Perpustakaan Digital ITB

The use of classical Smoothed Particle Hydrodynamics (SPH) within computational solid mechanics presents various challenges. These issues encompass concerns related to both consistency and stability, which, in turn, have the potential to significantly impact the overall quality of the results obtained. While the Total Lagrangian formulation of SPH effectively addresses one aspect of instability, specifically, the tensile instability, it cannot fully eliminate another crucial issue: the zero-energy or spurious mode of instability. This research proposes frameworks to overcome the challenges in SPH method, which include accuracy, consistency, stability, and practical implementation. An alternative approach for computing the gradient of a function is introduced. It combines the local gradient of each interaction pair with the average value at each particle by leveraging the convolution identity through the kernel method. To assess the method’s efficacy, it is subjected to testing across various problems in nonlinear solid dynamics and crack growth analysis, ranging from 1D to 3D complexities. The analysis encompasses the evaluation of convergence, stability, as well as the preservation of momentum and energy. In the practical implementation, contact framework is proposed for the total Lagrangian framework of SPH. This framework take the benefit of Lagrangian kernel which give better stability and computational time efficiency, as well as the benefit of Eulerian kernel for automatic surface detection. And the last is the framework to analyse crack propagation. Two crack modelling technique is presented: particle deletion, and interaction deletion. Qualitative and quantitative analysis is conducted to verify the method’s performance. The results show a good agreement with the reference, underscoring the substantial enhancements in stability and precision achieved through the proposed SPH method.