Acta Mechanica

This paper addresses the phenomena of mechanical creep and deformation in rock formations, coupled with the hydraulic effects of fluid flow. The theory is based on Biot's poroelasticity, generalized to encompass viscoelastic effects through the correspondence principle. Based on the resultant poroviscoelastic theory, stress and deformation analyses are performed. The interactions between the fluid pore pressure diffusion and the elastic/viscoelastic rock matrix deformation are illustrated via two important examples. First, the problem of a borehole subject to a non-hydrostatic stress state, but deforming under plane strain condition, is examined. Second, a cylinder under generalized plane strain conditions is solved. Three rocks, Berea Sandstone, Danian Chalk, and a deep water Gulf of Mexico Shale, covering a wide range of permeabilities, are considered. The significance of poro-and viscoelastic time-dependent effects is discussed.

This paper explores the possibilities of applying physics-informed neural networks (PINNs) in topology optimization (TO) by introducing a fully self-supervised TO framework based on PINNs. This framework solves the forward elasticity problem by the deep energy method (DEM). Instead of training a separate neural network to update the density distribution, we leverage the fact that the compliance minimization problem is self-adjoint to express the element sensitivity directly in terms of the displacement field from the DEM model. Thus, no additional neural network is needed for the inverse problem. The method of moving asymptotes is used as the optimizer for updating density distribution. The implementation of Neumann, Dirichlet, and periodic boundary conditions is described in the context of the DEM model. Three numerical examples are presented to demonstrate framework capabilities: (i) compliance minimization in 2D under different geometries and loading, (ii) compliance minimization in 3D, and (iii) maximization of homogenized shear modulus to design 2D metamaterial unit cells. The results show that the optimized designs from the DEM-based framework are very comparable to those generated by the finite element method and shed light on a new way of integrating PINN-based simulation methods into classical computational mechanics problems.

A bifurcation analysis of a strain hardening dilatant sand sample in the triaxial test is carried out. The analysis shows that the triaxial test yields only then the limiting soil properties if 1) the sample is compact enough and 2) if the confining pressure does not exceed a critical value depending on the soil anisotropy and the slenderness of the sample.

Die Eigenspannungen eines inkompressiblen Plattenstreifens, der elastisch-plastisch durch endliche Biegung verformt wird, werden ermittelt. Es zeigt sich, daß die sich ergebenden Eigenspannungen in hinreichender Genauigkeit auch mit Hilfe eines Superpositionsprinzips ermittelt werden können, indem man dem am Ende der Belastung sich ergebenden Spannungszustand die Spannungen einer elastischen Biegung mit entgegengesetztems gleich großen resultierenden Moment überlagert.

A mesoscopic combustion reaction model of multi-component PBX explosives by using a coupled thermo-mechanical constitutive model is studied. Thereinto, based on the heat balance equation, the present temperature can be calculated; the changing physical state of different materials is described by establishing different equations of state, and based on specially appointed constitutive equations, the microcracks in PBXs are described. Furthermore, the concept of combustion reaction degree is established, which takes temperature as a criterion for changing physical state. The model is implemented within the framework of the material point method so that the different gradient in the governing differential equations could be discretized in a single computational domain and that continuous remeshing is not required with increasing reaction time. The proposed model-based simulation procedure is verified with the burn rate, the peak pressure, and temperature of PBX explosives under macroscopic scale.

In this paper, we analyse the flow in a cylindrical cavity of aspect ratio H/R = 2, with a top lid rotating with a sinusoidal time-varying speed. The Reynolds numbers, based on the time-averaged rotating speed and the radius of the cavity (Re = $$ \Omega _0 R^2/\nu $$ ) are 2800, 3500 and 4100. Particle Image velocimetry measurements and numerical simulations are performed to determine the effect on the flow of different imposed frequencies on the rotating lid. The acceleration and deceleration of the lid produce a marked pulsatile flow behaviour. It is found that at low Reynolds numbers the frequencies measured in the flow coincide with the frequency imposed on the rotating lid, while at the largest Re considered the flow frequencies are significantly lower, especially when the frequency of the disk is large. The fluctuations induced in the vertical velocity component are about 100% of the instantaneous values while for the angular component the fluctuations are of the same order as the instantaneous values.

The present problem aims to study the scattering behavior of SH-waves by a circular cavity near two symmetrically permeable interface cracks in the piezoelectric bi-material half-space. The steady-state response of the problem is obtained, with the aid of the Green’s function method and the complex function method. Above all, the essential expression of Green’s function is constructed by the mirror method. This expression satisfies the conditions of being stress-free and electric insulation on the horizontal boundary of the orthogonal space where the circular cavity is located, and the condition of bearing a harmonic out-plane line source force on the vertical boundary. Next, on the basis of dividing the bi-material medium into two parts along the vertical boundary, the first kind of Fredholm integral equation with uncertain anti-plane forces is established by using the conjunction method and the crack-division technology. Then, the solution is obtained by solving an algebraic equation with finite terms, which is an effective truncation of the integral equation. Finally, the dynamic stress concentration factor around the edge of the circular cavity and the dynamic stress intensity factor at the crack tip are calculated numerically. On this basis, the effects of incident wave frequency, crack length, crack location and circular cavity position on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Anti-plane shear of piezoelectric fibrous composites is theoretically investigated. The geometry of composites is described by the 2-dimensional geometry in a section perpendicular to the unidirectional fibers. The previous constructive results obtained for scalar conductivity problems are extended to piezoelectric anti-plane problems. First, the piezoelectric problem is written in the form of the vector-matrix $${\mathbb{R}}$$ -linear problem in a class of double periodic functions. In particular, application of the zeroth-order solution to the $${\mathbb{R}}$$ -linear problem yields a vector-matrix extension of the famous Clausius–Mossotti approximation. The vector-matrix problem is decomposed into two scalar $${\mathbb{R}}$$ -linear problems. This reduction allows us to directly apply all the known exact and approximate analytical results for scalar problems to establish high-order formulae for the effective piezoelectric constants. Special attention is paid to non-overlapping disks embedded in a two-dimensional background.

A conceptual framework for damage processes in materials is presented. In this framework, the mechanics of damage processes in materials is investigated. These processes are categorized into either damage processes described in terms of stiffness degradation or damage processes described in terms of cross-sectional area reduction. Furthermore, the damage processes are visualized to occur as sequences either in series or in parallel. Schematic diagrams are used to illustrate these processes in a similar way to what is done with elastic springs and electric circuits. Different kinds of combinations and interactions of the damage processes are illustrated with various examples. The generalization to three-dimensional states of deformation and damage is also presented. This work is currently limited to linear elastic materials. The concepts presented in this work could be linked to homogenization methods. It is hoped that this work will lay the groundwork to open new areas of research in damage mechanics.