When simulating pressure-driven fracture with the Finite Element Method (FEM), significant difficulties can arise upon representing newly formed complex damage surfaces and their concurrent crack face loading. Application of this loading can also be required when additional physics is involved as in the case of hydraulic fracture where fluid physics inside a damage need to be considered. This paper presents a new Finite Element based practical numerical framework which can model pressure-driven fractures as they form on-the-fly without remeshing. The exact location of physical discontinuities passing through the element domain can be represented in the numerical model. The numerical framework can be implemented as a user-defined element and can be integrated into any FE package. A new element (called pressure element) is formulated with the capability to apply pressure and associated forces onto the crack surfaces in an adaptive manner. This element is verified using relevant examples from literature. The framework can also be configured for multi-physics problems where crack face loading is dictated by an additional physics. The element formulation is then extended for multi-physics problems involving fluid–solid interaction. The formulation provides the capability for multi-physics coupling adaptively as the crack propagates. The element is used to successfully simulate a test case from literature using different solution procedures (iterative and simultaneous). This element is also used to model failure in different pressure vessel problems to demonstrate its potential use in structural applications. A new higher-scale vessel element is developed which can represent different size, partitioning and failure states of composite vessel systems at element level. Composite vessel failure involving high number of pressurized cracks and delaminations as well as their interaction is modelled, and burst pressures are predicted for different vessel systems. The proposed numerical framework can be used towards designing more damage-tolerant vessels critical for the sustainable propulsion technologies.

Design and optimisation of large structures, including the positioning of lower-level components, typically require extensive user involvement and sequential mechanical analysis/optimisation iterations. This paper presents an original method that enables adaptive positioning of lower-level models (such as components) within higher level-models (such as large structures), and that achieves a combined mechanical/optimisation problem for the design of structures with various hierarchical levels (such as the positioning of stiffeners within a wingbox). As the position of the lower-level model evolves, our proposed method does not require re-generating of the geometry, remeshing or modifying the stiffness matrix of the elements corresponding to the various hierarchical levels. Instead, we achieve the adaptive positioning via an original concept that we propose here: Floating Connector (FC) elements. In this paper, we validate the FC elements against reference purely-mechanical solutions, show that they can be combined with gradient-descent method and genetic algorithms, and that they can be applied to optimise the positioning of a stiffener runout taking into account a debonding manufacturing defect.

This paper presents a new polymorphic element modelling approach for multi-scale simulation, with an application to fracture in composite structures. We propose the concept of polymorphic elements; these are elements that exist as an evolving superposition of various states, each representing the relevant physics with the required level of fidelity. During a numerical simulation, polymorphic elements can change their formulation to more effectively represent the structural state or to improve computational efficiency. This change is achieved by transitioning progressively between states and by repartitioning each state on-the-fly as required at any given instant during the analysis. In this way, polymorphic elements offer the possibility to carry out a multiscale simulation without having to define a priori where the local model should be located. Polymorphic elements can be implemented as simple user-defined elements which can be readily integrated in a Finite Element code. Each individual user-defined polymorphic element contains all the relevant superposed states (and their coupling), as well as the ability to self-refine. We implemented a polymorphic element with continuum (plain strain) and structural (beam) states for the multiscale simulation of crack propagation. To verify the formulation, we applied it to the multiscale simulation of known mode I, mode II andmixed-mode I and II crack propagation scenarios, obtaining good accuracy and up to 70% reduction in computational time —the reduction in computational time can potentially be even more significant for large engineering structures where the local model is a small portion of the total. We further applied our polymorphic element formulation to the multiscale simulation of a more complex problem involving interaction between cracks (delamination migration), thereby demonstrating the potential impact of the proposed multiscale modelling approach for realistic engineering problems.