A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

Abstract

Fracture of heterogeneous materials has emerged as a critical issue in many engineering applications, ranging from subsurface energy to biomedical applications, and requires a rational framework that allows linking local fracture processes with global fracture descriptors such as the energy release rate, fracture energy and fracture toughness. This is achieved here by means of a local and a global potential-of-mean-force (PMF) inspired Lattice Element Method (LEM) approach. In the local approach, fracture-strength criteria derived from the effective interaction potentials between mass points are shown to exhibit a scaling commensurable with the energy dissipation of fracture processes. In the global PMF-approach, fracture is considered as a sequence of equilibrium states associated with minimum potential energy states analogous to Griffith's approach. It is found that this global approach has much in common with a Grand Canonical Monte Carlo (GCMC) approach, in which mass points are randomly removed following a maximum dissipa-tion criterion until the energy release rate reaches the fracture energy. The duality of the two approaches is illustrated through the application of the PMF-inspired LEM for fracture propagation in a homogeneous linear elastic solid using different means of evaluating the energy release rate. Finally, by application of the method to a textbook example of fracture propagation in a heterogeneous material, it is shown that the proposed PMF-inspired LEM approach captures some well-known toughening mechanisms related to fracture energy contrast, elasticity contrast and crack deflection in the considered two-phase layered composite material.

Mode Coarsening or Fracture: Energy Transfer Mechanisms in Dynamic Buckling of Rods

“…To probe this hypothesis, we turn to molecular dynamics inspired structural simulations, and discretize the rod into mass points with interactions described by harmonic potentials of mean force suitable for structural members for both two-body (stretch) and three-body (bending) interactions [7,19] (potential parameters are given in Supplemental Material [16], which includes Ref. [20]). We simulate the dynamic buckling test in two thermodynamic ensembles: the microcanonical ensemble (NVE), and the canonical ensemble (NVT) using a Nosé-Hoover thermostat [21,22].…”

Implementing a non-local lattice particle method in the open-source large-scale atomic/molecular massively parallel simulator

“…Particle-based methods are wellsuited to handle problems involving discontinuities [6], especially crack initiation, growth, deflection, and branching. When combined with potential-of-mean-force formulations [7], the particle-based method can use Griffith's criteria to model fracture [8][9][10][11][12] in heterogeneous materials [13,14].…”

Phase diagram of brittle fracture in the semi-grand-canonical ensemble

“…Statistical lattice-based models of fracture addressed size effects of materials' strength, bursts of microfailures, and morphology of cracks [9][10][11][12][13]. Others consider the competition between crack propagation and dislocation mechanisms [14][15][16]; role of interatomic and mean force potentials [17][18][19][20][21]; role of phonons [18,22,23]; crack velocity and dynamic instability [20,[24][25][26][27]; crack growth kinetics of microcracks in crystals [28]; and effect of crystal orientation, grain boundaries, texture, chemical environment, and impurities [25,[29][30][31][32][33][34][35]. Compared to this rich and insistently increasing body of fracture literature, our approach differs in two fundamental aspects: (1) it defines the fracture process as bond rupture in the semi-grand-canonical ensemble ( μV T ), in contrast to the canonical (NV T ) and microcanonical (NV E ) ensembles that restrain our current knowledge of the physics of fracture processes; and by doing so (2) it enables a new understanding of fracture resistance of solids, in terms of energy and bond fluctuations, in the μV T ensemble.…”