Journal of The Mechanics and Physics of Solids最新文献

We investigate the conditions for crack nucleation in variational gradient damage models used as phase-field models of brittle and cohesive fracture. Viewing crack nucleation as a structural stability problem, we analyze how solutions with diffuse damage become unstable and bifurcate towards localized states, representing the smeared version of cracks. We consider gradient damage models with a linear softening response, incorporating distinct softening parameters for the spherical and deviatoric modes. These parameters are employed to adjust the peak pressure and shear stress, resulting in an equivalent cohesive behavior. Through analytical and numerical second-order stability and bifurcation analyses, we characterize the crack nucleation conditions in quasi-static, rate-independent evolutions governed by a local energy minimization principle. We assess the stability of crack development, determining whether it is preceded by a stable phase with diffuse damage or not. Our results quantitatively characterize the classical transition between brittle and cohesive-like behaviors. A fully analytical solution for a one-dimensional problem provides a clear illustration of the complex bifurcation and instability phenomena, underpinning their connection with classical energetic arguments. The stability analysis under multi-axial loading reveals a fundamental non-trivial influence of the loading mode on the critical load for crack nucleation. We show that volumetric-dominated deformation mode can remain stable in the softening regime, thus delaying crack nucleation after the peak stress. This feature depends only on the properties of the local response of the material and is insensitive to structural scale effects. Our findings disclose the subtle interplay among the regularization length, the material’s cohesive length-scale, structural size, and the loading mode to determine the crack nucleation conditions and the effective strength of phase-field models of fracture.

Recent technologies permit to build materials which have elastic spatially varying modulus which can also imitate solutions adopted in Nature to optimize some structures. It has been shown that for example the stress concentration due to a hole in an infinite plate can be cancelled with a radially varying modulus making it similar to load-bearing bones which seem to resist structural failures even in the presence of blood vessel holes (foramina). Here, we attempt to study the classical problem of a sharp wedge (which includes the important case of a crack) looking for stresses varying as power law of the distance from the notch tip, $\sigma \sim r^{\alpha }$, with a modulus varying as $E\sim r^{\beta }$. In the inhomogeneous case the order of singularity of the LEFM case decreases if $\beta >0$, as confirmed by FEM investigations. Hence, we can remove stress singularities, which suggests an interesting alternative to the “rounding” of the notch. More in general, since for many materials it has been found that both strength and modulus are power laws of the density, using the so called strength-modulus exponent ratio we can obtain optimal design by keeping the asymptotic stress constantly equal to the strength. The present investigation paves the way for a new optimization strategy in the problems which eliminates size-scale effects due to singular stress fields, with potentially very wide applications.

We present an analytical framework to study the impact of electromechanical properties on the growth of a ferroelectric nucleus. Ferroelectric domain evolution is typically simulated by phase-field models, which have shown that nuclei evolve from needle-like structures into complex domain patterns. However, there has been limited in-depth analysis of the interplay between electrostatics, mechanics and piezoelectricity and their effect on nucleus growth because of the complexity involved in the phase-field description. In this study, we describe the ferroelectric domain wall as a sharp interface and solve for the fields inside an elliptic ferroelectric nucleus via Eshelby’s inclusion problem. We analytically determine the driving traction profile around the nucleus to gain insight into the movement of the domain wall with and without applied electromechanical loading. We analyze how the growth is affected by the permittivity, elasticity, and piezoelectricity as well as the nucleus’ eccentricity. We further demonstrate that applied loads do not significantly affect nucleus growth, which is primarily determined by the self-equilibrated mechanical and electric field, and that the anisotropy in material properties is essential in determining the growth of a ferroelectric nucleus.

A discrete numerical analysis of the yield and damage properties associated with a cohesive granular system composed of ductile particles is hereby presented. Such a modelling approach aims at better understanding damage mechanisms which are often encountered during the powder compaction process, widely used in the metallurgical and pharmaceutical fields. The analysis was based on the micromechanical modelling of an idealised granular system in the framework of the multi-particle finite element method, in which particle deformation was fully taken into account. An adhesive interaction law, presented in Audry et al. (2024), was used in the purpose of estimating the averaged mechanical properties associated with the modelled elementary volume. The focus was put on tensile and highly deviatoric loadings, which are usually related to the failure of powder compacts. The specific contact area developed through inter-particles contacts was used as an indicator of the mechanical strength of the elementary volume. Threshold surfaces corresponding to yielding and contact decohesion mechanisms were plotted in the stress space.

The adhesion of soft materials often fails due to stress concentration at the interface. Structural design offers an effective approach to disperse stress at the interface and enhance adhesion properties. Herein, we introduce the concept of discretized stress dispersion to achieve ultrastrong adhesion of soft materials. This involves incorporating discrete structures at the adhesion interface, with each unit structure designed to efficiently disperse stress. We implement this concept by introducing periodic strategic cuts into the adhesive, enabling it to deform into discrete mushroom-shaped structures under peel forces. Utilizing fracture mechanics theory, we demonstrate that such structural design can significantly improve adhesion strength compared to adhesives without structural design. Through 3D printing, we fabricate adhesive samples with strategic cuts, achieving a peak peel force of 3479 N/m, over 100-fold higher than adhesives without cuts (25 N/m). We analyzed stress dispersion of each unit structure through experiments of with different geometric parameters and analyze collaborative effects of multiple structures with theoretical model. Finite element analysis of the peel process highlights the critical role of cohesive zone influenced by geometric parameters, which determines the peak peel force. This concept of discretized stress dispersion advances the development of soft materials with ultrastrong adhesion.

In this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

This study proposes a novel phase-field fracture model based on unified phase field theory, aiming to overcome current limitations in simulating material complex fracture behaviors. Through this model, analytical solutions for two-dimensional bars subjected to tensile or compressive stresses are provided, enabling the coupling of multiple failure criteria and further proficient simulation of mode-I, mode-II, and mixed mode-I/II fractures, effectively addressing challenges faced in modelling materials with different or complex failure modes under various loading conditions. Furthermore, to account for the strong anisotropic failure behavior of materials, a novel directional-dependent structural tensor is proposed. The tensor correlates fracture energy with crack surface orientation, facilitating precise characterization of material damage evolution with multiple potential crack orientations. This tensor ensures the consistency of phase-field fracture evolution with predefined fracture patterns. The effectiveness of the proposed model is validated through case studies, emphasizing its robustness and superior predictive capability in capturing fracture behavior under various conditions. This research provides a more accurate and universally applicable approach for simulating material failure, particularly for complex or multiple failure mode material failure simulations.

A criterion is developed for the unhomogeneous yielding of materials containing arbitrarily oriented ellipsoidal voids. The criterion is built upon classical estimates for pure pressure and pure shear. A data-driven approach is then followed to incorporate the effects of void shape and orientation. A large number of micromechanical unit cell results are used to calibrate the yield criterion. A key feature of the criterion is that it predicts a significant reduction of the effective shear yield strength due to mere void inclination, with the reduction increasing with the void dimension perpendicular to the shear. The coupling between tension and shear deformation results in an apparent rotation of the yield surface, which provides a sound micromechanical basis for predicting void closure in shear among other new features. Once supplemented with evolution equations of relevant internal parameters, the resulting constitutive formulation will enable ductile failure simulations heretofore impossible to carry out on a sound physical basis for general loading conditions.

Active solids are a large class of materials, including both living soft tissues and artificial matter, that share the ability to undergo strain even in absence of external loads. While in engineered materials the actuation is typically designed a priori, in natural materials it is an unknown of the problem. In such a framework, the identification of inactive regions in active materials is of particular interest. An example of paramount relevance is cardiac mechanics and the assessment of regions of the cardiac muscle with impaired contractility. The impossibility to measure the local active forces directly suggests us to develop a novel methodology exploiting kinematic data from clinical images by a variational approach to reconstruct the local contractility of the cardiac muscle. By finding the stationary points of a suitable cost functional we recover the contractility map of the muscle. Numerical experiments, including severe conditions with added noise to model uncertainties, and data knowledge limited to the boundary, demonstrate the effectiveness of our approach. Unlike other methods, we provide a spatially continuous recovery of the contractility map without compromising the computational efficiency.

Previous experiments have revealed that the controllable introduction of structural gradients in metallic glasses (MGs) can endow the materials with extra plasticity due to the gradient-induced deflection of shear bands. However, the relation between the spatial structural gradient and the initiation of shear band deflection remains unclear. The current study has been focused on investigating the relationship between the improved mechanical properties of MGs and structural gradients specified by the distribution of the intrinsic free volume. Molecular dynamics (MD) simulations are firstly performed on homogeneous MG models containing various initial free volume values, showing that the shear band angle increases with decreasing free volume under uniaxial compression, whereas higher shear band angle is observed under uniaxial tension with increasing free volume. Based on the asymmetric behaviors of MGs under compression and tension, a theoretical model is developed to quantitatively characterize the influence of free volume on the mechanical response of MGs, which incorporates a failure criterion based on free volume generation during external loadings. The model can be further utilized to interpret and predict the fracture strain, shear band angle, maximum stress, and fracture surface morphology of gradient structured MGs in both simulations and experiments. The relationship between free volume gradient and shear band deflection induced extra plasticity established in this study provides valuable guidance for the structural design of MGs with enhanced mechanical properties.