Deep learning and the collocation method are merged used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, von Mises plasticity isotropic kinematic hardening. The performance this deep (DCM) depends on architecture neural network corresponding hyper...

The behaviour of granular solid-liquid mixtures is key when deforming a wide range of materials from cornstarch slurries to soils, rock and magma flows. Here we demonstrate that treating semi-solid alloys as a granular fluid is critical to understanding flow behaviour and defect formation during casting. Using synchrotron X-ray tomography, we directly measure the discrete grain response during ...

physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum. Continuum mechanics refers to field descriptions of mechanical phenomena, which are usually modeled by partial differential equations. The Navier–Stokes equations for the velocity and pressure fields of Newtonian fluids provide an important example, but continuum modeling...

Department of Engineering Mechanics and University, Hangzhou 310027, China. E-ma Department of Civil Engineering and S University, Hangzhou 310058, China Department of Mechanical and Aerospace Gables, Florida 33146, USA Department of Electronics Engineering, Inc 772, Republic of Korea The Solid Mechanics Research Center, Bei China Department of Materials Science and Engin Laboratory, University...

We describe the Uintah Computational Framework (UCF), a set of software components and libraries that facilitate the simulation of partial differential equations on structured adaptive mesh refinement grids using hundreds to thousands of processors. The UCF uses a non-traditional approach to achieving parallelism, employing an abstract taskgraph representation to describe computation and commun...

The numerical analysis of spontaneously formed discontinuities such as cracks is a long-standing challenge in the engineering field. Approaches based on the mathematical framework of classical continuum mechanics fail to be directly applicable to describe discontinuities since the theory is formulated in partial differential equations, and a unique spatial derivative, however, does not exist on...

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolati...