowledge the financial support for this work from the US Department of Energy (DOE) through the Southern Regional Center for Lightweight Innovative Design (SRCLID) program at Mississippi State University (Grant No. DE-FC26-06NT42755). This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or

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