Zahur Ullah

Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods

Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Bely...

Energy consistent framework for continuously evolving 3D crack propagation

This paper presents an enhanced theoretical formulation and associated computational framework for brittle fracture in elastic solids within the context of configurational mechanics, building on the authors’ previous paper, Kaczmarczyk et al. (2014). The local form of the first law of thermodynamics provides an equilibrium condition for the crack front, expressed in terms of the configurational forces. Applying the principle of maximal energy dissipation, it is shown that the direction of the crack propagation is given by the direction of the configurational forces. In combination with a fracture criterion, these are utilised to determine the position of the continuously evolving crack front. This exploitation of the crack front equilibrium condition leads to a completely new, implicit, crack propagation formulation. A monolithic solution strategy is adopted, solving simultaneously for both the material displacements (i.e. crack extension) and the spatial displacements. The resulting crack path is resolved as a discrete displacement discontinuity, where the material displacements of the nodes on the crack front change continuously, without the need for mesh splitting or the use of enrichment techniques. In order to trace the dissipative loading path, an arc-length procedure is adopted that controls the incremental crack area growth. In order to maintain mesh quality, smoothing of the mesh is undertaken as a continuous process, together with face flipping, node merging and edge splitting where necessary. Hierarchical basis functions of arbitrary polynomial order are adopted to increase the order of approximation without the need to change the finite element mesh. Performance of the formulation is demonstrated by means of three representative numerical simulations, demonstrating both accuracy and robustness.

Multi-scale finite element based durability and reliability analysis of laminated fibre reinforced composites for civil engineering applications

Fibre reinforced polymer composite structures are expected to experience a range of hygro-thermal environmental conditions during their service life. Since the presence of moisture and temperate can cause plasticization of the polymer matrix, alter the stress state, and degrade the fibre/matrix interface, an understanding of moisture diffusion and heat transfer is essential for predicting structural performance. In this paper, the durability of fibre reinforced polymer composite plate is investigated using reliability analysis. A multi-scale finite element based reliability method is adopted to consider both micro-scale and macro-scale random variables. To investigate the degradation in material properties induced by temperature and moisture, and simulate the structure serving in hot/wet environment, computational homogenization is used to solve the coupled heat conduction and moisture transport problem in heterogeneous materials. A numerical study is carried out to demonstrate the applicability of the proposed method, and the evolution in time of the probability of failure is computed.