Bond graph¶

A domain-independent graphical model of power exchange in dynamic physical systems using effort–flow variable pairs and energy-conserving junctions.

Version: v2 · 2026-09-19 · History
Domain-specific #: 3509
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomain: Systems Engineering → Engineering & Design (beyond software)

Core Idea¶

Bond graphs unify electrical, mechanical, hydraulic, thermal and other domains through common power semantics; elements represent storage, dissipation, transformation and sources while causal strokes guide equation generation. Power bonds carry conjugate effort and flow, zero and one junctions enforce conservation relations and typed components transform or store energy to produce system equations. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

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Energy-Path Drawing

Imagine one special kind of drawing that works for all sorts of machines: electric circuits, bouncy springs, water pipes, even things that heat up. In a bond graph, lines show how energy moves between parts, and each part either stores energy, uses it up, changes its form, or supplies it. From the drawing, you can figure out how the whole machine will behave.

One Energy Map for Every Machine

Many machines mix different kinds of energy, like electricity turning a motor that pumps water. A bond graph is a drawing method that treats all of these the same way by following power. Each connection, called a bond, carries power as two paired quantities: an 'effort,' like voltage or force, and a 'flow,' like current or speed. Parts are labeled by what they do: store energy, lose it as heat, change it from one form to another, or supply it. Special junctions make sure energy is conserved, and marks on the bonds help engineers write the system's equations step by step.

Power-Based Multi-Domain Model

A bond graph is a modeling notation that represents physical systems across domains, such as electrical, mechanical, hydraulic, and thermal, using shared rules about power flow. Each bond is a connection that carries a pair of conjugate variables, effort and flow, whose product is power; for example voltage and current, or force and velocity. Elements are typed by what they do with energy: capacitive and inertial elements store it, resistive elements dissipate it, transformers and gyrators convert it, and sources supply it. Junctions enforce conservation: a 0-junction shares a common effort and sums flows, while a 1-junction shares a common flow and sums efforts. Small 'causal strokes' on bonds indicate which variable each element determines, which guides writing the system's equations systematically. To be valid, a bond graph must state the system boundary, the variables and units, bond directions, causality, and constitutive laws, and should pass conservation checks.

A bond graph is a domain-independent, energy-based graphical model of physical systems in which bonds carry power as the product of conjugate effort and flow variables (voltage-current, force-velocity, pressure-volume flow, and analogous thermal pairs). Element types encode energy roles: C (capacitive) and I (inertial) elements store energy, R elements dissipate it, TF and GY elements transform or gyrate it between variables or domains, and Se/Sf elements are effort and flow sources. Zero-junctions impose common effort with flow summation, and one-junctions impose common flow with effort summation, together enforcing power conservation. Half-arrows fix the assumed direction of positive power, and causal strokes assign which side determines effort and which determines flow, allowing systematic derivation of state equations and revealing algebraic loops or dependent storage elements. The modeling identity depends on an explicit physical boundary and domains, effort and flow variables with units, bond orientation and causality, junction structure, element types with constitutive laws, and conservation checks. Its value is unifying multi-domain systems, such as electromechanical or hydraulic-mechanical ones, under a single power-based semantics.

Scope of Application¶

Bond graph belongs to systems engineering and is useful where the analyst can specify the typed systems engineering carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the physical boundary and domains, effort and flow variables and units, bond orientation and causality, junctions, storage, resistance, sources and transformers, constitutive laws and conservation checks are explicit. The scope is broad within that domain but bounded by the need for the physical boundary and domains, effort and flow variables and units, bond orientation and causality, junctions, storage, resistance, sources and transformers, constitutive laws and conservation checks are explicit. Conceptual modeling identity only; physical-system design requires validated parameters and qualified engineering.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the physical boundary and domains, effort and flow variables and units, bond orientation and causality, junctions, storage, resistance, sources and transformers, constitutive laws and conservation checks are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Bond graph. Bond graph compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed systems engineering carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem.
Lock the constitutive rule. Express the physical boundary and domains, effort and flow variables and units, bond orientation and causality, junctions, storage, resistance, sources and transformers, constitutive laws and conservation checks are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of systems engineering because they reuse the typed systems engineering carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Power bonds carry conjugate effort and flow, zero and one junctions enforce conservation relations and typed components transform or store energy to produce system equations., and type the carrier, state every parameter and convention in the definition, test that the physical boundary and domains, effort and flow variables and units, bond orientation and causality, junctions, storage, resistance, sources and transformers, constitutive laws and conservation checks are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Bond graph Domain-specific

Parents (1) — outgoing typed relations

Bond graph is a kind of Representation Prime

It remains its own entry because its identity is fixed by the physical boundary and domains, effort and flow variables and units, bond orientation and causality, junctions, storage, resistance, sources and transformers, constitutive laws and conservation checks.

Hierarchy path (1) — routes to 1 parentless root

Bond graph → is a kind of Representation → presupposes Abstraction

Neighborhood in Abstraction Space¶

Bond graph sits in a crowded region of the domain-specific corpus (8^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Engineering Design & Systems Modeling (39 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25