Continua with Microstructure

Capriz, Gianfranco

doi:10.1007/978-1-4612-3584-2

Cited by 397 publications

(417 citation statements)

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“…It has been proposed to model such a behavior introducing one-dimensional microstructured continua in which a set of directors describes the deformations of the beam sections (see [9]). The most relevant kinematical descriptor of the state of these sections is represented by the attitude which was introduced by Euler and Bernoulli [10].…”

Section: Balance Equations and Boundary Conditionsmentioning

confidence: 99%

Modal coupling in one-dimensional electromechanical structured continua

Vidoli

Dell’Isola

2000

Acta Mechanica

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Summary.A passive continuously distributed control of mechanical vibrations is proposed. The piezoelectric actuators are interconnected by a linear electric transmission line. We introduce coupling and internal resonance criteria to determine the optimal choices for electric parameters. These criteria can be found decomposing the differential operator appearing in the linear evolution equations according to a partition of the state vector into mechanical and electrical parts. The results we find allow for the design of an experimental set up.

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Section: Balance Equations and Boundary Conditionsmentioning

confidence: 99%

Modal coupling in one-dimensional electromechanical structured continua

Vidoli

Dell’Isola

2000

Acta Mechanica

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“…DiCarlo and Quiligotti's method is a special application of the theory of generalized continua introduced by Germain in the 1970s 72,73 and further developed by Capriz and others in the late 1980s. 74 Applied to biological systems, the theory provides a mechanistic framework to describe non-mechanical phenomena, such as growth and remodeling, through their mechanical feedback. The theory, described briefly in the following sections, has since been further developed to describe the remodeling of bone tissue 75,76 as well as biological processes such as the growth of membranes and tissues (Fig.…”

Section: Predictive Multiscale Modeling Of Structure-function Relatimentioning

confidence: 99%

Emergence of form from function—Mechanical engineering approaches to probe the role of stem cell mechanoadaptation in sealing cell fate

Tate¹,

Gunning²,

Sansalone³

2016

BioArchitecture

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ABSTRACT. Stem cell "mechanomics" refers to the effect of mechanical cues on stem cell and matrix biology, where cell shape and fate are intrinsic manifestations of form and function. Before specialization, the stem cell itself serves as a sensor and actuator; its structure emerges from its local mechanical milieu as the cell adapts over time. Coupling of novel spatiotemporal imaging and computational methods allows for linking of the energy of adaptation to the structure, biology and mechanical function of the cell. Cutting edge imaging methods enable probing of mechanisms by which stem cells' emergent anisotropic architecture and fate commitment occurs. A novel cell-scale model provides a mechanistic framework to describe stem cell growth and remodeling through mechanical feedback; making use of a generalized virtual power principle, the model accounts for the rate of doing work or the rate of using energy to effect the work. This coupled approach provides a basis to elucidate mechanisms underlying the stem cell's innate capacity to adapt to mechanical stimuli as well as the role of mechanoadaptation in lineage commitment. An understanding of stem cell mechanoadaptation is key to deciphering lineage commitment, during prenatal development, postnatal wound healing, and engineering of tissues.

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“…Besides the small-strain displacement field u(x, t), generalized internal variable fieldsũ(x, t) are introduced to capture microstructural mechanisms, see CAPRIZ [1] u : (x, t) →ū(x, t) andũ : (x, t) →ũ(x, t)…”

Section: Basic Kinematics and Constitutive Functions For Continua Witmentioning

confidence: 99%

Variational Formulations and FE Active‐Set Strategies for Rate‐Independent Nonlocal Material Response

Welschinger

Miehé

2008

Proc Appl Math and Mech

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We propose a variational framework for the description of rate-independent nonlocal materials with microstructure and outline details of its numerical implementation. On the theoretical side, we focus on a multifield approach to microstructural dissipative mechanisms. To this end, the current state of the evolving microstructure is described by global fields of microscopic order parameters and their gradients, which together with the macroscopic deformation field define the multifield character of the problem under consideration. Focussing on rate-independent standard dissipative materials, the constitutive response is governed by an energy storage and a non-smooth dissipation function. For this scenario, we outline an incremental variational framework whose Euler equations define the macroscopic equilibrium along with the non-smooth global evolution of the order parameters. The formulation features fully-coupled macroscopic and microscopic field equations and associated boundary conditions. The key difficulty on the numerical side is the implementation of the global non-smooth evolution of the order parameters. Here, we outline a new active set strategy for the global finite element discretization of the multifield problem, where inequality constraints on the microscopic fields are taken into account by active nodal sets. An important consequence of the proposed variational approach is the symmetry of the coupled algebraic system. The proposed setting is specified for model problems of isotropic damage mechanics and crystal plasticity. The applicability of the proposed approach to nonlocal solids is highlighted by means of representative numerical examples. Basic Kinematics and Constitutive Functions for Continua with MicrostructureThis work focusses on a multiscale approach to describe rate-independent inelastic material response of a solid with microstructure, where dissipative effects are related to microstructural mechanisms. Besides the small-strain displacement field u(x, t), generalized internal variable fieldsũ(x, t) are introduced to capture microstructural mechanisms, see CAPRIZ [1]completed with the Dirichlet-type boundary conditionsū(, ideas of local standard dissipative materials are generalized and two constitutive functionals are introducedin terms of the reduced energy storage function ψ and dissipation function φ, satisfying a priori material frame invariance. For rate-independent processes φ is a homogeneous function of degree one. By restriction to the case where φ depends onu only, we evaluate the principle of maximum dissipation, which states that the current thermodynamical micro-force β maximizes the dissipation in comparison to all alternative admissible states bounded by the elastic domainin terms of the indicator function ϕ(β) for the elastic domain. Thus the dissipation function in its primary representation φ(u) is defined by a Legendre-Fenchel-transformation of its conjugate φ (β) and reflects the principle of maximum dissipation. Incremental Variational Formulation and Active-Set ...

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Continua with Microstructure

Cited by 397 publications

References 0 publications

Modal coupling in one-dimensional electromechanical structured continua

Modal coupling in one-dimensional electromechanical structured continua

Emergence of form from function—Mechanical engineering approaches to probe the role of stem cell mechanoadaptation in sealing cell fate

Variational Formulations and FE Active‐Set Strategies for Rate‐Independent Nonlocal Material Response

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