Continuum mechanics is a subfield of physics that focusses on the behavior of materials seen as continuous, non-discrete media. The concept originated from French mathematician Augustin-Louis Cauchy in the 19th century. This form of mechanics primarily handles deformable as opposed to rigid bodies, assuming that the content of the object entirely fills the space it occupies.
This concept discounts the atomic makeup of matter, providing an accurate representation of material behavior at lengths substantially larger than inter-atomic distances. It utilizes differential equations to predict matter behavior based on physical laws like conservation of mass, momentum, and energy. The specific substance details are highlighted in constitutive relationships.
Continuum mechanics handle the physical properties of solids and fluids without associating them with specific coordinate systems. This property is characterized using tensors, independent mathematical objects free of coordinate systems, allowing property definition at any apparant point in the continuum. The theories of elasticity, plasticity, and fluid mechanics are based on these concepts.
A continuum forms the basis of the mathematical framework used to study large-scale forces and deformations in materials. Despite the discrete molecular structure of matter, physical phenomena can often be modeled by viewing a substance as distributed throughout a region of space. A continuum is a body that can be indefinitely divided into infinitesimal elements with local material properties defined at specific points. Material properties can be described by continuous functions, and their progression is studied using calculus.
Common assumptions in continuum mechanics study are homogeneity (identical properties in all locations) and isotropy (directionally invariant vector properties). Typically, these assumptions are applied to specific sections of the material where they hold to simplify the analysis. For more complicated cases, one or both assumptions might be dropped, and computational methods are then employed to solve the differential equations that describe the evolution of material properties.
One distinct area covers elastomeric foams that display a hyperbolic stress-strain relationship. Though these are considered a continuum, the homogeneous distribution of voids gives it uniquely distinct properties.
Models in continuum mechanics are formulated by assigning a three-dimensional Euclidean space to the material body under scrutiny. Different body configurations or states correspond to different regions in this space. Physical properties of the body at any given time are denoted by parameters that define the model, and these properties must align with physical norms - they must be continuous, globally invertible, orientation-preserving, and twice continuously differentiable.
Investigating forces in a continuum is another crucial aspect of continuum mechanics. This typically necessitates a detailed understanding of the material's mechanical behavior and the forces that impact it. The effects of these forces are often measured and quantified using advanced mathematical models and experimental data.