Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

We propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

Study on Model of Penetration into Thick Metallic Targets with Finite Planar Sizes by Long Rods

A finite cylindrical cavity expansion model for metallic thick targets with finite planar sizes, composed of ideal elastic-plastic materials, with penetration of high-speed long rod is presented by using the unified strength theory. Considering the lateral boundary and mass abrasion of the target, the penetration resistance and depth formulas are proposed, solutions of which are obtained by MATLAB program. Then, a series of different criteria-based analytical solutions are obtained and the ranges of penetration depth of targets with different ratios of target radius to projectile radius (rt/rd) are predicted. Meanwhile, the numerical simulation is performed using the ANSYS/LS-DYNA finite element code to investigate the variations in residual projectile velocity, length, and mass abrasion. It shows that various parameters have influences on the antipenetration performance of the target, such as the strength coefficient b, rt/rd, the shape of the projectile nose, and the impact velocity of the projectile, among which the penetration depth has increased by 18.95% as b = 1 decreases to b = 0 and has increased by 32.28% as rt/rd = 19.88 decreases to rt/rd = 4.9.