Abstract
In the field of engineering materials, strength and toughness are typically two mutually exclusive properties. Structural biological materials such as bone, tendon or dentin have resolved this conflict and show unprecedented damage tolerance, toughness and strength levels. The common feature of these materials is their hierarchical heterogeneous structure, which contributes to increased energy dissipation before failure occurring at different scale levels. These structural properties are the key to exceptional bioinspired material mechanical properties, in particular for nanocomposites. Here, we develop a numerical model in order to simulate the mechanisms involved in damage progression and energy dissipation at different size scales in nano- and macro-composites, which depend both on the heterogeneity of the material and on the type of hierarchical structure. Both these aspects have been incorporated into a 2-dimensional model based on a Lattice Spring Model, accounting for geometrical nonlinearities and including statistically-based fracture phenomena. The model has been validated by comparing numerical results to continuum and fracture mechanics results as well as finite elements simulations, and then employed to study how structural aspects impact on hierarchical composite material properties. Results obtained with the numerical code highlight the dependence of stress distributions on matrix properties and reinforcement dispersion, geometry and properties, and how failure of sacrificial elements is directly involved in the damage tolerance of the material. Thanks to the rapidly developing field of nanocomposite manufacture, it is already possible to artificially create materials with multi-scale hierarchical reinforcements. The developed code could be a valuable support in the design and optimization of these advanced materials, drawing inspiration and going beyond biological materials with exceptional mechanical properties.
Highlights
Biological materials often display mechanical properties that differ from traditional engineering materials in that they are capable of simultaneously optimizing competing properties, such as stiffness and density or strength and toughness (Gao et al, 2003; Meyers et al, 2008; Giesa et al, 2011; Ritchie, 2011)
Model Validation The main mechanisms the computational model needs to correctly reproduce at microscale are strain concentrations, load transfer between the matrix and the reinforcement, fracture nucleation, etc. These aspects are addressed in preliminary validation simulations, where hierarchical lattice spring model (HLSM) results are compared to finite element method (FEM) calculations
The same geometry and boundary conditions are considered in FEM simulations, using a 2-D plane strain approximation, a free triangular element mesh refined in the vicinity of the crack tip, and second-order Lagrange elements
Summary
Biological materials often display mechanical properties that differ from traditional engineering materials in that they are capable of simultaneously optimizing competing properties, such as stiffness and density or strength and toughness (Gao et al, 2003; Meyers et al, 2008; Giesa et al, 2011; Ritchie, 2011). Hierarchical spring model for nanocomposites considerably different properties, but have yet to achieve the simultaneous strength/toughness or stiffness/density combinations obtained in biocomposites (Ashby et al, 1995). The challenge to further develop new materials with radically improved properties is to apply biomimetic strategies to synthetic composite materials (Beese et al, 2014) and where possible to implement complex hierarchical structures (Dimas et al, 2013). For models to be predictive, they must be able to capture the main relevant aspects, i.e., heterogeneity, complex geometry, scaling, stress concentrations, damage nucleation and evolution, etc
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