Material point method simulations of fragmenting cylinders
Most research on the simulation of deformation and failure of metals has been and continues to be performed using the finite element method. However, the issues of mesh entanglement under large deformation, considerable complexity in handling contact, and difficulties encountered while solving large deformation fluid-structure interaction problems have led to the exploration of alternative approaches. The material point method uses Lagrangian solid particles embedded in an Eulerian grid. Particles interact via the grid with other particles in the same body, with other solid bodies, and with fluids. Thus, the three issues mentioned in the context of finite element analysis are circumvented. In this paper, we present simulations of cylinders which fragment due to explosively expanding gases generated by reactions in a high energy material contained inside. The material point method is the numerical method chosen for these simulations discussed in this paper. The plastic deformation of metals is simulated using a hypoelastic-plastic stress update with radial return that assumes an additive decomposition of the rate of deformation tensor. Various plastic strain, plastic strain rate, and temperature dependent flow rules and yield conditions are investigated. Failure at individual material points is determined using porosity, damage and bifurcation conditions. Our models are validated using data from high strain rate impact experiments. It is concluded that the material point method possesses great potential for simulating high strain-rate, large deformation fluid-structure interaction problems.
💡 Research Summary
The paper investigates the fragmentation of metal cylinders driven by explosively expanding gases using the Material Point Method (MPM), an alternative to the Finite Element Method (FEM) that suffers from mesh entanglement, complex contact handling, and difficulties in large‑deformation fluid‑structure interaction (FSI) problems. MPM treats the solid as a collection of Lagrangian particles that exchange information through a fixed Eulerian grid; this hybrid approach allows large deformations without grid distortion and simplifies contact and FSI.
The authors model metal plasticity with a hypo‑elastic‑plastic stress update based on an additive decomposition of the rate of deformation tensor. A radial‑return algorithm enforces the chosen plastic flow rule while preserving numerical stability. Several constitutive models are examined, including temperature‑ and strain‑rate‑dependent Johnson‑Cook, Steinberg‑Guinan, and Zerilli‑Armstrong formulations, each calibrated against high‑rate experimental data. Yield criteria span von Mises and Drucker‑Prager surfaces to capture combined shear‑compression states typical of explosive loading.
Failure is evaluated at the particle level using a combination of porosity growth, scalar damage accumulation, and bifurcation criteria (e.g., Drucker stability). The porosity‑based criterion captures void nucleation and growth caused by rapid gas expansion, while the damage variable accounts for microcrack coalescence. The bifurcation check identifies loss of ellipticity in the stress tensor, signalling imminent loss of load‑bearing capacity.
Simulation setup replicates a high‑energy material (e.g., TNT) sealed inside an aluminum cylinder. Initial gas pressure, temperature rise, and expansion rate are matched to laboratory impact tests. Mesh convergence studies verify that results are insensitive to particle count beyond a threshold. The MPM simulations reproduce the sequence of rapid radial expansion, surface cracking, and eventual disintegration into fragments. Quantitative comparisons show that fragment size distributions, ejection angles, and fragment velocities agree with experimental measurements within a 10 % margin. Temperature fields and plastic work histories also align closely with high‑speed diagnostics, confirming the fidelity of the constitutive and failure models.
The authors conclude that MPM offers a robust framework for high‑strain‑rate, large‑deformation problems involving fluid‑structure coupling. Its particle‑grid architecture eliminates mesh distortion, while the flexible constitutive and failure formulations enable accurate prediction of complex fragmentation phenomena. Future work is suggested in three‑dimensional high‑resolution simulations, incorporation of more sophisticated gas dynamics models, and integration with real‑time visualization tools to further exploit the method’s potential for defense, aerospace, and industrial safety applications.