Open Collections

Tong, Zhiyuan

University of British Columbia

Two projects are included in the thesis. The two projects study different aspects of fracture and damage as the geometry changes. For Project 1, topology optimization is applied to optimize the fracture toughness of fibrillar adhesives towards initiated cracks. Project 1 applies to applications where the crack initiation is unavoidable and the crack initiation location is fixed. Multiple materials are considered. The objective is to minimize a weighted sum of the compliance and the J-integral, which ensures the load carrying ability and reduces the energy release rate at the crack tip. Three cases are analyzed in plane strain: double edge cracks in tension, single center crack in tension, and single edge crack in shear. With more weight put on reducing the J-integral, the load carrying structure is moved away from the crack. Highly similar results can be obtained for short cracks of different lengths. The methods are verified by: a benchmark topology optimization problem, benchmark J-integral computation problems, and the domain independence of the J-integral in topology optimization. For Project 2, deep indentation of hyperelastic materials in axisymmetry is simulated, which is important for predicting fracture. Frictionless contact and no-slip contact are considered. Four types of indenters are used. Effects of friction, indenter geometries and material constants on the potential crack shapes are studied. Among various types of finite elements, the 3-node triangular elements are chosen by analyzing the order of the numerical integration. The accuracy and the stability of the simulation are increased by modifying the traditional displacement conditions of contact to recover existing penetration. Using remeshing, the indentation can be extended to depth uncapable by commercial finite element software. The large deformation formulation is verified by comparing with the solution of Euler-Bernoulli beams in large bending. The hyperelastic formulation is verified by checking the energy conservation, as well as the agreement with linear elasticity when undeformed.

Text

2022-09-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/82685

Mechanical Engineering

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/