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Physics-informed neural networks provide a mesh-free framework for solving partial differential equation-governed problems in solid mechanics. However, most existing formulations in linear elasticity still learn the displacement field…
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…
Accurate modeling of spin-orbit coupling and noncollinear magnetism requires noncollinear density functionals within the two-component generalized Kohn-Sham (GKS) framework, yet constructing and implementing noncollinear functionals remains…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented…
The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of…
A finite element framework is presented for the analysis of crack-tip phenomena in an elastic material containing a single edge crack under compressive loading. The mechanical response of the material is modeled by a nonlinear constitutive…
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
In this paper, we consider multiscale methods for nonlinear elasticity. In particular, we investigate the Generalized Multiscale Finite Element Method (GMsFEM) for a strain-limiting elasticity problem. Being a special case of the naturally…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with…
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
Most theories and applications of elasticity rely on an energy function that depends on the strains from which the stresses can be derived. This is the traditional setting of Green elasticity, also known as hyper-elasticity. However, in its…
A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress…
The conventional model governing the spread of fractures in elastic material is formulated by coupling linear elasticity with deformation systems. The classical linear elastic fracture mechanics (LEFM) model is derived based on the…
The paper deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin-Nunziato model. We propose a method based upon a reducing of stress concentration problem for cracks to…
We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion…
This paper presents a finite element model for the analysis of crack-tip fields in a transversely isotropic strain-limiting elastic body. A nonlinear constitutive relationship between stress and linearized strain characterizes the material…
Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…