Dedicated to the 120th anniversary of Peter the Great St. Petersburg Polytechnic University ABSTRACTS St. Petersburg 2019 XLVII International Conference “Advanced Problems in Mechanics” June 24-29, 2019, St. Petersburg, Russia APM 2019 BOOK OF ABSTRACTS WWW.APM-CONF.SPB.RU PARAMETER DETERMINATION OF METAMATERIALS IN GENERALIZED MECHANICS VIA COMPUTATIONAL HOMOGENIZATION Abali B.E.1, Yang H.1, Papadopoulos P.2 1 - Technische Universitat Berlin, Institute of Mechanics 2 - University of California, Berkeley, Department of Mechanical Engineering [email protected] In continuum mechanics, conventional theory of elasticity fails to model structures, where the inner substructure starts affecting the material response. An intuitive explanation for this phenomenon relies on the length scale of the geometry, macroscale, and the inner substructure, microscale. As the ratio of macroscale with respect to the microscale approaches one, and as both length scales lead to the same order, the effects of the substructure shall be incorporated and we call this structure related material system metamaterial. Modeling of metamaterial incorporates additional parameters and it is indeed possible to do computations by using the finite element method [1], [2], [3], as long as we know all parameters. Therefore, we need an approach leading to a unique determination of all parameters. For an isotropic and centrosymmetric metamaterial, there are seven parameters to determine. It is challenging to define experimental studies for obtaining all of these parameters. As these parameters result after a homogenization approach by involving the inner substructure, we can acquire these parameters purely based on computations at the microscale. By using the finite element method for detailed computations at the microscale for seven distinct cases, we masterfully generate a way to determine the seven material parameters uniquely [4]. In this talk, this method is exploited and a practical application has been studied in order to present its capability for modeling the metamaterial response. References [1] B. E. Abali, W. H. Müller, and V. A. Eremeyev. Numerical investigation of thin films with strain gradient elasticity. Advanced Problems in Mechanics, International Summer School – Conference Proceedings. 2015, pp. 2-8. [2] B. E. Abali, W. H. Müller, and V. A. Eremeyev. Strain gradient elasticity with geometric nonlinearities and its computational evaluation. Mechanics of Advanced Materials and Modern Processes. 2015, 1(1), pp. 1-11. [3] B. E. Abali, W. H. Müller, and F. dell’Isola. Theory and computation of higher gradient elasticity theories based on action principles. In: Archive of Applied Mechanics 87.9 (2017), pp. 1495–1510. [4] B. E. Abali, H. Yang, and P. Papadopoulos. A computational approach for determination of parameters in generalized mechanics. In: Abali, B. E., Altenbach, H., and Müller, W. H. (Edi tors), Higher Gradient Materials and Related Generalized Continua (2019), pp. 1–18. Springer Nature, Singapore. A MODEL OF HYDRAULIC FRACTURED HORIZONTAL WELL FOR DEBIT COMPUTATION OF SLANGED GAS AND OIL Abramov I.A. Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russia [email protected] The purpose of work is to make mathematical model and finite difference algorithm for 3-dimensional dynamic model for debit and pressure computation in a region of hydraulically fractured horizontal well and compare results with commercial simulators. The composite model of hydraulic fractured horizontal well divides reservoir into three main flow areas: hydraulic fractures distributed along the horizontal well with different length and conductivity, but the fractures propagation is limited and obeys Darcy's law; stimulated reservoir volume SRV: natural fractures are opened and connected. SRV is made up of matrix and micro-fractures and can be described with dual porosity model. The permeability of matrix system is very low compared with micro-fracture system. So, the inter-porosity flow between them is pseudo-steady and it can be determined only by pressure difference between matrix and micro-fracture system; unstimulated reservoir: the matrix characteristics are the same in unstimulated and stimulated reservoir. It has the same permeability and porosity. Assuming fluid flow in the hydraulic fractures obeys Darcy's law, the pressure is equal on the boundary of fractures and matrix. The mathematical model for hydraulic fractures is given by analog of heat equation, initial and boundary conditions. The algorithm is based on solving heat equation with finite implicit methods on rectangular greed. These methods were chosen because of absolute convergent and second-order accuracy in time. Boundary condition can be used conditions of first (isolation) and third (non-transitory) types. Numerical computational algorithm realized on Python using numpy and matplotlib packages. This language was used because of simplicity of future integration into existing program packages. 2 GRADIENT & FRACTIONAL/FRACTAL MODELS FOR ELASTICITY, DIFFUSION, PLASTICITY AND DISLOCATIONS: APPLICATIONS TO LIBS AND DMCS Aifantis E.C., Tsagrakis I., Konstantopoulos I., Sidiropoulos A. Aristotle University of Thessaloniki [email protected] Hooke’s law of elasticity and Fick’s law of diffusion are routinely used for theoretical interpretations of chemomechanical behavior and design of new materials and processes. The same is true for the use of classical plasticity and dislocation theories. However, the new experimental tools developed recently and associated computational methods suggest that the aforementioned “classical laws” often fail to interpret observed behavior. The lecture will show that a new possibility for sustaining the validity of the classical laws is to enrich them with nonlocal gradient, fractional and fractal terms. Physically unacceptable singularities predicted from classical elasticity for dislocations and cracks are eliminated within its gradient and fractional/fractal counterparts. Similarly, diffusion penetration profiles in nanopolycrystals and plasticity size effects in micro/nano pillars that could not be interpreted by classical theories can effectively be captured by their nonclassical counterparts. Examples will be chosen from the fields of Lithium-ion batteries and disclinated microcrystals fabricated by electrodecomposition under mechanical steering. References [1] E.C. Aifantis, Internal length gradient (ILG) material mechanics across scales & disciplines, Adv. Appl. Mech. 49, 1- 110 (2016). [2] I. Tsagrakis, I. S. Yasnikov and E.C. Aifantis, Gradient elasticity for disclinated micro crystals, Mech. Res. Comm. 93, 159-162 (2018); [3] I. Tsagrakis and E.C. Aifantis, Gradient and size effects on spinodal and miscibility gaps, Cont. Mech. and Thermod. 30, 1185-1199 (2018). [4] K. Parisis, I. Konstantopoulos and E.C. Aifantis, Non-singular solutions of GradEla models for dislocations: An extension to fractional GradEla, J. Micr. Mole. Phys. 4, 1840013 (2018). Acknowledgment: Hellenic Foundation for Research and Innovation (HFRI) MIS 5005134: "Nano-chemomechanics in Deformation and Fracture: Theory and Applications in LiBs and SGS". PHASE-CHANGE IN NANOSCALE CONFINEMENT Akhatov I. Center for Design, Manufacturing and Materials, Skolkovo Institute of Science and Technology, Moscow [email protected] A two-dimensional (2D) material placed on an atomically flat substrate can lead to the formation of surface nanobubbles trapping different types of substances. This observation for graphene was first reported by group of A.Geim, along with modeling based on continuous theory of elastic membranes (Nature Communications, 2016). In our paper graphene nanobubbles are studied using atomistic and continuous multiscale modeling that allows direct numerical monitoring of phase change of the matter trapped inside nanobubbles (Scientific Reports, 2017; Nanotechnology, 2019). All modeled graphene nanobubbles except for the smallest ones exhibit a universal shape, i.e., a constant ratio of a bubble height to its footprint radius, which is in an agreement with experimental studies and their interpretation using the elastic theory of membranes. MD simulations reveal that argon does exist in a solid close-packed phase, although the internal pressure in the nanobubble is not sufficiently high for the ordinary crystallization that would occur in a bulk system. The smallest graphene bubbles with a radius of 7 nm exhibit an unusual “pancake” shape. Previously, nanobubbles with a similar pancake shape were experimentally observed in completely different systems at the interface between water and a hydrophobic surface. This research clearly demonstrates the possibility that nanobubbles in heterostructures can be used to investigate the fundamentally interesting phenomenon of phase transition in confined systems. 3 CONSTRAINT-RELAXATION BASED INTERACTIVE SYNTHESIS OF A BIPED ROBOT LEG MECHANISM Al-Dwairi A.1, Bataineh O.1, Abdelal E.1, Al-Lubani S.1,2 1 - Industrial Engineering Department, Jordan University of Science and Technology 2 - Mechanical Engineering Department, Al-Balqaa Applied University [email protected] The paper presents an approach to kinematic synthesis of a leg mechanism for biped walking robots. The mechanism used is a six-bar, Watt-I type linkage. Selection of the kinematic scheme was based on the requirement to have the overall shape of the mechanism resemble the human leg outline shape. In addition, the Watt-I scheme is known for having