A Novel Total Lagrangian Smoothed Particle Hydrodynamics Approach For Modeling Damage In Elastic Solids And Deformation Of Composite Structures

This thesis comprehensively investigates Total Lagrangian Smoothed Particle Hydrodynamics(TLSPH) for modeling complex failure and deformation in solid mechanicsby focusing on dynamic brittle fracture and quasi-static deformation oflaminated composite structures. In the first part, a novel TLSPH framework forcrack initiation and propagation is developed. Overcoming mesh-based methodlimitations such as FEM’s mesh dependence and remeshing, this mesh-free modelsolves the strong form of linear momentum equations using a fully Lagrangian particleformulation. Damage is modeled via a stretch-based criterion, with particleinteractions deactivated at critical stretch. Numerical instabilities are mitigatedby enhanced diffusion and velocity filtering in damaged zones. Validated against2D and 3D benchmarks (e.g., Kalthoff-Winkler experiment, dynamic crack branching),the framework demonstrates accuracy, robustness, and captures complex crackpaths without remeshing. The second part extends TLSPH to model quasi-staticdeformation of laminated composite beams and plates. This is the first comprehensive3D TLSPH application to orthotropic composite laminates, discretizing eachply through thickness using corrected kernel gradients. Laminae are modeled asorthotropic continua, with global stiffness via exact tensor transformations. Hourglasscontrol and artificial viscosity ensure stabilization. Benchmark studies (bi-layercarbon/epoxy cantilever beams, clamped square plate) confirm accuracy against high-fidelity FEM by capturing linear through-thickness in-plane displacements andbending-stretching coupling. A parametric study of hourglass coefficients furtherexplores damping-accuracy trade-offs. Overall, this thesis establishes TLSPH as aversatile, robust, mesh-independent tool for simulating deformation and fracture inisotropic and anisotropic media, bridging a key gap by unifying fracture mechanicsand composite structural analysis within a single framework.