We consider a frame-indifferent variational model for magnetoelastic solids in the large-strain setting with the magnetization field defined on the unknown deformed configuration. Through a simultaneous linearization of the deformation and sharp-interface limit of the magnetization with respect to the easy axes, performed in terms of Γ-convergence, we identify a variational model describing the formation of domain structures and accounting for magnetostriction in the small-strain setting. Our analysis incorporates the effect of magnetic fields and, for uniaxial materials, ensures the regularity of minimizers of the effective energy.

In this paper, an elastic-constant stress cohesive zone model is developed to analyze the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film bonded to a couple-stress half-plane substrate, with surface effects taken into account. By imposing perfect bonding conditions and adopting a membrane assumption, the governing integral equation is constructed and numerically solved using the Chebyshev polynomial expansions. An iterative method is proposed to determine the cohesive zone size, and analytical expressions for the stress and strain distributions are derived. Systematic parametric studies are performed to elucidate the effects of characteristic length scales, substrate couple-stress length, film’s aspect ratio, and substrate-to-film stiffness ratio on the stress–strain fields and the evolution of the cohesive zone. The results provide foundational insights into interfacial mechanics and offer design guidelines for developing reliable, high-performance piezoelectric quasicrystal film devices.

An analytical framework is developed to explore the dispersion behavior of Rayleigh waves in a functionally graded piezoelectric (FGP) plate interfaced with a dry sandy foundation, accounting for nonlocal elasticity effects and interfacial imperfections. The governing equations are formulated using nonlocal elasticity theory and solved analytically via harmonic wave analysis approach. Interface effects are modeled using normal and tangential stiffness parameters, allowing for partial bonding at the interface. Numerical simulations are performed considering both electrically open and electrically short surface conditions. The influence of key parameters including material gradation, nonlocal scale effects, interfacial stiffness, and substrate properties on the phase velocity of Rayleigh waves is examined in detail. Parametric analysis reveals that variations in the plate thickness and nonlocal parameter considerably affect the phase velocity and dispersion behavior of Rayleigh waves. The 2D and 3D plots of the displacement and electric potential fields are generated using Mathematica , illustrating the spatial variation and confinement of wave energy within the FGP layer. The results not only validate classical trends under limiting conditions but also reveal important coupled effects that are absent in traditional local models. These findings contribute to a deeper understanding of wave mechanics in smart-layered structures and offer valuable guidance for the design and optimization of advanced piezoelectric sensors, actuators, and SAW devices.

Based on micropolar theory, we develop a novel mathematical framework for modeling finite elastoplastic deformations. The proposed formulation accommodates both large strains and finite rotations while exploiting the ability of micropolar theory to represent underlying material microstructure. The balance equations are obtained from an invariance principle with respect to general observer transformations. Within the setting of material uniformity, the plastic evolution laws are expressed as first-order differential equations for a set of material transplants, subject to the formal restrictions dictated by micropolar material symmetries and the constraints of the second law of thermodynamics. In addition, we identify the micropolar Mandel stress tensors as the energetic driving forces governing the local rearrangement of material inhomogeneities.

A multiple contact problem for a system of interacting flat-ended cylindrical punches perfectly bonded to the surface of an elastic half-space is considered under the assumption that each of the punches is loaded by external forces which produce the punch’s translational displacements in three coordinate directions and small-angle rotations about the coordinate axes. An approximate solution is obtained by the Kachanov method that is based on the ideas of Kachanov originally introduced for the multiple crack problems. The obtained results are applied to the problem of the equilibrium stability of two neighboring rigid columns with their circular footings bonded to an elastic half-space.

The aim of this paper is to use a technique introduced by Bruyère in order to prove an exponential rate of convergence for solutions to linear elliptic problems in generalized cylinders of the type ℓ ω 1 × ω 2 , as ℓ goes to infinity and ω 1 and ω 2 being two fixed bounded domains. This method allows to avoid the use of the iteration technique introduced by Chipot and Yeressian. However, the method of Bruyère only works in the case where ω 1 is a ball centered at the origin. We will prove here that this method can be adapted to the case where ω 1 is a bounded domain, star-shaped with respect to an open ball centered at the origin. This approach is possible thanks to a remarkable property of such domains, that will be proved in the second section of this paper.

The robust topology optimization (RTO) design of multi-material structures holds significant practical implications and theoretical value. The main contribution of this paper is to study the RTO problem of multi-material structures considering load uncertainty, and to propose an innovative non-gradient multi-material RTO approach to multi-material structures considering load uncertainty. To this end, the alternating active-phase algorithm (AAPA) is first applied to decouple this RTO problem, and combined with these approaches (probabilistic approach, density-based approach, and linear combination approach) to construct the RTO model of multi-material structures considering load uncertainty and taking the linear combination of the mean and standard deviation of the structural compliance as the objective function. Subsequently, the superposition principle of linear theory, Monte Carlo simulation (MCS), and orthogonal diagonalization of a symmetric matrix are applied to derive the computational equation for the objective function suitable for an improved proportional topology optimization (IPTO) approach. Based on this, the IPTO approach is employed to solve this RTO model, thereby forming an innovative multi-material non-gradient RTO approach. Finally, two numerical examples are applied to illustrate the efficacy of this new approach and the influence of the filtering radius on the structural RTO design. The results showcase that this new approach can tackle the robust optimization design issues of multi-material structures and yield an optimal structure with enhanced robustness. Moreover, the proposed approach's filtering radius directly influences the shape of the optimized structure.

A one-dimensional model for tape springs is proposed to capture their essential mechanical behavior, including membrane and bending effects. A key feature of the model is the incorporation of Gaussian curvature, for which a one-dimensional estimate is provided. The bending energy is derived from shell theory using a suitable kinematic Ansatz. Equilibrium configurations with uniform curvature are analyzed under prescribed end rotations, and critical rotations are determined through analytical estimates of the stability conditions. An inextensible version of the model is also considered, allowing for the prediction of the post-localization bending moment and the explanation of the linear energy growth observed at large rotations. Numerical results are presented and compared with both experimental data and existing numerical predictions from the literature, confirming the model’s capability to accurately capture curvature localization phenomena.

The present work illustrates a dynamic nonlinear analysis of structures characterized by plan irregularity and base isolated by friction devices. Base isolation systems with friction pendulums are analysed to properly regularize the dynamic nonlinear behaviour of structures. Different isolation solutions with friction pendulums are investigated to optimize and regularize the dynamic nonlinear behaviour of structures with irregularities in plan. The nonlinear behaviour of the base-isolated structure is investigated when subject to representative dynamic events. Criteria for regularizing the dynamic behaviour of plan irregular structures are presented. The beneficial effects are illustrated for the adopted optimized isolation solution of friction pendulum system. The nonlinear behaviour of the isolation devices is determined as well as the nonlinear dynamic behaviour of the irregular in plan structure. A comparative dynamic nonlinear analysis is presented for the structure base isolated by the adopted solution of friction isolation system and the corresponding fixed base structure. In the comparative analysis, recorded accelerograms associated with dynamic events are considered and the nonlinear hysteretic cycles of isolation devices are presented, along with the time history of the base acceleration, the base shear, the base displacement and the inter-storey drifts of the structure.

A static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175–209) composite materials (CMs) of the periodic structures are analyzed. A body force with compact support is applied to a thermoelastically mismatched CM at constant temperature. Within the framework of computational analytical micromechanics (CAM)—a branch of micromechanics referred to as the second background—it has been established that local micromechanics (LM) and peridynamic micromechanics (PM) exhibit formal equivalence for CMs with random and periodic structures. This equivalence facilitates a seamless extension of LM methodologies to their PM analogs. Specifically, key LM concepts, such as the decomposition of real fields into load and residual components, as well as isolating matrix-specific properties from material properties of phases, have been successfully generalized to PM. The concept of the representative volume element (RVE), pivotal in LM, has also been adapted and extended to PM. For inhomogeneous body forces with compact support, CAM is employed to estimate the effective behavior of CMs, leading to the creation of innovative compressed data sets. These data sets are developed using a fundamentally new RVE concept that does not depend on the constitutive laws of the individual phases or the form of the predicted effective (surrogate) operator. The data sets incorporating this novel RVE concept serve as a critical foundation for integration into existing machine learning (ML) and neural network (NN) approaches for predicting nonlocal surrogate operators for both locally elastic and peridynamic CMs. The new RVE concept systematically eliminates size scale inaccuracies, boundary layer effects, and edge effects, ensuring robust and reliable predictions for periodic CMs.