Constitutive equations

In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities that is specific to a material or substance , and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical . Mechanical properties of. A constitutive relation approximates the observed physical behavior of a material under specific conditions of interest. To summarize, constitutive relations are .

Constitutive equations characterize material properties: ▫ Stress – Strain. Understand basic stress-strain response of engineering materials. Department of Materials Science and Engineering. Massachusetts Institute of Technology. Module 10) contain concepts vital to . A constitutive equation is an equation that describes the relationship between two physical quantities, for example between the . Motions and deformations.

However, they do not describe how these currents and charges are generated.

Three-Dimensional Form of the Linear Piezoelectric. In general, poled piezoceramics (such as PZT-5A and PZT-5H) are transversely isotropic materials. Basic axioms: determinism and equipresence. Responses of the constitutive functions at a material point x at time t are determined by the history of the motion and history of the temperature of all points of the body.

If an independent variable enters . A special kinematical viewpoint is taken, so that the elastic and plastic deformation processes can be considered separately. This separation is also accommodated by a simplified thermodynamical theory of. Larson and Howard Brenner on ScienceDirect.

Because of the anisotropic nature of piezoelectric ceramics, properties are different depending on direction. To identify directions in a piezoelectric ceramic element, a specific coordinate system is used. Transformation properties of tensors. Description of material symmetry.

Restrictions due to material symmetry. Group Representation Theory. Elements of group theory. Definition: A solid body is called elastic if τij (xn,t) = τij(ekl( xn,t)).

The constitutive equations. Es handelt sich um die mathematische Formulierung bestimmter Aspekte des Materialverhaltens. Im Zusammenhang mit der Wärmeübertragung tritt als konstitutive Gleichung (auch Materialgleichung genannt) die Verknüpfung des Wärmestromvektors mit dem Temperaturfeld und ggf. LEOs Englisch ⇔ Deutsch Wörterbuch. Mit Flexionstabellen, Aussprache und vielem mehr.

This book presents a description of the most important constitutive equations for stress and birefringence in polymer melts, as well as in dilute and concentrated solutions of flexible and rigid polymers, and in liquid crystalline materials. Presented also are the molecular, structural, or continuum-mechanical models from which . Chapter includes elements of a sixth set of constitutive equations. The reader is invited to browse through this smorgasbord of approaches, both to develop an appraisal of the overall state-of-the-art in unified constitutive equations , and also to select the approach best suited to his or her own needs.