A program package FIDESYS is dedicated to solving static and dynamic strength problems of stress and strain states of solids under finite strains with the use of the finite-elements method (FEM), the spectral-elements method (SEM), and the discontinuous Galerkin method (DG).
A complex has been developed so that the system requirements are not high: it could be executed on an ordinary PC, and while having a powerful video card with CUDA support PC computations are performed on it (which speeds up calculations approximately 40–60 times). On the other hand it could be adopted for supercomputer usage.
A package is highly demanded in areas where large deformations and their redistribution must be taken into account in nonlinear strength and destruction mechanics, and in the mechanics of phase transitions. Applications include:
Traditional rubber-like materials and polymers (rubber and tire industry)
Biomaterials (use of biomaterials in medicine)
During designing of materials with varying properties under loading (development of new constructional materials)
Physics of soft materials
Nano-sized crystalline templates (nano-particles, thin films, and defectless domains near growing nano-size defects)
Problems of defects’ origination and growth (monitoring problems)
During strength analysis of porous solids containing defects (where an estimation of the effective material properties is necessary, including pores with inner pressure) under finite strains
During solving research problems (universities, research laboratories)
Acoustic problems by means of discontinuous Galerkin method (DG) (problems of acoustic logging)
Connected problems of a viscous fluid’s propagation in a developing crack under finite strains (hydrocrack).
A uniqueness of the package is a possibility to solve problems in which new boundary surfaces (cavities) are originated under loading in the solid or material properties are changed in some part of the solid that leads to the redistribution of the finite strains in the solid. The package allows us to directly take into account the redistribution of the finite strains, and unlike schemes connected with “elements’ killing” or changing of material properties inside an element (when boundary conditions are not taken into account precisely) it uses an approach based on the exact expressions of the full analytical problem statement, including a forced removal of the solid’s part.
In addition, the method of sequential loading is not used while solving problems under finite strains. Usage of this method can lead in some cases to results that do not correspond to a general nonlinear problem statement, and it does not allow (in particular) one to determine unloading zones while solving plasticity problems in an exact formulation and under large deformations.
An approach based on the direct replacement of the system of nonlinear partial differential equations by the system of nonlinear algebraic ones by means of FEM or SEM and their further solving is used in the package. In addition, the package allows us to solve problems for incompressible materials without approximating their properties as nearly incompressible.
For solving viscoelastic problems, a complex allows use of integral constitutive equations with singular kernels.
Also, the package allows us (including a case of finite strains):
to model a destruction process taking into account an origination and a growth of prefracture zones
to solve coupled problems, including phase transformations in solids
to solve problems of ductile growth of cracks (with non-zero opening) with a consecutive absorption of secondary cracks by the main one while solving strength problems
to take into account either local or non-local strength criteria
to solve problems of a shape’s determination for the removed part of the loaded body when the solid’s shape is given after a removal and a consecutive deformation
to estimate effective material properties under finite strains (including pore solids).
Improvement of the computational capabilities is performed due to:
Improvement of models, computational schemes and methods, in particular:
More precise estimation of nonlinear effects arising under finite strains and their redistribution
A possibility to take into account a forced change of the solid’s shape (structure’s element) under large deformations and loading, origination of new surfaces in a loaded solid
A possibility to take into account a change of material properties (including phase transitions in solids) under large deformations and loading, including calculations for nano-size templates
Taking into account modern views of constitutive equations
A possibility to solve different types of coupled problems, including the case of finite strains
An application of the newest calculus schemes of solving problems of mathematical physics; for example, a fully explicit spectral-element method, discontinuous Galerkin.
Use of modern computational software, and hardware approaches, and methods.
Use of modern program libraries and tools that allow us to drastically simplify a development and speed-up a computational process.
Parallelization of computational processes. Use of shared memory systems. Massively parallel systems. Calculations on clusters.
Application of the newest technologies using additional PC resources—for example, CUDA.
The program package FIDESYS is supplemented with a program complex FIDESYS—SUPERPOSITION based on semi-analytical/numerical, and purely analytical calculations on a computer, which allows obtaining approximate analytical solutions of plane problems under finite strains. These solutions could be considered like testing or checking examples for FEM-type packages for the case of finite strains and their redistribution.
There are few testing possibilities (checking problems) in industry packages for complex nonlinear problems to check a the correctness of acquired results. The given addition for the package supplements testing possibilities in a large number of cases up to some strain level (especially for incompressible materials). The given package allows us to get obtain approximate solutions for complex problems of nonlinear elasticity in the form of analytical expressions depending on coordinates, material parameters, etc., which drastically simplifies further analysis and application of acquired results.
There is a possibility to integrate the package into existing market program products.