A Novel Notion of Local and Nonlocal Deformation-Gamuts to Model Elastoplastic Deformation

Localization and nonlocalization are characterized as a measure of degrees of separation between two material points in material’s discrete framework and as a measure of unshared and shared information, respectively, manifested as physical quantities between them, in the material’s continuous domain. A novel equation of motion to model the deformation dynamics of material is proposed. The shared information between two localizations is quantified as nonlocalization via a novel multiscale notion of Local and Nonlocal Deformation-Gamuts or DG Localization and Nonlocalization. Its applicability in continuum mechanics to model elastoplastic deformation is demonstrated. It is shown that the stress–strain curves obtained using local and nonlocal deformation-gamuts are found to be in good agreement with the Ramberg–Osgood equation for the material considered. It is also demonstrated that the cyclic strain hardening exponent and cyclic stress–strain coefficient computed using local and nonlocal deformation-gamuts are comparable with the experimental results as well as the theoretical estimations published in the open literature.

Challenge on conservation of angular momentum

In order to fix some important concepts of Fundamental Physics, either because they are not usually discussed in depth in theoretical classes and much less at laboratories, or because they are not sufficiently developed in textbooks, it is more effective not to tackle them directly, but to propose a mental or practical experiment to attract the student’s attention by questioning their beliefs about it (erroneous preconceptions). We propose a new example about the conservation of angular momentum of a system of material points in this way previously explained.

An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

We propose an explicit GPU-based solver within the material point method (MPM) framework using graphics processing units (GPUs) to resolve elastoplastic problems under two- and three-dimensional configurations (i.e. granular collapses and slumping mechanics). Modern GPU architectures, including Ampere, Turing and Volta, provide a computational framework that is well suited to the locality of the material point method in view of high-performance computing. For intense and non-local computational aspects (i.e. the back-and-forth mapping between the nodes of the background mesh and the material points), we use straightforward atomic operations (the scattering paradigm). We select the generalized interpolation material point method (GIMPM) to resolve the cell-crossing error, which typically arises in the original MPM, because of the C0 continuity of the linear basis function. We validate our GPU-based in-house solver by comparing numerical results for granular collapses with the available experimental data sets. Good agreement is found between the numerical results and experimental results for the free surface and failure surface. We further evaluate the performance of our GPU-based implementation for the three-dimensional elastoplastic slumping mechanics problem. We report (i) a maximum 200-fold performance gain between a CPU- and a single-GPU-based implementation, provided that (ii) the hardware limit (i.e. the peak memory bandwidth) of the device is reached. Furthermore, our multi-GPU implementation can resolve models with nearly a billion material points. We finally showcase an application to slumping mechanics and demonstrate the importance of a three-dimensional configuration coupled with heterogeneous properties to resolve complex material behaviour.

The principle of materiality of space and the theory of fundamental fields

The work formulates the principle of materiality of space and on its basis a brief critical analysis of the general ideology of the Special and General Theories of Relativity is carried out. The connection of the new principle with the previously developed Topological Theory of Fundamental Fields (TTFF) is considered. A method of constructive implementation of the principle of materiality in the framework of the physical theory of fundamental fields is considered. General equations of the dynamics of markers of material points of physical space are derived and their physical meaning is established.

Physics of evolution and unity of physics

The article considers the question of the possibility of constructing classical mechanics and empirical branches of physics, such as thermodynamics, statistical physics and kinetics on a general theoretical basis. The principles of constructing mechanics, thermodynamics, statistical physics, and kinetics are briefly given. It is shown how the construction of the above sections of physics on a unified basis became possible, relying on the mechanics of a structured body. The essence of this mechanics is that, unlike Newton’s mechanics, built for a body model in the form of a material point, this mechanics is built based on a body model in the form of a structured body. Moreover, the structured body is specified in the form of an equilibrium system of potentially interacting material points. It is shown how the equation of motion of a structured body is derived. The peculiarity of this equation is that it takes into account the transformation of the energy of motion of a structured body into internal energy when it moves in an inhomogeneous field of forces. This makes it possible to describe dissipative processes within the framework of the mechanics of a structured body without invoking statistical laws. Examples are given of how the empirical principles of the phenomenological branches of physics directly follow from the fundamental laws of physics.

Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics

Reliable evaluation of mechanical response in a porous solid might be challenging without any simplified assumptions. Peridynamics (PD) perform very well on a medium including pores owing to its definition, which is valid for entire domain regardless of any existed discontinuities. Accordingly, porosity is defined by randomly removing the PD interactions between the material points. As wave propagation in a solid body can be regarded as an indication of the material properties, wave propagation in porous media under an impact loading is studied first and average wave speeds are compared with the available reference results. A good agreement between the present and the reference results is achieved. Then, micro-cracks are introduced into porous media to investigate their influence on the elastic wave propagation. The micro-cracks are considered in both random and regular patterns by varying the number of cracks and their orientation. As the porosity ratio increases, it is observed that wave propagation speed drops considerably as expected. As for the cases with micro-cracks, the average wave speeds are not influenced significantly in random micro-crack configurations, while regular micro-cracks play a noticeable role in absorbing wave propagation depending on their orientation as well as the number of crack arrays in y-direction.

An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

We propose an explicit GPU-based solver within the material point method (MPM) framework on a single graphics pro- cessing unit (GPU) to resolve elastoplastic problems under two- and three-dimensional configurations (i.e., granular collapses and slumping mechanics). Modern GPU architectures, including Ampere, Turing and Volta, provide a computational framework that is well suited to the locality of the material point method in view of high-performance computing. For intense and nonlocal computational aspects (i.e., the back-and-forth mapping between the nodes of the background mesh and the material points), we use straightforward atomic operations (the scattering paradigm). We select the generalized interpolation material point method (GIMPM) to resolve the cell-crossing error, which typically arises in the original MPM, because of the C0 continuity of the linear basis function. We validate our GPU-based in-house solver by comparing numerical results for granular collapses with the available experimental data sets. Good agreement is found between the numerical results and experimental results for the free surface and failure surface. We further evaluate the performance of our GPU-based implementation for the three-dimensional elastoplastic slumping mechanics problem. We report i) a maximum performance gain of x200 between a CPU- and GPU-based implementation, provided that ii) the hardware limit (i.e., the peak memory bandwidth) of the device is reached. We finally showcase an application to slumping mechanics and demonstrate the importance of a three-dimensional configuration coupled with heterogeneous properties to resolve complex material behaviour.

Applications of 2D and 3D-Dynamic Representations of DNA/RNA Sequences for a description of genome sequences of viruses

: The aim of the studies is to show that graphical bioinformatics methods are good tools for the description of genome sequences of viruses. A new approach to the identification of unknown virus strains is proposed. Methods: Biological sequences have been represented graphically through 2D and 3D-Dynamic Representations of DNA/RNA Sequences - theoretical methods for the graphical representation of the sequences developed by us earlier. In these approaches, some ideas of the classical dynamics have been introduced to bioinformatics. The sequences are represented by sets of material points in 2D or 3D spaces. The distribution of the points in space is characteristic of the sequence. The numerical parameters (descriptors) characterizing the sequences correspond to the quantities typical for classical dynamics. Results: Some applications of the theoretical methods have been reviewed briefly. 2D-dynamic graphs representing the complete genome sequences of SARS-CoV-2 are shown. Conclusion: It is proved that the 3D-Dynamic Representation of DNA/RNA Sequences, coupled with the random forest algorithm, classifies successfully the subtypes of influenza A virus strains.

Plastic flow of isotropic rigid body at uniform deformation

The mathematical analysis of plastic flow processes under uniform plane, axisymmetric and volumetric deformation is carried out. The analysis is based on the external shape change of the body, which determines the movement of material points. It is shown that the plastic flow of an isotropic rigid-plastic body under plane deformation obeys the hyperbolic law, and for axisymmetric and volumetric deformations – the inverse square law. Spatial-geometric expressions of these laws made it possible to reveal and explain in a new way the physical essence of plastic shear. It is proved that the stressed state of a body under uniform tension-compression deformation is complex and cannot be defined as “linear”. The normal stress, which coincides with the direction of the resulting deformation force, is not the main one, since in the areas perpendicular to this direction, the shear stresses are not equal to zero. Examples of solving technological problems are given: extrusion of cylindrical billets and wire drawing, rolling of a wide strip of rectangular profile. It is shown that the problems of determining the stress-strain state of isotropic rigid-plastic bodies along the known trajectories of movement of material points are statically definable.