Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.

A viscoelastic damage model with applications to stable and unstable fracturing

Abstract: SUMMARY A viscoelastic damage rheology model is presented that provides a generalization of Maxwell viscoelasticity to a non-linear continuum mechanics framework incorporating material degradation and recovery, transition from stable to unstable fracturing and gradual accumulation of non-reversible deformation. The model is a further development of the damage rheology framework of Lyakhovsky et al. for evolving effective elasticity. The framework provides a quantitative treatment for macroscopic effects of evolving distributed cracking with local density represented by an intensive state variable. The formulation, based on thermodynamic principles, leads to a system of kinetic equations for the evolution of damage. An effective viscosity inversely proportional to the rate of damage increase is introduced to account for gradual accumulation of irreversible deformation due to dissipative processes. A power-law relation between the damage variable and elastic moduli leads to a non-linear coupling between the rate of damage evolution and the damage variable itself. This allows the model to reproduce a transition from stable to unstable fracturing of brittle rocks and the Kaiser effect. 3-D numerical simulations based on the model formulation for homogeneous and heterogeneous materials account for the main features of rock behaviour under large strain. The model coefficients are constrained, using triaxial laboratory experiments with low-porosity Westerly granite and high-porosity Berea sandstone samples.

Using the material-point method to model sea ice dynamics

Abstract: [1] The material-point method (MPM) is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics.

A thermodynamic framework for the study of crystallization in polymers

Abstract: In this paper, we present a new thermodynamic framework within the context of continuum mechanics, to predict the behavior of crystallizing polymers. The constitutive models that are developed within this thermodynamic setting are able to describe the main features of the crystallization process. The model is capable of capturing the transition from a fluid like behavior to a solid like behavior in a rational manner without appealing to any adhoc transition criterion. The anisotropy of the crystalline phase is built into the model and the specific anisotropy of the crystalline phase depends on the deformation in the melt. These features are incorporated into a recent framework that associates different natural configurations and material symmetries with distinct microstructural features within the body that arise during the process under consideration. Specific models are generated by choosing particular forms for the internal energy, entropy and the rate of dissipation. Equations governing the evolution of the natural configurations and the rate of crystallization are obtained by maximizing the rate of dissipation, subject to appropriate constraints. The initiation criterion, marking the onset of crystallization, arises naturally in this setting in terms of the thermodynamic functions. The model generated within such a framework is used to simulate bi-axial extension of a polymer film that is undergoing crystallization. The predictions of the theory that has been proposed are consistent with the experimental results (see [28] and [7]).

On the application of dual variables in continuum mechanics

Abstract: Stress and strain tensors that arise in the expression of the stress power are called “conjugate variables”. More special is the term “dual variables” which has been introduced in connection with incremental constitutive relations of hypoelasticity and plasticity, where the rates of both tensors arise. We propose a rational rule from which the most natural form of tensor-valued kinematic and dynamic variables (strain and stress tensors) including their corresponding time rates can be deduced. Dual variables and their associated dual derivatives are characterized by the property that apart from the stress power also the incremental stress power is invariant under a group of transformations that corresponds to a set of physically reasonable intermediate configurations. We outline the precursory history of these concepts and then discuss in detail how the invariance properties can be realized in the various stress and strain measures. We finally demonstrate the concept in three different applications: The rate form of the principle of virtual work, the formulation of constitutive relations in viscoelasticity and the formulation of incremental constitutive assumptions of rate-independent plasticity.