Continuum mechanics

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

Continuum limit of amorphous elastic bodies II: Linear response to a point source force

Abstract: The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress, and displacement fields, we find strong relative fluctuations of order 1 close to the source, which, however, average out readily to the classical predictions of isotropic continuum elasticity. The stress fluctuations decay (essentially) exponentially with distance from the source. Only beyond a surprisingly large distance, $b\ensuremath{\approx}30$ interatomic distances, self-averaging dominates, and the quenched disorder becomes irrelevant for the response of an individual configuration. We argue that this self-averaging length $b$ also sets the lower wavelength bound for the applicability of classical eigenfrequency calculations. Particular attention is paid to the displacements of the source, allowing a direct measurement of the local rigidity. The algebraic correlations of these displacements demonstrate the existence of domains of slightly different rigidity without, however, revealing a characteristic length scale, at least not for the system sizes we are able to probe.

Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory

Abstract: A general framework for the analysis of heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic viscodamage evolution is formulated for-impact related problems within the framework of thermodynamic laws and nonlinear continuum mechanics. The proposed formulations include thermo-elasto-viscoplastici- ty with anisotropic thermo-elasto-viscodamage, a dynamic yield criterion of a von Mises type and a dynamic viscodamage criterion, the associated flow rules, non-linear strain hardening, strain-rate hardening, and temperature softening. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. That is, the damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The evolution laws are impeded in a finite deformation framework based on the multiplicative decomposition of the deformation gradient into elastic, viscoplastic, and viscodamage parts. Since the material macroscopic thermomechanical response under high-impact loading is governed by different physical mechanisms on the macroscale level, the proposed three-dimensional kinematical model is introduced with manifold structure accounting for discontinuous fields of dislocation interactions (plastic hardening), and crack and void interactions (damage hardening). The non-local theory of viscoplasticity and viscodamage that incorporates macroscale interstate variables and their higher-order gradients is used here to describe the change in the internal structure and in order to investigate the size effect of statistical inhomogeneity of the evolution-related viscoplasticity and viscodamage hardening variables. The gradients are introduced here in the hardening internal state variables and are considered to be independent of their local counterparts. It also incorporates the thermomechanical coupling effects as well as the internal dissipative effects through the rate-type covariance constitutive structure with a finite set of internal state variables. The model presented in this paper can be considered as a framework, which enables one to derive various non-local and gradient viscoplasticity and viscodamage theories by introducing simplifying assumptions.

Elastic waves propagation in 1D fractional non-local continuum

Abstract: Aim of this paper is the study of waves propagation in a fractional, non-local 1D elastic continuum. The non-local effects are modeled introducing long-range central body interactions applied to the centroids of the infinitesimal volume elements of the continuum. These non-local interactions are proportional to a proper attenuation function and to the relative displacements between non-adjacent elements. It is shown that, assuming a power-law attenuation function, the governing equation of the elastic waves in the unbounded domain, is ruled by a Marchaud-type fractional differential equation. Wave propagation in bounded domain instead involves only the integral part of the Marchaud fractional derivative. The dispersion of elastic waves, as well as waves propagation in unbounded and bounded domains are discussed in detail.

Validation of a non-orthogonal constitutive model for woven composite fabrics via hemispherical stamping simulation

Abstract: A non-orthogonal constitutive model was previously developed to characterize the anisotropic material behavior of woven composite fabrics under large shear deformation. This paper presents a validation of the constitutive model via hemispherical stamping simulation of a square woven composite fabric by a fully continuum mechanics-based approach with finite element (FE) method. The constitutive model is imposed on conventional shell elements to equivalently characterize the global mechanical behavior of woven composite fabric during forming. A balanced plain woven composite is taken as an example. The stamping results from the non-orthogonal model and the corresponding orthogonal constitutive model are compared with experimental data. It is shown that the results predicted by the non-orthogonal model are in a good agreement with the experimental results, while those from the orthogonal model have large discrepancies. The numerical simulation demonstrates the necessity and efficiency of the non-orthogonal constitutive model in capturing the anisotropic material behavior that woven composite fabrics render in forming.