A boundary-element scheme for analyzing initial boundary-value problems of 3-D porelasticity is considered. The scheme is based on a time-step method of numerically inverting Laplace transform. According to the method, a solution in time is calculated using quadrature formulas, based on complex values of the function in specific points. The choice of the points is determined by Lobatto method being one of Runge-Kutta methods. A possibility of using two- and three-stage Lobatto methods is considered. Using as an example the problem about a force, acting upon end of a prismatic poroelastic body, the effect of time-step on the dynamic responses of the forces is studied. The present results are compared with the results obtained on the nodes of Radau method.

The issue of evaluating service life of engineering objects, the exploitation properties of which are characterized by multi-parametric nonstationary thermal-mechanical effects, is discussed. The main degradation mechanisms of structural materials (metals and their alloys) are considered. To evaluate the stressed-strained state (SSS) and fatigue life of materials and structures from the modern viewpoint of mechanics of damaged media (MDM), a mathematical model is developed which describes processes of cyclic thermoplastic deformation and fatigue damage accumulation in structural alloys under multiaxial non-proportional paths of combined thermal-mechanical loading. The reliability of the defining relations of MDM for low-cycle modes of thermal-cyclic loading is corroborated by comparing the numerical and experimental results on fatigue life of a compact notched specimen in the conditions of non-uniaxial stressed state under block-type modes of thermal-cyclic loading. The results of numerically modeling fatigue life of a compact specimen with a blunted notch are given for two loading histories. It is shown that several cycles of intensive loading at the beginning of the deformation history can result in that the rule of linear summation of damage may yield inaccuracies of both conservative and non-conservative character. The effect of the inclination angle of cooling channels on thermal-cyclic life of combustion chamber tubes has been numerically analyzed. It is shown that the MDM model adequately describes the test data and can be used for evaluating thermal-cyclic life of materials and structures under multiaxial non-proportional paths of thermal-cyclic loading.

A Laplace domain direct boundary element approach for the three-dimensional dynamic analysis of the composite piezoelectric solids is presented. Integral representations of the fundamental solutions are used. Time domain solutions are obtained by the modified Durbin's method. Proposed boundary element formulation is verified through numerical examples.

An investigation of high-rate deformation and spall fracture of some metals in a wide range of strain rate was carried out by using the Kolsky method and plane-wave shock experiment. The dynamic stress-strain curves were obtained and speed dependences of the strength characteristics were constructed for commercially pure aluminum and copper, as well as for stainless steel. The strength limits and their dependences on the strain rate and temperature are determined. Based on the obtained mechanical characteristics, the parameters of Johnson-Cook model for stainless steel were determined with due allowance for the influence of the strain rate and temperature on the yield surface radius. It is noted that the time dependence of the spall strength weakly dependent on temperature. A rationale is offered that explains the results within the framework of Zhurkov's kinetic theory of strength.

The issue of determining material parameters and scalar functions in models and criteria of dynamic spallation fracture is discussed. An experimental-theoretical methodology to obtain them for the dynamics of failing elastoplastic media is presented, which consists in analyzing inverse problems. The methodology involves testing specimens of the studied material, using special regimes of dynamic loading, followed by analyzing a number of numerical modeling problems. For models and criteria of dynamic spallation fracture, the methodology is based on minimizing the quadratic deviation between experimental and analytical data containing information on the kinetics of the spallation fracture process. The reliability and unambiguity of the determined material parameters is demonstrated by comparing the experimental and analytical data.

The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas.

The main physical laws of the failure process in structural materials under dynamic loading modes and mathematical models of such processes are considered. To describe dynamic spallation fracture, a version of governing equations of damaged medium mechanics is developed, consisting of three interrelated parts: governing equations describing plastic behavior of the material as a function of the failure process, evolution equations of damage accumulation, and a strength criterion of the damaged material. A methodology for determining material parameters of kinetic equations of damage accumulation, based on minimizing the quadratic deviation between theoretical and experimental data is used. Comparison of the obtained computational results with the experimental data on dynamic spallation fracture in plates during plane impact shows that the present model of damaged medium mechanics adequately describes experimental data and can be effectively used in analyzing dynamic spallation fracture.

The paper contains a brief introduction to the state of the art in poroelasticity models, in BIE & BEM methods application to solve dynamic problems in Laplace domain. Convolution Quadrature Method is formulated, as well as Runge-Kutta convolution quadrature modification and scheme with a key based on the highly oscillatory quadrature principles. Several approaches to Laplace transform inversion, including based on traditional Euler stepping scheme and Runge-Kutta stepping schemes, are numerically compared. A BIE system of direct approach in Laplace domain is used together with the discretization technique based on the collocation method. The boundary is discretized with the quadrilateral 8-node biquadratic elements. Generalized boundary functions are approximated with the help of the Goldshteyn’s displacement-stress matched model. The time-stepping scheme can rely on the application of convolution theorem as well as integration theorem. By means of the developed software the following 3d poroelastodynamic problem were numerically treated: a Heaviside-shaped longitudinal load acting on the face of a column.