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In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…
We present a new approach to calculate the particle distribution function about relativistic shocks including synchrotron losses using the method of lines with an explicit finite difference scheme. A steady, continuous, one dimensional…
The Fragile Points Method (FPM) is an elementarily simple Galerkin meshless method, employing Point-based discontinuous trial and test functions only, without using element-based trial and test functions. In this study, the algorithmic…
Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel…
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…
In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary…
Magma-driven fractures are the main mechanism for magma emplacement in the crust. A fundamental question is how the released fluid controls the propagation dynamics and fracture geometry (depth and breadth) in three dimensions. Analog…
The failure of materials and interfaces is mediated by cracks, nearly singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation -- the dynamic process of…
An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…
A thermo-mechanical fracture modeling is proposed to address thermal failure issues, where the temperature field is calculated by a heat conduction model based on classical continuum mechanics (CCM), while the deformation field with…
Crack micro-geometries and tribological properties pose an important impact on the elastic characteristics of fractured rocks. Numerical simulation as a promising way for this issue still faces some challenges. With the rapid development of…
As a consequence of shearing, wing cracks can emerge from pre-existing fractures. The process involves the interaction of sliding of the existing fracture surfaces and the tensile material failure that creates wing cracks. This work devises…
Crack nucleation is crucial in many industrial applications. The phase field method for fracture transforms the crack nucleation problem into a minimization problem of the sum of the elastic potential energy and the crack surface energy.…
The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of one-dimensional linear…
We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…
In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time…
In the hydraulic fracturing of natural rocks, understanding and predicting crack penetrations into the neighboring layers is crucial and relevant in terms of cost-efficiency in engineering and environmental protection. This study…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
Hydraulic systems are widely utilized in industrial applications due to their high force generation, precise control, and ability to function in harsh environments. Hydraulic cylinders, as actuators in these systems, apply force and…
Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize…