A meshless adaptive multiscale method for fracture

The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the Phantom node method. A molecular statics approach is employed in the fine scale where crack propagation is modelled naturally by breaking of bonds. The triangular lattice corresponds to the lattice structure of the (1 1 1) plane of an FCC crystal in the fine scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively refined and coarsened as the crack propagates. The centro symmetry parameter is used to detect the crack tip location. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement

A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples

Engineered interphase mechanics in single lap joints: analytical and PINN formulations

Adhesively bonded joints showcase non-uniform stress distribution, along their length as the load is transferred through layers of dissimilar stiffness. For efficient transfer of loads, the peak interfacial shear stress is required to be engineered. In this study, inspired by electric pulses, the interphase modulus is modified according to square, sinusoidal and triangular pulses. The variation in peak stresses with increased number of pulses up to four is also investigated. The developed analytical model is solved for the interfacial shear stresses as well as the peel stresses, using energy functional approach, through MAPLE software. The abrupt changes in modulus in square pulse graded interphase are observed to create highest interfacial shear stresses among the considered grading profiles. Furthermore, the peak interfacial stresses are observed to increase with increased number of pulses. An effective elastic modulus parameter is defined to indicate the area under the modulus profile curve. The effective modulus is found to be gradually increasing with increase number of pulses in square graded interphase. Whereas, it is constant for sinusoidal- and triangular-graded interphases. A deep machine learning-based physics informed neural network model is developed to quickly solve the developed governing differential equations. Therefore, results from the machine leaning model are compared to the analytical results