Related papers: Nonlinear Mechanics of Remodeling
This paper introduces a model for the mechanical response of anisotropic soft materials undergoing large inelastic deformations. The composite is constituted by a soft isotropic matrix reinforced with stiff fibres, that can evolve…
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…
We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical…
One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues.…
In this paper we revisit the mathematical foundations of nonlinear viscoelasticity. We study the underlying geometry of viscoelastic deformations, and in particular, the intermediate configuration. Starting from the multiplicative…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental…
We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of…
The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…
Anelasticity, as an intrinsic property of amorphous solids, plays a significant role in understanding their relaxation and deformation mechanism. However, due to the lack of long-range order in amorphous solids, the structural origin of…
In this paper, we formulate a geometric theory of the mechanics of arterial growth. An artery is modeled as a finite-length thick shell that is made of an incompressible nonlinear anisotropic solid. An initial radially-symmetric…
Local rearrangements are the elements of plastic deformation in an amorphous solid. In oscillatory shear, they can switch reversibly between two distinct configurations. While these repeating relaxations are typically considered in the…
We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure.…
In articular cartilage the orientation of collagen fibres is not uniform, varying mostly with the depth on the tissue. Besides, the biomechanical response of each layer of the articular cartilage differs from the neighbouring ones, evolving…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their…