Recent finite-element results by S. Cl. Larsson and A. J. Carlsson suggest a limited range of validity to the ‘small scale yielding approximation’, whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor, It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting p...

In this paper we study the effects of negative Poisson’s ratios on elastic problems containing singularities. Materials with a negative Poisson’s ratio are termed auxetic. We present a brief review of such materials. The elasticity problem of a bimateral wedge is presented, then two particular cases of this problem are investigated: the free-edge problem and the interface crack problem. We stud...

This paper introduces a new approach to identify singularities of planar parallel manipulators (PPMs). This method is based on Maxwell’s reciprocal figure theory which establishes a duality between self-stress frameworks and reciprocal figures. We use line geometry tools to introduce a new graphical construction called the Mechanism’s Line of action Graph (MLG). The MLG is introduced in order t...

Multi-layered stacks are commonly used in microelectronic packaging. Traditionally, these systems are designed using linear-elastic analysis either with analytical solutions or finite element method. Linear-elastic analysis for layered structures yields very conservative results due to stress singularity at the free edge. In this paper, it is shown that a damage mechanics based nonlinear analys...

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress–energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar f...

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for i...

We investigate a flat FLRW-model in $f(R,T)$-gravity, which includes the quadratic variation scalar curvature $R$ and linear term of trace stress-energy tensor $T$. In turn, we establish model has behaviour late time Universe, is accelerated expanding ends up big rip. Using parametrization scale factor $a(t)$, propose model, begins with point-type singularity, i.e., starts point zero volume, in...

The analytic behavior of the heavy-light meson form factor is investigated using several relativistic examples including unconfined, weakly confined, and strongly confined mesons. It is observed that confinement erases the anomalous threshold singularity and also induces an essential singularity at the normal annihilation threshold. In the weak confinement limit, the would be anomalous threshol...

In this paper, the numerical modelling of complete sliding contact and its associated singularity is carried out using the partition of unity finite element method. Sliding interfaces in engineering components lead to crack nucleation and growth in the vicinity of the contact zone. To accurately capture the singular stress field at the contact corner, we use the partition of unity framework to ...