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Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal…
We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in…
We report on a novel extension of the recent phase-field crystal (PFC) method introduced in [Elder et al., Phys. Rev. Lett., Vol. 88, 245701:1-4 (2002)], which incorporates elastic interactions as well as crystal plasticity and diffusive…
In this paper, we extend a micromechanics-based phase-field framework for fatigue fracture to incorporate cyclic plasticity with ratcheting. This mechanism is particularly relevant for low-cycle fatigue, where the accumulation of inelastic…
This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity, with constraints on bulk volume and surface area. We develop efficient numerical…
Plasticity with softening and fracture mechanics lead to ill-posed mathematical problems due to the loss of monotonicity. Multiple co-existing solutions are possible when softening elements are coupled together, and solutions cannot be…
In this paper, we investigate some micromechanical aspects of elasto-plasticity in heterogeneous geomaterials. The aim is to upscale the elasto-plastic behavior for a representative volume of the material which is indeed a very challenging…
We present Monte Carlo simulations on a lattice system that displays a first order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of…
The importance of surface tension effects is being recognized in the context of soft composite solids, where it is found to significantly affect the mechanical properties, such as the elastic response to an external stress. It has recently…
By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen's…
Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…
The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
Phase separation of a liquid mixture embedded within an elastic network is relevant to a wide range of natural and industrial systems, including biomolecular condensates interacting with the cytoskeleton, structural colouring in bird…
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model for binary alloys. By surveying the dependence of the elastic energy on chemical composition and lattice misfit, we…
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…