Lower hardness than strength: The auxetic composite microstructure of limpet tooth.

The limpet tooth is widely recognized as nature's strongest material, with reported strength values up to 6.5 GPa. Recently, microscale auxeticity has been discovered in the leading part of the tooth, providing a possible explanation for this extreme strength. Utilizing micromechanical experiments, we find hardness values in nanoindentation that are lower than the respective strength observed in micropillar compression tests. Using micromechanical modeling, we show that this unique behavior is a result of local tensile strains during indentation, originating from the microscale auxeticity. As the limpet tooth lacks ductility, these tensile strains lead to microdamage in the auxetic regions of the microstructure. Consequently, indentation with a sharp indenter always probes a damaged version of the material, explaining the lower hardness and modulus values gained from nanoindentation. Micropillar tests were found to be mostly insensitive to such microdamage due to the lower applied strain and are therefore the suggested method for characterizing auxetic nanocomposites. STATEMENT OF SIGNIFICANCE: This work explores the micromechanical properties of limpet teeth, nature's strongest biomaterial, using micropillar compression testing and nanoindentation. The limpet tooth microstructure consists of ceramic nanorods embedded in a matrix of amorphous SiO2 and arranged in a pattern that leads to local auxetic behavior. We report lower values for nanoindentation hardness than for compressive strength, a unique behavior usually not achievable in conventional materials. Utilizing micromechanical finite element simulations, we identify the reason for this behavior to be microdamage formation resultant of the auxetic behavior, sharp indenter tip and lack of ductility of the limpet tooth microstructure. This formation of microdamage is not expected in micropillar compression tests due to lower locally imposed strain.

Limpet teeth microstructure unites auxeticity with extreme strength and high stiffness.

Materials displaying negative Poisson's ratio, referred to as auxeticity, have been found in nature and created in engineering through various structural mechanisms. However, uniting auxeticity with high strength and high stiffness has been challenging. Here, combining in situ nanomechanical testing with microstructure-based modeling, we show that the leading part of limpet teeth successfully achieves this combination of properties through a unique microstructure consisting of an amorphous hydrated silica matrix embedded with bundles of single-crystal iron oxide hydroxide nanorods arranged in a pseudo-cholesteric pattern. During deformation, this microstructure allows local coordinated displacement and rotation of the nanorods, enabling auxetic behavior while maintaining one of the highest strengths among natural materials. These findings lay a foundation for designing biomimetic auxetic materials with extreme strength and high stiffness.

Computational modeling of damage in the hierarchical microstructure of skeletal muscles.

One of the skeletal muscle's exceptional properties is its high damage tolerance in terms of its high toughness, which allows the muscle to withstand cracks of millimeter length while maintaining most of its strength (Taylor et al., 2012). In skeletal muscles, damage occurs on different hierarchical levels of the microstructure. We analyze the damage behavior on hierarchy levels 3 (muscle fiber) and 4 (fascicle) on which the most common serious muscle injuries occur. Our model captures damage initiation and rupture of activated muscle fibers resulting from eccentric contractions. We consider the interaction between muscle fibers and endomysium and investigate the influence of the components titin and endomysium on the mechanical behavior in pre-damaged fascicles. Endomysium generally transmits contractile forces. Our results show that high strains in pre-damaged fiber regions are not transferred by the endomysium and, thus, adjacent undamaged fibers are well protected. Moreover, the results show titin's extraordinary stabilization properties of pre-damaged muscle fibers, so that macroscopic strains of fascicles are hardly reduced in case of strongly pre-damaged fibers and intact titin.

Orientation-dependent micromechanical behavior of nacre: In situ TEM experiments and finite element simulations.

Nacre's superior mechanical properties and failure behavior are strongly orientation-dependent due to its brick-and-mortar microstructure. In this work, the anisotropic microscopic deformation and the resulting macroscopic mechanical properties are evaluated under different loading conditions. Our in situ transmission electron microscopy deformation experiments and finite element simulations reveal that nacre possesses enhanced indentation resistance along the direction normal to the tablets through delocalization of indentation-induced deformation by taking advantage of its layered structure. In addition, nacre's ability to recover from large deformations is observed. We study the strong loading direction dependence of nacre's macroscopic mechanical properties and elucidate the underlying microscopic deformation patterns in the tablets and the soft matrix. Particularly, its performance along the transverse direction is optimized to withstand the loading conditions in nature. We show the importance of the vertical matrix for the initial stiffness and fracture toughness of the composite. These findings provide guidelines for designing nacre-inspired artificial composites with enhanced mechanical properties. STATEMENT OF SIGNIFICANCE: Nacre is widely recognized as an excellent structural model for designing bio-inspired tough and strong artificial composites. Due to its brick-and-mortar microstructure, it exhibits loading direction-dependent mechanical behavior. In this contribution, we investigate the macroscopic mechanical properties and microscopic deformation behavior of nacre under different loading conditions by means of in situ TEM deformation tests and FE simulations. It is found that effective elastic moduli and microscopic deformation strongly depend on the loading direction. The organic matrix is highly deformable. The indentation resistance along the direction normal to tablets is enhanced via deformation delocalization. Our quantitative and qualitative results provide guidelines on optimizing the mechanical properties of nacre-inspired novel composites.

Skeletal muscle: Modeling the mechanical behavior by taking the hierarchical microstructure into account.

Skeletal muscles ensure the mobility of mammals and are complex natural fiber-matrix-composites with a hierarchical microstructure. In this work, we analyze the muscle's mechanical behavior on the level of fascicles and muscle fibers. We introduce continuum mechanics hyperelastic material models for the connective tissue endomysium and the embedded muscle fibers. The coupled electrical, chemical and mechanical processes taking place in activated contracting muscle fibers are captured including the temporal change of the activation level and the spatial propagation of the activation potential in fibers. In our model, we investigate the material behavior of fascicle, fiber and endomysium in the fiber direction and examine interactions between muscle fiber and endomysium by considering the temporal and spatial change of muscle fiber activation. In addition, a loading case of normal and shear forces is applied to analyze the fiber lifting force and the lifting height of unipennate muscles with different pennation angles. Moreover, the development of local stresses and strains in fibers and endomysium for different strains are studied. The simulation results allow to identify regions in high risk of damage. Optimal arrangements of unipennate muscle microstructure are found for either very small or very large pennation angles.

Hierarchical Microstructure of Tooth Enameloid in Two Lamniform Shark Species, Carcharias taurus and Isurus oxyrinchus.

Shark tooth enameloid is a hard tissue made up of nanoscale fluorapatite crystallites arranged in a unique hierarchical pattern. This microstructural design results in a macroscopic material that is stiff, strong, and tough, despite consisting almost completely of brittle mineral. In this contribution, we characterize and compare the enameloid microstructure of two modern lamniform sharks, Isurus oxyrinchus (shortfin mako shark) and Carcharias taurus (spotted ragged-tooth shark), based on scanning electron microscopy images. The hierarchical microstructure of shark enameloid is discussed in comparison with amniote enamel. Striking similarities in the microstructures of the two hard tissues are found. Identical structural motifs have developed on different levels of the hierarchy in response to similar biomechanical requirements in enameloid and enamel. Analyzing these structural patterns allows the identification of general microstructural design principles and their biomechanical function, thus paving the way for the design of bioinspired composite materials with superior properties such as high strength combined with high fracture resistance.

An Enhanced Method to Evaluate Tensile Yield Stress by Small Punch Tests Using Deflection Curves.

While force-displacement curves are often preferred in Small Punch (SP) tests due to the ease of the experimental set-up, they encompass significant uncertainties arising from frame compliance. In this work, a methodology is presented to predict yield stresses from the force vs. deflection curves. The present method relies on determining different force levels from the initial part of the force-deflection curve to reflect both the slope and the curvature instead of using a single force level only. The predicted yield stresses for different types of materials, that is, low- and high-strength alloys, are found to be in good agreement with the actual proof stresses with a maximum error of 16%.

Nature's design solutions in dental enamel: Uniting high strength and extreme damage resistance.

The most important demand of today's high-performance materials is to unite high strength with extreme fracture toughness. The combination of withstanding large forces (strength) and resistance to fracture (toughness), especially preventing catastrophic material failure by cracking, is of utmost importance when it comes to structural applications of these materials. However, these two properties are commonly found to be mutually exclusive: strong materials are brittle and tough materials are soft. In dental enamel, nature has combined both properties with outstanding success - despite a limited number of available constituents. Made up of brittle mineral crystals arranged in a sophisticated hierarchical microstructure, enamel exhibits high stiffness and excellent toughness. Different species exhibit a variety of structural adaptations on varying scales in their dental enamel which optimise not only fracture toughness, but also hardness and abrasion behaviour. Nature's materials still outperform their synthetic counterparts due to these complex structure-property relationships that are not yet fully understood. By analysing structure variations and the underlying mechanical mechanisms systematically, design principles which are the key for the development of advanced synthetic materials uniting high strength and toughness can be formulated. STATEMENT OF SIGNIFICANCE: Dental enamel is a hard protective tissue that combines high strength with an exceptional resistance to catastrophic fracture, properties that in classical materials are commonly found to be mutually exclusive. The biological material is able to outperform its synthetic counterparts due to a sophisticated hierarchical microstructure. Between different species, microstructural adaptations can vary significantly. In this contribution, the different types of dental enamel present in different species are reviewed and connections between microstructure and (mechanical) properties are drawn. By consolidating available information for various species and reviewing it from a materials science point of view, design principles for the development of advanced biomimetic materials uniting high strength and toughness can be formulated.

Gradient Crystal Plasticity: A Grain Boundary Model for Slip Transmission.

Interaction between dislocations and grain boundaries (GBs) in the forms of dislocation absorption, emission, and slip transmission at GBs significantly affects size-dependent plasticity in fine-grained polycrystals. Thus, it is vital to consider those GB mechanisms in continuum plasticity theories. In the present paper, a new GB model is proposed by considering slip transmission at GBs within the framework of gradient polycrystal plasticity. The GB model consists of the GB kinematic relations and governing equations for slip transmission, by which the influence of geometric factors including the misorientation between the incoming and outgoing slip systems and GB orientation, GB defects, and stress state at GBs are captured. The model is numerically implemented to study a benchmark problem of a bicrystal thin film under plane constrained shear. It is found that GB parameters, grain size, grain misorientation, and GB orientation significantly affect slip transmission and plastic behaviors in fine-grained polycrystals. Model prediction qualitatively agrees with experimental observations and results of discrete dislocation dynamics simulations.

A Class of Rate-Independent Lower-Order Gradient Plasticity Theories: Implementation and Application to Disc Torsion Problem.

As the characteristic scale of products and production processes decreases, the plasticity phenomena observed start to deviate from those evidenced at the macroscale. The current research aims at investigating this gap using a lower-order gradient enhanced approach both using phenomenological continuum level as well as crystal plasticity models. In the phenomenological approach, a physically based hardening model relates the flow stress to the density of dislocations where it is assumed that the sources of immobile dislocations are both statistically stored (SSDs) as well as geometrically necessary dislocations (GNDs). In the crystal plasticity model, the evolution of the critical resolved shear stress is also defined based on the total number of dislocations. The GNDs are similarly incorporated in the hardening based on projecting the plastic strain gradients through the Burgers tensor on slip systems. A rate-independent formulation is considered that eliminates any artificial inhomogeneous hardening behavior due to numerical stabilization. The behavior of both models is compared in simulations focusing on the effect of structurally imposed gradients versus the inherent gradients arising in crystal plasticity simulations.

Experimental and Computational Study of Ductile Fracture in Small Punch Tests.

A unified experimental-computational study on ductile fracture initiation and propagation during small punch testing is presented. Tests are carried out at room temperature with unnotched disks of different thicknesses where large-scale yielding prevails. In thinner specimens, the fracture occurs with severe necking under membrane tension, whereas for thicker ones a through thickness shearing mode prevails changing the crack orientation relative to the loading direction. Computational studies involve finite element simulations using a shear modified Gurson-Tvergaard-Needleman porous plasticity model with an integral-type nonlocal formulation. The predicted punch load-displacement curves and deformed profiles are in good agreement with the experimental results.

Accessing Colony Boundary Strengthening of Fully Lamellar TiAl Alloys via Micromechanical Modeling.

In this article, we present a strategy to decouple the relative influences of colony, domain and lamella boundary strengthening in fully lamellar titanium aluminide alloys, using a physics-based crystal plasticity modeling strategy. While lamella and domain boundary strengthening can be isolated in experiments using polysynthetically twinned crystals or mircomechanical testing, colony boundary strengthening can only be investigated in specimens in which all three strengthening mechanisms act simultaneously. Thus, isolating the colony boundary strengthening Hall-Petch coefficient K C experimentally requires a sufficient number of specimens with different colony sizes λ C but constant lamella thickness λ L and domain size λ D , difficult to produce even with sophisticated alloying techniques. The here presented crystal plasticity model enables identification of the colony boundary strengthening coefficient K C as a function of lamella thickness λ L . The constitutive description is based on the model of a polysynthetically twinned crystal which is adopted to a representative volume element of a fully lamellar microstructure. In order to capture the micro yield and subsequent micro hardening in weakly oriented colonies prior to macroscopic yield, the hardening relations of the adopted model are revised and calibrated against experiments with polysynthetically twinned crystals for plastic strains up to 15%.

The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals.

The mechanical behavior of single crystalline, micro-sized copper is investigated in the context of cantilever beam bending experiments. Particular focus is on the role of geometrically necessary dislocations (GNDs) during bending-dominated load conditions and their impact on the characteristic bending size effect. Three different sample sizes are considered in this work with main variation in thickness. A gradient extended crystal plasticity model is presented and applied in a three-dimensional finite-element (FE) framework considering slip system-based edge and screw components of the dislocation density vector. The underlying mathematical model contains non-standard evolution equations for GNDs, crystal-specific interaction relations, and higher-order boundary conditions. Moreover, two element formulations are examined and compared with respect to size-independent as well as size-dependent bending behavior. The first formulation is based on a linear interpolation of the displacement and the GND density field together with a full integration scheme whereas the second is based on a mixed interpolation scheme. While the GND density fields are treated equivalently, the displacement field is interpolated quadratically in combination with a reduced integration scheme. Computational results indicate that GND storage in small cantilever beams strongly influences the evolution of statistically stored dislocations (SSDs) and, hence, the distribution of the total dislocation density. As a particular example, the mechanical bending behavior in the case of a physically motivated limitation of GND storage is studied. The resulting impact on the mechanical bending response as well as on the predicted size effect is analyzed. Obtained results are discussed and related to experimental findings from the literature.

Anisotropic constitutive model incorporating multiple damage mechanisms for multiscale simulation of dental enamel.

An anisotropic constitutive model is proposed in the framework of finite deformation to capture several damage mechanisms occurring in the microstructure of dental enamel, a hierarchical bio-composite. It provides the basis for a homogenization approach for an efficient multiscale (in this case: multiple hierarchy levels) investigation of the deformation and damage behavior. The influence of tension-compression asymmetry and fiber-matrix interaction on the nonlinear deformation behavior of dental enamel is studied by 3D micromechanical simulations under different loading conditions and fiber lengths. The complex deformation behavior and the characteristics and interaction of three damage mechanisms in the damage process of enamel are well captured. The proposed constitutive model incorporating anisotropic damage is applied to the first hierarchical level of dental enamel and validated by experimental results. The effect of the fiber orientation on the damage behavior and compressive strength is studied by comparing micro-pillar experiments of dental enamel at the first hierarchical level in multiple directions of fiber orientation. A very good agreement between computational and experimental results is found for the damage evolution process of dental enamel.

Characterization of the Microstructure Evolution in IF-Steel and AA6016 during Plane-Strain Tension and Simple Shear.

In the current work, the evolutions of grain and dislocation microstructures are investigated on the basis of plane strain tension and simple shear tests for an interstitial free steel (DC06) and a 6000 series aluminum alloy (AA6016-T4). Both materials are commonly-used materials in the automobile industry. The focus of this contribution is on the characterization and comparison of the microstructure formation in DC06 and AA6016-T4. Our observations shed light on the active mechanisms at the micro scale governing the macroscopic response. This knowledge is of great importance to understand the physical deformation mechanisms, allowing the control and design of new, tailor-made materials with the desired material behavior.