Soft robots, characterised by compliant mechanisms (CMs) made from low-stiffness materials, offer improved adaptability compared to traditional, rigid robots. These CMs are often actuated by pressure loads. Moreover, soft robots provide new possibilities in the area of robotics. They can be used in search and rescue and interact safely in collaboration with humans.

The current state-of-the-art in Topology Optimisation (TO) for design-dependent pressure-actuated CMs (PACMs) relies heavily on linear models. The determination of design-dependent pressure loads involves employing the Darcy method, which integrates Darcy's law with the drainage term to obtain the pressure field. Subsequently, the finite element method (FEM) is used to transform the pressure field into consistent nodal forces. However, it is crucial to acknowledge that these linear models are only valid for small displacements.

This thesis introduces a novel approach by incorporating nonlinearities into the solid mechanics of the TO process for PACMs in conjunction with the Darcy method. Additionally, this work incorporates nonlinearities into the solid mechanics of the TO process for PA multi-material compliant mechanisms, presenting another novel method.

Four nonlinearities in the solid mechanics of PA soft robots may occur, two of which are addressed in this thesis: geometric nonlinearities and a hyperelastic material model. Geometric nonlinearities arise from large deformations caused by high applied pressures. The Neo-Hookean material model is implemented to describe the low-stiffness material accurately.

The TO of pressure-actuated (PA) soft robots is simulated using COMSOL, a commercial software program for multi-physics simulation. This research presents a detailed comparison between theoretical predictions and practical outcomes as realised in COMSOL. Furthermore, this thesis includes a case study validating the successful implementation of the new method, covering a PA inverter, a PA compliant gripper, a PA member of the Pneumatic Networks, and a PA multi-material compliant gripper. The obtained results indicate limitations on the allowable applied pressure loads for the mechanisms, specifically in the case of the PA member of the Pneumatic Networks and a PA multi-material-compliant gripper. However, the PA inverter and PA compliant gripper validate the expectation that incorporating a hyperelastic material model yields significantly different results than the linear elastic material model. Moreover, the TO with the hyperelastic material model can predict displacements more accurately than the linear TO, as the differences between the displacements obtained from the TO and the analysis align more closely.

The Wang method is investigated to observe its influence on the range of the applied pressure loads during the TO of PA soft robots. The Wang method employs an interpolation technique that interpolates between linear and nonlinear theories. In this approach, void elements are described using linear theory, while solid elements are characterised by nonlinear theory. This interpolation method is developed to address distorted elements during large displacements. It effectively extended the range of applied loads during the TO of structures. However, it is found that this method does not influence the range of the applied load during the TO of CMs.